1
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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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Dynamic Effects in Nucleation of Receptor Clusters. ENTROPY 2021; 23:e23101245. [PMID: 34681969 PMCID: PMC8534492 DOI: 10.3390/e23101245] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/14/2021] [Revised: 09/21/2021] [Accepted: 09/22/2021] [Indexed: 11/16/2022]
Abstract
Nucleation theory has been widely applied for the interpretation of critical phenomena in nonequilibrium systems. Ligand-induced receptor clustering is a critical step of cellular activation. Receptor clusters on the cell surface are treated from the nucleation theory point of view. The authors propose that the redistribution of energy over the degrees of freedom is crucial for forming each new bond in the growing cluster. The expression for a kinetic barrier for new bond formation in a cluster was obtained. The shape of critical receptor clusters seems to be very important for the clustering on the cell surface. The von Neumann entropy of the graph of bonds is used to determine the influence of the cluster shape on the kinetic barrier. Numerical studies were carried out to assess the dependence of the barrier on the size of the cluster. The asymptotic expression, reflecting the conditions necessary for the formation of receptor clusters, was obtained. Several dynamic effects were found. A slight increase of the ligand mass has been shown to significantly accelerate the nucleation of receptor clusters. The possible meaning of the obtained results for medical applications is discussed.
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3
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Zanotto FM, Steinbock O. Asymmetric synchronization in lattices of pinned spiral waves. Phys Rev E 2021; 103:022213. [PMID: 33736004 DOI: 10.1103/physreve.103.022213] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2020] [Accepted: 02/03/2021] [Indexed: 11/07/2022]
Abstract
Networks of coupled oscillators show a wealth of fascinating dynamics and are capable of storing and processing information. In biological and social networks, the coupling is often asymmetric. We use the chirality of rotating spiral waves to introduce this asymmetry in an excitable reaction-diffusion model. The individual vortices are pinned to unexcitable disks and arranged at a constant spacing L along straight lines or simple geometric patterns. In the case of periodic boundaries or pinning disks arranged along the edge of a closed shape, small L values lead to synchronization via repeated wave collisions. The rate of synchronization as a function of L shows a single maximum and is determined by the dispersion behavior of a continuous wave train traveling along the system boundary. For finite systems, spirals are affected by their upstream neighbor, and a single dominant spiral exists along each chain. Specific initial conditions can decouple neighboring vortices even for small L values. We also present a time-delay differential equation that reproduces the phase dynamics in periodic systems.
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Affiliation(s)
- Franco M Zanotto
- Florida State University, Department of Chemistry and Biochemistry, Tallahassee, Florida 32306-4390, USA
| | - Oliver Steinbock
- Florida State University, Department of Chemistry and Biochemistry, Tallahassee, Florida 32306-4390, USA
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4
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Budroni MA, De Wit A. Localized stationary and traveling reaction-diffusion patterns in a two-layer A+B→ oscillator system. Phys Rev E 2016; 93:062207. [PMID: 27415255 DOI: 10.1103/physreve.93.062207] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2015] [Indexed: 05/07/2023]
Abstract
When two solutions containing separate reactants A and B of an oscillating reaction are put in contact in a gel, localized spatiotemporal patterns can develop around the contact zone thanks to the interplay of reaction and diffusion processes. Using the Brusselator model, we explore analytically the deployment in space and time of the bifurcation diagram of such an A+B→ oscillator system. We provide a parametric classification of possible instabilities as a function of the ratio of the initial reactant concentrations and of the reaction intermediate species diffusion coefficients. Related one-dimensional reaction-diffusion dynamics are studied numerically. We find that the system can spatially localize waves and Turing patterns as well as induce more complex dynamics such as zigzag spatiotemporal waves when Hopf and Turing modes interact.
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5
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Budroni MA, Lemaigre L, Escala DM, Muñuzuri AP, De Wit A. Spatially Localized Chemical Patterns around an A + B → Oscillator Front. J Phys Chem A 2016; 120:851-60. [DOI: 10.1021/acs.jpca.5b10802] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- M. A. Budroni
- Department
of Chemistry and Pharmacy, University of Sassari, 07100 Sassari, Italy
| | - L. Lemaigre
- Université libre de Bruxelles (ULB), Nonlinear
Physical Chemistry Unit, Faculté
des Sciences, CP231, 1050 Brussels, Belgium
| | - D. M. Escala
- Nonlinear
Physics Group, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain
| | - A. P. Muñuzuri
- Nonlinear
Physics Group, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain
| | - A. De Wit
- Université libre de Bruxelles (ULB), Nonlinear
Physical Chemistry Unit, Faculté
des Sciences, CP231, 1050 Brussels, Belgium
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6
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Ayass MM, Lagzi I, Al-Ghoul M. Targets, ripples and spirals in a precipitation system with anomalous dispersion. Phys Chem Chem Phys 2015; 17:19806-14. [PMID: 26154951 DOI: 10.1039/c5cp01879j] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We present a novel reaction-diffusion system that exhibits three-dimensional superdiffusive traveling waves without utilizing any external forces. These waves include single circular targets, spirals, and ripples as well as phase-like waves. The system is based on the interplay of the precipitation reaction of mercuric iodide in a gel medium, its polymorphic transformation to a different crystalline form, and its redissolution in excess iodide. A phase diagram is constructed as a function of the initial concentrations of the reagents. The spatiotemporal evolution of these waves is thoroughly analyzed and seems to be a consequence of an anomalous dispersion relationship. Pattern selection and wavelengths of propagating waves are found to depend on initial concentrations of the reactants. The breakup of the waves is also investigated. While the breakdown of ripples and spirals is shown to be a consequence of a Doppler-like instability in conjunction with anomalous dispersion, the targets undergo a boundary defect-mediated breakup.
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Affiliation(s)
- Mahmoud M Ayass
- Department of Chemistry, American University of Beirut, P.O. Box 11-0236, Riad El-Solh 1107 2020, Beirut, Lebanon.
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7
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Yochelis A, Knobloch E, Köpf MH. Origin of finite pulse trains: Homoclinic snaking in excitable media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:032924. [PMID: 25871189 DOI: 10.1103/physreve.91.032924] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2013] [Indexed: 06/04/2023]
Abstract
Many physical, chemical, and biological systems exhibit traveling waves as a result of either an oscillatory instability or excitability. In the latter case a large multiplicity of stable spatially localized wavetrains consisting of different numbers of traveling pulses may be present. The existence of these states is related here to the presence of homoclinic snaking in the vicinity of a subcritical, finite wavenumber Hopf bifurcation. The pulses are organized in a slanted snaking structure resulting from the presence of a heteroclinic cycle between small and large amplitude traveling waves. Connections of this type require a multivalued dispersion relation. This dispersion relation is computed numerically and used to interpret the profile of the pulse group. The different spatially localized pulse trains can be accessed by appropriately customized initial stimuli, thereby blurring the traditional distinction between oscillatory and excitable systems. The results reveal a new class of phenomena relevant to spatiotemporal dynamics of excitable media, particularly in chemical and biological systems with multiple activators and inhibitors.
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Affiliation(s)
- Arik Yochelis
- Department of Solar Energy and Environmental Physics, Swiss Institute for Dryland Environmental and Energy Research, Jacob Blaustein Institutes for Desert Research (BIDR), Ben-Gurion University of the Negev, Sede Boqer Campus, Midreshet Ben-Gurion 84990, Israel
| | - Edgar Knobloch
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Michael H Köpf
- Département de Physique, École Normale Supérieure, 24 rue Lhomond, 75005 Paris, France
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8
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Kwon O, Kim TY, Lee KJ. Period-2 spiral waves supported by nonmonotonic wave dispersion. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:046213. [PMID: 21230371 DOI: 10.1103/physreve.82.046213] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2010] [Indexed: 05/30/2023]
Abstract
Rotating spiral waves appear ubiquitously in a wide range of nonlinear systems, and they play important roles in many biological phenomena. Recently, unusual spiral waves, which support period-2 dynamics, have been found in several different systems including cardiac tissues as well as nonlinear chemical reaction-diffusion systems. They are potentially significant as an intermediate dynamic state linking regularly rotating period-1 spiral waves to complex dynamic states such as cardiac fibrillations; for example, it is intrinsic of period-2 spiral waves to have "line defects" and their instability can lead to a spatiotemporal chaos. Previous mathematical models regarding period-2 spiral waves are mostly based on a coupled system of period-2 oscillators, but these are inappropriate for the description of a large class of systems that are composed of (nonoscillatory) excitable elements--a good example being the heart. In this paper we hypothesize that excitable media, which support a nonmonotonic conduction velocity dispersion relation, can sustain period-2 oscillatory spiral waves. We explicitly demonstrate that the new mechanism can create period-2 spirals by computer simulations on a simple mathematical model describing spiral wave front dynamics.
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Affiliation(s)
- Okyu Kwon
- Department of Physics, Korea University, Center for Cell Dynamics, Seoul 136-701, Korea
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9
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Zemskov EP, Loskutov AY. Traveling waves in a piecewise-linear reaction-diffusion model of excitable medium. Biophysics (Nagoya-shi) 2010. [DOI: 10.1134/s0006350909050145] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022] Open
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10
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Yochelis A, Knobloch E, Xie Y, Qu Z, Garfinkel A. Generation of finite wave trains in excitable media. EUROPHYSICS LETTERS 2008; 83:64005p1-64005p6. [PMID: 21572974 PMCID: PMC3092297 DOI: 10.1209/0295-5075/83/64005] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
Spatiotemporal control of excitable media is of paramount importance in the development of new applications, ranging from biology to physics. To this end, we identify and describe a qualitative property of excitable media that enables us to generate a sequence of traveling pulses of any desired length, using a one-time initial stimulus. The wave trains are produced by a transient pacemaker generated by a one-time suitably tailored spatially localized finite amplitude stimulus, and belong to a family of fast pulse trains. A second family, of slow pulse trains, is also present. The latter are created through a clumping instability of a traveling wave state (in an excitable regime) and are inaccessible to single localized stimuli of the type we use. The results indicate that the presence of a large multiplicity of stable, accessible, multi-pulse states is a general property of simple models of excitable media.
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Affiliation(s)
- A Yochelis
- Department of Medicine (Cardiology), University of California - Los Angeles, CA 90095, USA
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11
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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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12
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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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13
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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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14
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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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15
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Bánsági T, Steinbock O. Negative filament tension of scroll rings in an excitable system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:045202. [PMID: 17995050 DOI: 10.1103/physreve.76.045202] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2007] [Indexed: 05/25/2023]
Abstract
Scroll rings are three-dimensional spiral waves of excitation that rotate around circular filaments. In a modified Belousov-Zhabotinsky reaction, these filaments expand, buckle, and build up gradients in rotation phase. The instability is caused by negative filament tension (-4.3x10;{-4}cm;{2}s) . Initial deformations are strongest in the direction normal to the filament's osculating plane, and their growth rates decrease rapidly with increasing wave number.
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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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Röder G, Bordyugov G, Engel H, Falcke M. Wave trains in an excitable FitzHugh-Nagumo model: bistable dispersion relation and formation of isolas. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:036202. [PMID: 17500764 DOI: 10.1103/physreve.75.036202] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2006] [Indexed: 05/15/2023]
Abstract
We investigate the dispersion relations of nonlinear periodic wave trains in excitable systems which describe the dependence of the propagation velocity on the wavelength. Pulse interaction by oscillating pulse tails within a wave train leads to bistable wavelength bands, in which two stable and one unstable wave train coexist for the same wavelength. The essential spectra of the unstable wave trains exhibit a circle of eigenvalues with positive real parts which is detached from the imaginary axis. We describe the destruction of the bistable dispersion curve and the formation of isolas of wave trains in a sequence of transcritical bifurcations unfolding into pairs of saddle-node bifurcations. It turns out that additional dispersion curves of unstable wave trains play an important role in the destruction of the bistable dispersion curve.
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Affiliation(s)
- Georg Röder
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany.
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17
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Bánsági T, Steinbock O. Nucleation and collapse of scroll rings in excitable media. PHYSICAL REVIEW LETTERS 2006; 97:198301. [PMID: 17155661 DOI: 10.1103/physrevlett.97.198301] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2006] [Indexed: 05/12/2023]
Abstract
We describe a novel nucleation mechanism of scroll rings in three-dimensional reaction-diffusion systems with anomalous dispersion. The vortices form after the collision of two spherical wave fronts from a third, trailing wave that only partially annihilates in the wake of its predecessor. Depending on the relative positions of the three relevant wave sources, one obtains untwisted or twisted scroll rings. The formation of both vortex structures is demonstrated for a modified Belousov-Zhabotinsky reaction.
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Affiliation(s)
- Tamás Bánsági
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, FL 32306-4390, USA
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18
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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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19
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Kettunen P, Yamaguchi T, Hashimoto H, Amemiya T, Steinbock B, Müller SC. Emergent reaction-diffusion phenomena in capillary tubes. CHAOS (WOODBURY, N.Y.) 2006; 16:037111. [PMID: 17014245 DOI: 10.1063/1.2191621] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
Pattern formation in the Belousov-Zhabotinsky reaction experiments carried out by filling capillary glass tubes with catalyst-immobilized gel for the reaction is reported. Under unperturbed and oscillatory conditions, helicoidal waves appear spontaneously. Quantitative structural data of those helices are obtained by devising an optical tomography technique for extracting rotationally symmetric structures from time-lapse data. Space-time representation of the catalyst oxidation reveals wave transmission phenomenon that is studied further by numerical simulations of a reduced spatial model.
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Affiliation(s)
- Petteri Kettunen
- Nanotechnology Research Institute, National Institute of Advanced Industrial Science and Technology, AIST Central 5-2, Higashi 1-1-1, Tsukuba, Ibaraki 305-8565, Japan
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20
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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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21
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Park JS, Lee KJ. Line-defects-mediated complex-oscillatory spiral waves in a chemical system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:066219. [PMID: 16906958 DOI: 10.1103/physreve.73.066219] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2005] [Revised: 05/11/2006] [Indexed: 05/11/2023]
Abstract
In this paper, we summarize our experimental observations on complex-oscillatory spiral waves that arise in a Belousov-Zhabotinsky (BZ) reaction-diffusion system. The observed wave structures generically bear line defects across which the phase of local oscillation changes by a multiple of 2 pi. The local oscillation at every spatial point along a line defect of period-2 (P-2) oscillatory media is period-1 (P-1) oscillatory. For the homogeneous BZ reaction can be excitable, simply periodic, complex periodic, or chaotic as the control parameters are tuned, a number of different complex wave states are revealed. A two-dimensional phase diagram, which includes domains of P-2 oscillatory spirals, intermittently breathing spirals, period-3 (P-3) oscillatory spirals, two different types of mixed-mode periodic spirals, and line-defect-mediated turbulence, is constructed. Several different transitions among different dynamic states are described systematically. In all cases, line defects are found to play an important role.
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Affiliation(s)
- Jin-Sung Park
- National Creative Research Initiative Center for Neuro-dynamics and Department of Physics, Korea University, Seoul 136-701, Korea
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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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Liao HM, Zhou LQ, Zhang CX, Ouyang Q. Wave grouping of a meandering spiral induced by Doppler effects and oscillatory dispersion. PHYSICAL REVIEW LETTERS 2005; 95:238301. [PMID: 16384351 DOI: 10.1103/physrevlett.95.238301] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2005] [Indexed: 05/05/2023]
Abstract
A new type of meandering spiral pattern, in which the dense waves form groups while the sparse waves keep evenly spaced, is observed in a spatial open reactor using a ferroin-catalyzed Belousov-Zhabotinsky reaction. Such a phenomenon is related to both the Doppler effect of a meandering spiral and the oscillatory dispersion relation of the system. Simulation in the two-dimensional Oregonator reaction-diffusion model with an oscillatory dispersion relation gives very similar results.
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Affiliation(s)
- Hui-Min Liao
- School of Physics, Peking University, Beijing 100871, China
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24
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Ginn BT, Steinbock O. Front aggregation in multiarmed excitation vortices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:046109. [PMID: 16383470 DOI: 10.1103/physreve.72.046109] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2005] [Indexed: 05/05/2023]
Abstract
Using the Belousov-Zhabotinsky reaction, we study the pinning of multiarmed spiral waves to nonexcitable obstacles. With increasing obstacle size, the individual arms switch from a repulsive to an attractive state. This transition yields densely aggregated spiral arms and is caused by anomalous dispersion. A kinematic model reproduces the measurements quantitatively and identifies the transition as a supercritical pitchfork bifurcation.
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Affiliation(s)
- Brent T Ginn
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
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25
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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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