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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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Suematsu NJ, Nakata S. Instability of the Homogeneous Distribution of Chemical Waves in the Belousov-Zhabotinsky Reaction. MATERIALS 2021; 14:ma14206177. [PMID: 34683766 PMCID: PMC8537810 DOI: 10.3390/ma14206177] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/17/2021] [Revised: 10/12/2021] [Accepted: 10/14/2021] [Indexed: 11/16/2022]
Abstract
Chemical traveling waves play an important role in biological functions, such as the propagation of action potential and signal transduction in the nervous system. Such chemical waves are also observed in inanimate systems and are used to clarify their fundamental properties. In this study, chemical waves were generated with equivalent spacing on an excitable medium of the Belousov–Zhabotinsky reaction. The homogeneous distribution of the waves was unstable and low- and high-density regions were observed. In order to understand the fundamental mechanism of the observations, numerical calculations were performed using a mathematical model, the modified Oregonator model, including photosensitive terms. However, the homogeneous distribution of the traveling waves was stable over time in the numerical results. These results indicate that further modification of the model is required to reproduce our experimental observations and to discover the fundamental mechanism for the destabilization of the homogeneous-distributed chemical traveling waves.
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Affiliation(s)
- Nobuhiko J. Suematsu
- School of Interdisciplinary Mathematical Sciences, Meiji University, 4-21-1 Nakano, Nakano-ku, Tokyo 164-8525, Japan
- Graduate School of Advanced Mathematical Sciences, Meiji University, 4-21-1 Nakano, Nakano-ku, Tokyo 164-8525, Japan
- Meiji Institute for Advanced Study of Mathematical Sciences (MIMS), Meiji University, 4-21-1 Nakano, Nakano-ku, Tokyo 164-8525, Japan
- Correspondence: ; Tel.: +81-3-5343-8348
| | - Satoshi Nakata
- Graduate School of Integrated Sciences for Life, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima 739-8526, Japan;
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Tsyganov MA, Biktashev VN. Classification of wave regimes in excitable systems with linear cross diffusion. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:062912. [PMID: 25615169 DOI: 10.1103/physreve.90.062912] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2014] [Indexed: 06/04/2023]
Abstract
We consider principal properties of various wave regimes in two selected excitable systems with linear cross diffusion in one spatial dimension observed at different parameter values. This includes fixed-shape propagating waves, envelope waves, multienvelope waves, and intermediate regimes appearing as waves propagating at a fixed shape most of the time but undergoing restructuring from time to time. Depending on parameters, most of these regimes can be with and without the "quasisoliton" property of reflection of boundaries and penetration through each other. We also present some examples of the behavior of envelope quasisolitons in two spatial dimensions.
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Affiliation(s)
- M A Tsyganov
- Institute of Theoretical and Experimental Biophysics, Pushchino, Moscow Region, 142290, Russia
| | - V N Biktashev
- College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, UK
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Suematsu NJ, Sato T, Motoike IN, Kashima K, Nakata S. Density wave propagation of a wave train in a closed excitable medium. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:046203. [PMID: 22181241 DOI: 10.1103/physreve.84.046203] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/21/2011] [Indexed: 05/31/2023]
Abstract
A wave train in an excitable reaction-diffusion medium shows a variety of spatiotemporal patterns as a result of interactions between the individual waves. In this paper, we report a novel spatiotemporal pattern in a wave train in a closed excitable medium. We carried out experiments using a photosensitive Belousov-Zhabotinsky reaction with Ru(bpy)(3)(2+) as a catalyst and a numerical calculation using the FitzHugh-Nagumo equation. A wave train was locally distributed as an initial condition and the number of waves was systematically varied. In both the experiment and numerical calculation, density wave propagation was formed in a wave train during relaxation with a large number of waves. Our results suggest that density wave propagation originates from inhibitory interaction between the waves.
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Affiliation(s)
- Nobuhiko J Suematsu
- Graduate School of Advanced Mathematical Sciences, Meiji University, 1-1-1 Higashimita, Tamaku, Kawasaki 214-8571, Japan.
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Spatial Symmetry Breaking in the Revival Wave of the Belousov-Zhabotinsky Reaction Containing 1,4-Cyclohexanedione. B KOREAN CHEM SOC 2009. [DOI: 10.5012/bkcs.2009.30.4.907] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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Schneider FM, Schöll E, Dahlem MA. Controlling the onset of traveling pulses in excitable media by nonlocal spatial coupling and time-delayed feedback. CHAOS (WOODBURY, N.Y.) 2009; 19:015110. [PMID: 19335014 DOI: 10.1063/1.3096411] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
The onset of pulse propagation is studied in a reaction-diffusion (RD) model with control by augmented transmission capability that is provided either along nonlocal spatial coupling or by time-delayed feedback. We show that traveling pulses occur primarily as solutions to the RD equations, while augmented transmission changes excitability. For certain ranges of the parameter settings, defined as weak susceptibility and moderate control, respectively, the hybrid model can be mapped to the original RD model. This results in an effective change in RD parameters controlled by augmented transmission. Outside moderate control parameter settings new patterns are obtained, for example, stepwise propagation due to delay-induced oscillations. Augmented transmission constitutes a signaling system complementary to the classical RD mechanism of pattern formation. Our hybrid model combines the two major signaling systems in the brain, namely, volume transmission and synaptic transmission. Our results provide insights into the spread and control of pathological pulses in the brain.
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Affiliation(s)
- Felix M Schneider
- Institut fur Theoretische Physik, Technische Universitat Berlin, Berlin, Germany
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Luo J, Zhan M. Electric-field-induced wave groupings of spiral waves with oscillatory dispersion relation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:016214. [PMID: 18764042 DOI: 10.1103/physreve.78.016214] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2008] [Indexed: 05/26/2023]
Abstract
The dynamic behavior of spiral-shaped excitation patterns with oscillatory dispersion is investigated under the influence of externally applied direct current or alternating current. For these two types of electric field, wave-grouping phenomena are generally observed. For the direct current field, the spiral wave drifts approximately along a straight line and wave groupings appear in certain ranges of spatial polar angles when the strength of the external field is larger than a threshold. In terms of the Doppler effect induced by the drift of the spiral tip and the oscillatory dispersion, we propose a theory model to predict the spatial distribution of wave grouping and the critical strength of the current. In contrast, for the alternating current field, the spiral wave may stay stationary and wave grouping may appear in the whole space with a different manner. This finding indicates that movement of the spiral tip is not necessary for the appearance of wave grouping.
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Affiliation(s)
- Jinming Luo
- Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
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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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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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