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Ahmed B, Mersing D, Tinsley MR, Showalter K. Propagating wave merging in a precipitation reaction. CHAOS (WOODBURY, N.Y.) 2023; 33:043105. [PMID: 37097957 DOI: 10.1063/5.0139698] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2022] [Accepted: 03/13/2023] [Indexed: 06/19/2023]
Abstract
Propagating precipitation waves are a remarkable form of spatiotemporal behavior that arise through the coupling of reaction, diffusion, and precipitation. We study a system with a sodium hydroxide outer electrolyte and an aluminum hydroxide inner electrolyte. In a redissolution Liesegang system, a single propagating precipitation band moves down through the gel, with precipitate formed at the band front and precipitate dissolved at the band back. Complex spatiotemporal waves occur within the propagating precipitation band, including counter-rotating spiral waves, target patterns, and annihilation of waves on collision. We have also carried out experiments in thin slices of gel, which have revealed propagating waves of a diagonal precipitation feature within the primary precipitation band. These waves display a wave merging phenomenon in which two horizontally propagating waves merge into a single wave. Computational modeling permits the development of a detailed understanding of the complex dynamical behavior.
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Affiliation(s)
- Boshir Ahmed
- C. Eugene Bennett Department of Chemistry, West Virginia University, Morgantown, West Virginia 26506-6045, USA
| | - David Mersing
- C. Eugene Bennett Department of Chemistry, West Virginia University, Morgantown, West Virginia 26506-6045, USA
| | - Mark R Tinsley
- C. Eugene Bennett Department of Chemistry, West Virginia University, Morgantown, West Virginia 26506-6045, USA
| | - Kenneth Showalter
- C. Eugene Bennett Department of Chemistry, West Virginia University, Morgantown, West Virginia 26506-6045, USA
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2
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Caraway BD, Pearlstein AJ. Temporally quasiperiodic data, propagating in the laboratory frame, can be rendered periodic by Galilean transformation. Phys Rev E 2022; 106:024607. [PMID: 36109965 DOI: 10.1103/physreve.106.024607] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2021] [Accepted: 07/06/2022] [Indexed: 06/15/2023]
Abstract
For a broad class of distributions of temperature, concentration, or another quantity propagating rectilinearly, we show that temporally quasiperiodic behavior in the laboratory frame can be rendered periodic by Galilean transformation. The approach is illustrated analytically and numerically using as an example a closed-form model distribution generated from a one-dimensional partial differential equation, and a detailed process is developed to determine frame speed from more general quasiperiodic, one-dimensional, temporally- and spatially-discretized data. The approach is extended to two- and three-dimensional rectilinear propagation, and its application to nonrectilinear propagation, along with implications for interpreting noise-corrupted data, are also discussed.
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Affiliation(s)
- Bill D Caraway
- Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, Illinois 61801, USA
| | - Arne J Pearlstein
- Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, Illinois 61801, USA
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3
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Budroni MA, Polo A, Upadhyay V, Bigaj A, Rongy L. Chemo-hydrodynamic pulsations in simple batch A + B → C systems. J Chem Phys 2021; 154:114501. [PMID: 33752375 DOI: 10.1063/5.0042560] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
Spatio-temporal oscillations can be induced under batch conditions with ubiquitous bimolecular reactions in the absence of any nonlinear chemical feedback, thanks to an active interplay between the chemical process and chemically driven hydrodynamic flows. When two reactants A and B, initially separated in space, react upon diffusive contact, they can power convective flows by inducing a localized variation of surface tension and density at the mixing interface. These flows feedback with the reaction-diffusion dynamics, bearing damped or sustained spatio-temporal oscillations of the concentrations and flow field. By means of numerical simulations, we detail the mechanism underlying these chemohydrodynamic oscillations and classify the main dynamical scenarios in the relevant space drawn by parameters ΔM and ΔR, which rule the surface tension- and buoyancy-driven contributions to convection, respectively. The reactor height is found to play a critical role in the control of the dynamics. The analysis reveals the intimate nature of these oscillatory phenomena and the hierarchy among the different phenomena at play: oscillations are essentially hydrodynamic and the chemical process features the localized trigger for Marangoni flows unstable toward oscillatory instabilities. The characteristic size of Marangoni convective rolls mainly determines the critical conditions and properties of the oscillations, which can be further tuned or suppressed by the buoyancy competition. We finally discuss the possible experimental implementation of such a class of chemo-hydrodynamic oscillator and its implications in fundamental and applied terms.
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Affiliation(s)
- Marcello A Budroni
- Department of Chemistry and Pharmacy, University of Sassari, Via Vienna 2, 07100 Sassari, Italy
| | - Alessandro Polo
- Department of Chemistry and Pharmacy, University of Sassari, Via Vienna 2, 07100 Sassari, Italy
| | - Virat Upadhyay
- Nonlinear Physical Chemistry Unit, Service de Chimie Physique et Biologie Théorique, Université Libre de Bruxelles, CP 231 - Campus Plaine, 1050 Brussels, Belgium
| | - Adam Bigaj
- Nonlinear Physical Chemistry Unit, Service de Chimie Physique et Biologie Théorique, Université Libre de Bruxelles, CP 231 - Campus Plaine, 1050 Brussels, Belgium
| | - Laurence Rongy
- Nonlinear Physical Chemistry Unit, Service de Chimie Physique et Biologie Théorique, Université Libre de Bruxelles, CP 231 - Campus Plaine, 1050 Brussels, Belgium
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4
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Tang A, Green JR, Wang J. Long-Lasting Complex Reaction Behavior in a Closed Ferroin-Bromate-Hydroxybenzenesulfonate System. J Phys Chem A 2018; 122:8301-8307. [PMID: 30289717 DOI: 10.1021/acs.jpca.8b07766] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The bromate-phenolsulfonate reaction was found to exhibit spontaneous oscillations in a batch reactor, where the addition of small amounts of ferroin would result in nonoscillatory behavior. As the ferroin concentration was increased, the system produced very rich nonlinear behavior, including three isolated oscillatory regimes that were separated by as long as 48 h nonoscillatory period. The long-lasting nonlinear behavior may be attributed to the slow desulfonation of phenolsulfonate in an acidic solution, forming phenol-like intermediates. However, unlike the bromate-phenol oscillator, oxygen was found to greatly influence the reaction, and various complex oscillations could be observed by tuning the oxygen concentration. Mechanistic studies performed through employing 1H NMR spectroscopy and mass spectrometry to measure intermediate species at different stages of the reaction were able to identify 1,4-benzoquinone, 2-bromo-1,4-benzoquinone, 2,6-dibromo-1,4-benzoquinone, and 2,4,6-tribromophenol as major components during the reaction.
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Affiliation(s)
- Alexander Tang
- Department of Chemistry and Biochemistry , University of Windsor , Windsor , ON N9B 3P4 , Canada
| | - James R Green
- Department of Chemistry and Biochemistry , University of Windsor , Windsor , ON N9B 3P4 , Canada
| | - Jichang Wang
- Department of Chemistry and Biochemistry , University of Windsor , Windsor , ON N9B 3P4 , Canada
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5
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Oikawa N, Bodenschatz E, Zykov VS. Unusual spiral wave dynamics in the Kessler-Levine model of an excitable medium. CHAOS (WOODBURY, N.Y.) 2015; 25:053115. [PMID: 26026327 DOI: 10.1063/1.4921879] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
The Kessler-Levine model is a two-component reaction-diffusion system that describes spatiotemporal dynamics of the messenger molecules in a cell-to-cell signaling process during the aggregation of social amoeba cells. An excitation wave arising in the model has a phase wave at the wave back, which simply follows the wave front after a fixed time interval with the same propagation velocity. Generally speaking, the medium excitability and the refractoriness are two important factors which determine the spiral wave dynamics in any excitable media. The model allows us to separate these two factors relatively easily since the medium refractoriness can be changed independently of the medium excitability. For rigidly rotating waves, the universal relationship has been established by using a modified free-boundary approach, which assumes that the front and the back of a propagating wave are thin in comparison to the wave plateau. By taking a finite thickness of the domain boundary into consideration, the validity of the proposed excitability measure has been essentially improved. A novel method of numerical simulation to suppress the spiral wave instabilities is introduced. The trajectories of the spiral tip observed for a long refractory period have been investigated under a systematic variation of the medium refractoriness.
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Affiliation(s)
- N Oikawa
- Max Planck Institute for Dynamics and Self-Organization, D-37077 Goettingen, Germany
| | - E Bodenschatz
- Max Planck Institute for Dynamics and Self-Organization, D-37077 Goettingen, Germany
| | - V S Zykov
- Max Planck Institute for Dynamics and Self-Organization, D-37077 Goettingen, Germany
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Berenstein I, Beta C. Cross-diffusion in the two-variable Oregonator model. CHAOS (WOODBURY, N.Y.) 2013; 23:033119. [PMID: 24089955 DOI: 10.1063/1.4816937] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
We explore the effect of cross-diffusion on pattern formation in the two-variable Oregonator model of the Belousov-Zhabotinsky reaction. For high negative cross-diffusion of the activator (the activator being attracted towards regions of increased inhibitor concentration) we find, depending on the values of the parameters, Turing patterns, standing waves, oscillatory Turing patterns, and quasi-standing waves. For the inhibitor, we find that positive cross-diffusion (the inhibitor being repelled by increasing concentrations of the activator) can induce Turing patterns, jumping waves and spatially modulated bulk oscillations. We qualitatively explain the formation of these patterns. With one model we can explain Turing patterns, standing waves and jumping waves, which previously was done with three different models.
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Affiliation(s)
- Igal Berenstein
- Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam, Germany
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7
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Harati M, Li N. Chemical oscillations in the metal ion-catalyzed bromate-4-aminophenol reaction. Sci China Chem 2012. [DOI: 10.1007/s11426-012-4736-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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8
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Two staged pattern formation and spontaneous wave breakup in the ferroin-bromate-pyrocatechol reaction. OPEN CHEM 2011. [DOI: 10.2478/s11532-011-0018-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
Abstract
AbstractThis report investigated nonlinear spatiotemporal behavior in the ferroin-bromate-pyrocatechol reaction, in which two stages of wave formation, separated by several hours of quiescent period, were observed. In addition to its great photosensitivity, the second stage wave activity could undergo spontaneous breakups at broad reaction conditions. Analysis based on one-dimensional space-time plot suggests that the breakup was caused by propagation slowdown of the leading wave. Due to the presence of coupled autocatalytic reactions, the propagation of the initial and the second stage waves exhibited different and subtle responses to the variation of the concentration of each reagent.
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Szabo E, Adamčíková L, Ševčík P. Are Uncatalyzed Bromate Oscillators Truly Gas-Free? J Phys Chem A 2011; 115:6518-24. [DOI: 10.1021/jp202906d] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Erik Szabo
- Department of Physical and Theoretical Chemistry, Faculty of Natural Sciences, Comenius University in Bratislava, Mlynská dolina, 842 15 Bratislava, Slovakia
| | - Lubica Adamčíková
- Department of Physical and Theoretical Chemistry, Faculty of Natural Sciences, Comenius University in Bratislava, Mlynská dolina, 842 15 Bratislava, Slovakia
| | - Peter Ševčík
- Department of Physical and Theoretical Chemistry, Faculty of Natural Sciences, Comenius University in Bratislava, Mlynská dolina, 842 15 Bratislava, Slovakia
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10
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Feng J, Green JR, Johnson SA, Wang J. CO2production in the bromate-1,4-cyclohexanedione oscillatory reaction. J PHYS ORG CHEM 2010. [DOI: 10.1002/poc.1795] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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11
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Harati M, Green JR, Cooper BFT, Wang J. Gas production in the bromate-pyrocatechol oscillator. J Phys Chem A 2009; 113:6548-51. [PMID: 19459616 DOI: 10.1021/jp903097t] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
A significant amount of gas production has been observed in the bromate-pyrocatechol oscillator under high concentrations of bromate and pyrocatechol. The observation is in contrast to the general perception that aromatic compounds can form bromate-based oscillators that are free of gas bubbles, which is a desired property in investigating pattern formation. Analysis with (1)H NMR, (13)C NMR, mass spectrometry, and X-ray crystallography illustrate the production of 5-(dibromomethylene)-2(5H)-furanone from pyrocatechol, where the loss of one carbon atom from the aromatic ring causes the formation of gas bubbles. Possible mechanisms have been proposed to explain the observed phenomenon.
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12
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Harati M, Wang J. Propagation failures, breathing fronts, and nonannihilation collisions in the ferroin-bromate-pyrocatechol system. CHAOS (WOODBURY, N.Y.) 2009; 19:023116. [PMID: 19566251 DOI: 10.1063/1.3133823] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
The emergence of propagating pulses was investigated with the photosensitive ferroin-bromate-pyrocatechol reaction in capillary tubes, in which various interesting spatiotemporal behaviors such as propagation failure, breathing fronts, and transitions between propagating pulses and fronts have been observed. Rather than a mutual annihilation, the collision of a propagating pulse and a growing front forces the front to recede gradually. A phase diagram in the pyrocatechol-bromate concentration space shows that the pulse instabilities take place throughout the conditions at which the system generates wave activities, suggesting that the presence of coupled autocatalytic feedbacks may facilitate the onset of pulse instabilities.
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Affiliation(s)
- Mohammad Harati
- Department of Chemistry and Biochemistry, University of Windsor, Ontario N9B 3P4, Canada
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13
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Li N, Zhang Y, Wang J. Numerical Investigation of Photochemical Behavior in Bromate−1,4-Cyclohexanedione Reactions. J Phys Chem A 2009; 113:833-8. [DOI: 10.1021/jp808093y] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Nan Li
- Institute for Chemical Physics, Beijing Institute of Technology, Beijing 100081, People’s Republic of China, and Department of Chemistry and Biochemistry, University of Windsor, Ontario, Canada N9B 3P4
| | - Yunhong Zhang
- Institute for Chemical Physics, Beijing Institute of Technology, Beijing 100081, People’s Republic of China, and Department of Chemistry and Biochemistry, University of Windsor, Ontario, Canada N9B 3P4
| | - Jichang Wang
- Institute for Chemical Physics, Beijing Institute of Technology, Beijing 100081, People’s Republic of China, and Department of Chemistry and Biochemistry, University of Windsor, Ontario, Canada N9B 3P4
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14
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Yanagita T, Suetani H, Aihara K. Bifurcation analysis of solitary and synchronized pulses and formation of reentrant waves in laterally coupled excitable fibers. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:056208. [PMID: 19113201 DOI: 10.1103/physreve.78.056208] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2008] [Indexed: 05/27/2023]
Abstract
We study the dynamics of a reaction-diffusion system comprising two mutually coupled excitable fibers. We consider a case in which the dynamical properties of the two fibers are nonidentical due to the parameter mismatch between them. By using the spatially one-dimensional FitzHugh-Nagumo equations as a model of a single excitable fiber, synchronized pulses are found to be stable in some parameter regime. Furthermore, there exists a critical coupling strength beyond which the synchronized pulses are stable for any amount of parameter mismatch. We show the bifurcation structures of the synchronized and solitary pulses and identify a codimension-2 cusp singularity as the source of the destabilization of synchronized pulses. When stable solitary pulses in both fibers disappear via a saddle-node bifurcation on increasing the coupling strength, a reentrant wave is formed. The parameter region, where a stable reentrant wave is observed in direct numerical simulation, is consistent with that obtained by bifurcation analysis.
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Affiliation(s)
- Tatsuo Yanagita
- Research Institute for Electronic Science, Hokkaido University, Sapporo 001-0020, Japan.
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15
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Bánsági T, Steinbock O. Three-dimensional spiral waves in an excitable reaction system: initiation and dynamics of scroll rings and scroll ring pairs. CHAOS (WOODBURY, N.Y.) 2008; 18:026102. [PMID: 18601504 DOI: 10.1063/1.2896100] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
We report experimental results on spiral and scroll waves in the 1,4-cyclohexanedione Belousov-Zhabotinsky reaction. The propagating concentration waves are detected by two-dimensional photometry and optical tomography. Wave pulses can disappear in front-to-front and front-to-back collisions. This anomaly causes the nucleation of vortices from collisions of three nonrotating waves. In three-dimensional systems, these vortices are scroll rings that rotate around initially circular filaments. Depending on reactant concentrations, the filaments shrink or expand indicating positive and negative filament tensions, respectively. Shrinkage results in vortex annihilation. Expansion is accompanied by filament buckling and bending, which is interpreted as developing Winfree turbulence. We also describe the initiation of scroll ring pairs in four-wave collisions. The two filaments are stacked on top of each other and their motion suggests filament repulsion.
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Affiliation(s)
- Tamás Bánsági
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
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16
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Bordyugov G, Engel H. Anomalous pulse interaction in dissipative media. CHAOS (WOODBURY, N.Y.) 2008; 18:026104. [PMID: 18601506 DOI: 10.1063/1.2943307] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
We review a number of phenomena occurring in one-dimensional excitable media due to modified decay behind propagating pulses. Those phenomena can be grouped in two categories depending on whether the wake of a solitary pulse is oscillatory or not. Oscillatory decay leads to nonannihilative head-on collision of pulses and oscillatory dispersion relation of periodic pulse trains. Stronger wake oscillations can even result in a bistable dispersion relation. Those effects are illustrated with the help of the Oregonator and FitzHugh-Nagumo models for excitable media. For a monotonic wake, we show that it is possible to induce bound states of solitary pulses and anomalous dispersion of periodic pulse trains by introducing nonlocal spatial coupling to the excitable medium.
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Affiliation(s)
- Grigory Bordyugov
- Institut für Physik und Astronomie, Universität Potsdam, Karl-Liebknecht-Strasse 24/25, D-14476 Potsdam, Germany.
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17
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Harati M, Wang J. Chemical oscillations and waves in the catalyzed bromate-pyrocatechol reaction. J Phys Chem A 2008; 112:4241-5. [PMID: 18373364 DOI: 10.1021/jp710200y] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Long time series of temporal oscillations and wave formation are observed in the catalyzed bromate-pyrocatechol reaction conducted in a batch reactor, in which the induction time is insensitive to the presence of ferroin but is greatly shortened by Ce(III) or Mn(II). On the other hand, the number of oscillations is significantly increased by ferroin, while it is less sensitive to Ce(III) and Mn(II). The ferroin-catalyzed system also exhibits strong photosensitivity, in which illumination could quench the oscillatory behavior. A phase diagram illustrates that the oscillatory behavior of the studied system is more sensitive to the ratio of [pyrocatechol]/[bromate] than their absolute concentrations. Reactions conducted in a spatially extended medium show that the ferroin-catalyzed system supports a two-stage pattern formation with the wave activity surviving for up to 10 h.
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Affiliation(s)
- Mohammad Harati
- Department of Chemistry and Biochemistry, University of Windsor, Ontario, N9B 3P4 Canada
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18
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Abstract
Scroll waves are three-dimensional excitation patterns that rotate around one-dimensional space curves. Typically these filaments are closed loops or end at the system boundary. However, in excitable media with anomalous dispersion, filaments can be pinned to the wake of traveling wave pulses. This pinning is studied in experiments with the 1,4-cyclohexanedione Belousov-Zhabotinsky reaction and a three-variable reaction-diffusion model. We show that wave-pinned filaments are related to the coexistence of rotating and translating wave defects in two dimensions. Filament pinning causes a continuous expansion of the total filament length. It can be ended by annihilating the pinning pulse in a frontal wave collision. Following such an annihilation, the filament connects itself to the system boundary. Its postannihilation shape that is initially the exposed rim of the scroll wave unwinds continuously over numerous rotation periods.
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Affiliation(s)
- Tamás Bánsági
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
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19
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Li N, Green JR, Wang J. The concurrence of photoreduction and bromination of 1,4-benzoquinone in aqueous solution. Chem Phys Lett 2007. [DOI: 10.1016/j.cplett.2007.09.025] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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20
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Initiation of waves in the Belousov–Zhaboyinsky system via the reaction-diffusion process of wet stamping. Chem Phys Lett 2007. [DOI: 10.1016/j.cplett.2007.05.002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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21
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Dynamics of bromate oscillators with 1,4-cyclohexanedione in a continuously fed stirred tank reactor. Chem Phys Lett 2006. [DOI: 10.1016/j.cplett.2006.07.060] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Manz N, Steinbock O. Propagation failures, breathing pulses, and backfiring in an excitable reaction-diffusion system. CHAOS (WOODBURY, N.Y.) 2006; 16:037112. [PMID: 17014246 DOI: 10.1063/1.2266993] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
We report results from experiments with a pseudo-one-dimensional Belousov-Zhabotinsky reaction that employs 1,4-cyclohexanedione as its organic substrate. This excitable system shows traveling oxidation pulses and pulse trains that can undergo complex sequences of propagation failures. Moreover, we present examples for (i) breathing pulses that undergo periodic changes in speed and size and (ii) backfiring pulses that near their back repeatedly generate new pulses propagating in opposite direction.
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Affiliation(s)
- Niklas Manz
- Florida State University, Department of Chemistry and Biochemistry, Tallahassee, Florida 32306-4390, USA
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23
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Bordyugov G, Engel H. Creating bound states in excitable media by means of nonlocal coupling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:016205. [PMID: 16907175 DOI: 10.1103/physreve.74.016205] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2006] [Revised: 05/11/2006] [Indexed: 05/11/2023]
Abstract
We consider pulses of excitation in reaction-diffusion systems subjected to nonlocal coupling. This coupling represents long-range connections between the elements of the medium; the connection strength decays exponentially with the distance. Without coupling, pulses interact only repulsively and bound states with two or more pulses propagating at the same velocity are impossible. Upon switching on nonlocal coupling, pulses begin to interact attractively and form bound states. First we present numerical results on the emergence of bound states in the excitable Oregonator model for the photosensitive Belousov-Zhabotinsky reaction with nonlocal coupling. Then we show that the appearance of bound states is provided solely by the exponential decay of nonlocal coupling and thus can be found in a wide class of excitable systems, regardless of the particular kinetics. The theoretical explanation of the emergence of bound states is based on the bifurcation analysis of the profile equations that describe the spatial shape of pulses. The central object is a codimension-4 homoclinic orbit which exists for zero coupling strength. The emergence of bound states is described by the bifurcation to 2-homoclinic solutions from the codimension-4 homoclinic orbit upon switching on nonlocal coupling. We stress that the high codimension of the bifurcation to bound states is generic, provided that the coupling range is sufficiently large.
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Affiliation(s)
- Grigory Bordyugov
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergerstrasse 36, 10623 Berlin, Germany.
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Manz N, Ginn BT, Steinbock O. Propagation failure dynamics of wave trains in excitable systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:066218. [PMID: 16906957 DOI: 10.1103/physreve.73.066218] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2006] [Indexed: 05/11/2023]
Abstract
We report experimental and numerical results on temporal patterns of propagation failures in reaction-diffusion systems. Experiments employ the 1,4-cyclohexanedione Belousov-Zhabotinsky reaction. The propagation failures occur in the frontier region of the wave train and can profoundly affect its expansion speed. The specific rhythms observed vary from simple periodic to highly complex and possibly chaotic sequences. All but the period-1 sequences are found in the transition region between "merging" and "tracking" dynamics, which correspond to wave behavior caused by two qualitatively different types of anomalous dispersion relations.
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Affiliation(s)
- Niklas Manz
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
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Wang J, Zhao J, Chen Y, Gao Q, Wang Y. Coexistence of Two Bifurcation Regimes in a Closed Ferroin-Catalyzed Belousov−Zhabotinsky Reaction. J Phys Chem A 2005; 109:1374-81. [PMID: 16833454 DOI: 10.1021/jp0456279] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The ferroin-catalyzed Belousov-Zhabotinsky (BZ) reaction was studied in a batch reactor under anaerobic conditions and was found to evolve through two separated regimes of complex oscillations. Significantly, the two bifurcation regimes exhibited qualitatively different dependence on compositions of the reaction mixture, i.e., initial concentrations of bromate, sulfuric acid, malonic acid, and ferroin. The reaction temperature also showed opposite effects on the two bifurcation regimes, in which complexities of the first bifurcation regime were enhanced while oscillations in the second bifurcation regime became simpler as a result of decreasing temperature. Numerical simulations with a 12-variable model developed specifically for the ferroin-BZ system were able to reproduce transient complex oscillations observed in experiments. These calculations further illustrated that reactions such as ferroin and HOBr, ferroin and HBrO2, and ferriin and Br- were not essential in describing complex dynamics of the ferroin-BZ reaction.
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Affiliation(s)
- Jichang Wang
- Department of Chemistry and Biochemistry, The University of Windsor, Windsor, ON N9B 3P4, Canada.
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Manz N, Steinbock O. Dynamics of excitation pulses with attractive interaction: kinematic analysis and chemical wave experiments. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:066213. [PMID: 15697490 DOI: 10.1103/physreve.70.066213] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2004] [Indexed: 05/24/2023]
Abstract
We present a theoretical analysis of stacking and destacking wave trains in excitable reaction-diffusion systems with anomalous velocity-wavelength dependence. For linearized dispersion relations, kinematic analysis yields an analytical function that rigorously describes front trajectories. The corresponding accelerations have exactly one extremum that slowly decays with increasing pulse number. For subsequent pulses these maxima occur with a lag time equal to the inverse slope of the linearized dispersion curve. These findings are reproduced in experiments with chemical waves in the 1,4-cyclohexanedione Belousov-Zhabotinsky reaction but should be also applicable to step bunching on crystal surfaces and certain traffic phenomena.
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Affiliation(s)
- Niklas Manz
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, FL 32306-4390, USA
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Wang J, Yadav K, Zhao B, Gao Q, Huh DS. Photocontrolled oscillatory dynamics in the bromate-1,4-cyclohexanedione reaction. J Chem Phys 2004. [DOI: 10.1063/1.1809111] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Manz N, Hamik CT, Steinbock O. Tracking waves and vortex nucleation in excitable systems with anomalous dispersion. PHYSICAL REVIEW LETTERS 2004; 92:248301. [PMID: 15245136 DOI: 10.1103/physrevlett.92.248301] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/09/2004] [Indexed: 05/24/2023]
Abstract
We report experimental results obtained from a chemical reaction-diffusion system in which wave propagation is limited to a finite band of wavelengths and in which no solitary pulses exist. Wave patterns increase their size through repeated annihilation events of the frontier pulse that allow the succeeding pulses to advance farther. A related type of wave dynamics involves a stable but slow frontier pulse that annihilates subsequent waves in front-to-back collisions. These so-called merging dynamics give rise to an unexpected form of spiral wave nucleation. All of these phenomena are reproduced by a simple, three-species reaction-diffusion model that reveals the importance of the underlying anomalous dispersion relation.
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Affiliation(s)
- N Manz
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
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Ginn BT, Steinbock B, Kahveci M, Steinbock O. Microfluidic Systems for the Belousov−Zhabotinsky Reaction. J Phys Chem A 2004. [DOI: 10.1021/jp0358883] [Citation(s) in RCA: 50] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Brent T. Ginn
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390
| | - Bettina Steinbock
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390
| | - Murat Kahveci
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390
| | - Oliver Steinbock
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390
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Manz N, Ginn BT, Steinbock O. Meandering Spiral Waves in the 1,4-Cyclohexanedione Belousov−Zhabotinsky System Catalyzed by Fe[batho(SO3)2]34-/3-. J Phys Chem A 2003. [DOI: 10.1021/jp036008n] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Niklas Manz
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390
| | - Brent T. Ginn
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390
| | - Oliver Steinbock
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390
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Szalai I, Kurin-Csörgei K, Epstein IR, Orbán M. Dynamics and Mechanism of Bromate Oscillators with 1,4-Cyclohexanedione. J Phys Chem A 2003. [DOI: 10.1021/jp0360523] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- István Szalai
- Department of Inorganic and Analytical Chemistry, L. Eötvös University, P.O. Box 32, H-1518 Budapest 112, Hungary, and Department of Chemistry, MS 015, Brandeis University, Waltham, Massachusetts 02454-9110
| | - Krisztina Kurin-Csörgei
- Department of Inorganic and Analytical Chemistry, L. Eötvös University, P.O. Box 32, H-1518 Budapest 112, Hungary, and Department of Chemistry, MS 015, Brandeis University, Waltham, Massachusetts 02454-9110
| | - Irving R. Epstein
- Department of Inorganic and Analytical Chemistry, L. Eötvös University, P.O. Box 32, H-1518 Budapest 112, Hungary, and Department of Chemistry, MS 015, Brandeis University, Waltham, Massachusetts 02454-9110
| | - Miklós Orbán
- Department of Inorganic and Analytical Chemistry, L. Eötvös University, P.O. Box 32, H-1518 Budapest 112, Hungary, and Department of Chemistry, MS 015, Brandeis University, Waltham, Massachusetts 02454-9110
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Affiliation(s)
- Lingfa Yang
- Department of Chemistry and Center for Complex Systems, MS 015, Brandeis University, Waltham, Massachusetts 02454-9110
| | - Irving R. Epstein
- Department of Chemistry and Center for Complex Systems, MS 015, Brandeis University, Waltham, Massachusetts 02454-9110
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Fenton FH, Cherry EM, Hastings HM, Evans SJ. Multiple mechanisms of spiral wave breakup in a model of cardiac electrical activity. CHAOS (WOODBURY, N.Y.) 2002; 12:852-892. [PMID: 12779613 DOI: 10.1063/1.1504242] [Citation(s) in RCA: 316] [Impact Index Per Article: 14.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/18/2023]
Abstract
It has become widely accepted that the most dangerous cardiac arrhythmias are due to reentrant waves, i.e., electrical wave(s) that recirculate repeatedly throughout the tissue at a higher frequency than the waves produced by the heart's natural pacemaker (sinoatrial node). However, the complicated structure of cardiac tissue, as well as the complex ionic currents in the cell, have made it extremely difficult to pinpoint the detailed dynamics of these life-threatening reentrant arrhythmias. A simplified ionic model of the cardiac action potential (AP), which can be fitted to a wide variety of experimentally and numerically obtained mesoscopic characteristics of cardiac tissue such as AP shape and restitution of AP duration and conduction velocity, is used to explain many different mechanisms of spiral wave breakup which in principle can occur in cardiac tissue. Some, but not all, of these mechanisms have been observed before using other models; therefore, the purpose of this paper is to demonstrate them using just one framework model and to explain the different parameter regimes or physiological properties necessary for each mechanism (such as high or low excitability, corresponding to normal or ischemic tissue, spiral tip trajectory types, and tissue structures such as rotational anisotropy and periodic boundary conditions). Each mechanism is compared with data from other ionic models or experiments to illustrate that they are not model-specific phenomena. Movies showing all the breakup mechanisms are available at http://arrhythmia.hofstra.edu/breakup and at ftp://ftp.aip.org/epaps/chaos/E-CHAOEH-12-039203/ INDEX.html. The fact that many different breakup mechanisms exist has important implications for antiarrhythmic drug design and for comparisons of fibrillation experiments using different species, electromechanical uncoupling drugs, and initiation protocols. (c) 2002 American Institute of Physics.
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Affiliation(s)
- Flavio H. Fenton
- Center for Arrhythmia Research at Hofstra University and The Heart Institute, Beth Israel Medical Center, New York, New York 10003
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Manz N, Davydov VA, Zykov VS, Müller SC. Excitation fronts in a spatially modulated light-sensitive Belousov-Zhabotinsky system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:036207. [PMID: 12366224 DOI: 10.1103/physreve.66.036207] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2002] [Indexed: 05/23/2023]
Abstract
The evolution of excitation wave fronts in a spatially modulated light-sensitive Belousov-Zhabotinsky system is investigated experimentally and theoretically. The excitation wave propagates in a thin, quasi-two-dimensional reaction layer, which is illuminated through a periodical gray level mask. The light-induced differences in excitability and velocity give rise to a temporal and spatial modulation of the initially flat fronts. The experimental front evolution is described in the framework of a kinematical theory as developed earlier for nonuniformly curved systems.
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Affiliation(s)
- N Manz
- Institut für Experimentelle Physik, Otto-von-Guericke-Universität, D-39106 Magdeburg, Germany
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Hamik CT, Steinbock O. Shock structures and bunching fronts in excitable reaction-diffusion systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:046224. [PMID: 12005993 DOI: 10.1103/physreve.65.046224] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/16/2001] [Indexed: 05/23/2023]
Abstract
We report experimental results on the dynamics of excitation waves in a modified Belousov-Zhabotinsky reaction. The waves in this system obey nonmonotonic dispersion relations. This anomaly induces the stacking of excitation fronts into patterns with stable interpulse distances. The stacking process creates either a traveling shock structure or a cascade of bunching events in which metastable wave packets are formed. The direction and the speed of the shock are explained in terms of a simple geometrical analysis. We also present experimental evidence for the corresponding instabilities in two-dimensional systems. Here, wave stacking generates atypical structures in the collision of target patterns and wave bunching is accompanied by complex front deformations.
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Affiliation(s)
- Chad T Hamik
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
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Agladze K, Thouvenel-Romans S, Steinbock O. Electrochemical Waves on Patterned Surfaces: Propagation through Narrow Gaps and Channels. J Phys Chem A 2001. [DOI: 10.1021/jp011294t] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Konstantin Agladze
- Department of Chemistry, The Florida State University, Tallahassee, Florida 32306-4390
| | | | - Oliver Steinbock
- Department of Chemistry, The Florida State University, Tallahassee, Florida 32306-4390
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Hamik CT, Manz N, Steinbock O. Anomalous Dispersion and Attractive Pulse Interaction in the 1,4-Cyclohexanedione Belousov−Zhabotinsky Reaction. J Phys Chem A 2001. [DOI: 10.1021/jp010270j] [Citation(s) in RCA: 60] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Chad T. Hamik
- Florida State University, Department of Chemistry, Tallahassee, Florida 32306-4390
| | - Niklas Manz
- Florida State University, Department of Chemistry, Tallahassee, Florida 32306-4390
| | - Oliver Steinbock
- Florida State University, Department of Chemistry, Tallahassee, Florida 32306-4390
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