Anomalous Dispersion and Attractive Pulse Interaction in the 1,4-Cyclohexanedione Belousov−Zhabotinsky Reaction

Hamik, Chad T.; Manz, Niklas; Steinbock, Oliver

doi:10.1021/jp010270j

Cited by 66 publications

(73 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] While in most of the bromate-cyclic compound oscillators the oscillatory behavior is short-lived when studied in a batch system, [1,2] over 200 oscillation peaks have been achieved in the closed bromate-1,4-cyclohexanedione (CHD). [3] The long lasting oscillatory dynamics, coupled with the absence of gas production, has made the bromate-CHD reaction a new popular model system for the investigation of nonlinear spatial-temporal dynamics, [13][14][15] an important behavior that has been encountered in a variety of systems ranging from physical to biological systems.…”

Section: Introductionmentioning

confidence: 99%

CO₂ production in the bromate‐1,4‐cyclohexanedione oscillatory reaction

Feng

Green

Johnson

et al. 2010

J of Physical Organic Chem

View full text Add to dashboard Cite

NMR and GC/MS spectroscopy of the organic extracts of the oscillatory bromate-1,4-cyclohexanedione reaction illustrate the presence of ring-opening products 5-(dibromomethylene)-2(5H)-furanone, (E)-5,5,5-tribromo-4-oxo-2-pentenoic acid, and dibromoacetic acid, particularly at elevated temperatures. The loss of a carbon atom from the six-membered ring after ring opening led to gas formation and such a process became more vigorous at >60 -C, with the direct observation of bubbles in a stirred batch reactor. Gravimetric experiments confirm that the amount of carbon dioxide gas produced increases rapidly with reaction temperature. Parallel experiments suggest that the ring-opening process involves the oxidation of brominated benzoquinones by bromate.

show abstract

Section: Introductionmentioning

confidence: 99%

CO₂ production in the bromate‐1,4‐cyclohexanedione oscillatory reaction

Feng

Green

Johnson

et al. 2010

J of Physical Organic Chem

View full text Add to dashboard Cite

show abstract

“…Such behavior has been discovered in various experiments in chemical reaction-diffusion systems [4,5]. It has been found to coincide with attractive long-range interaction between pulses that may lead to stable bound states [6] merging or bunching of pulses [7].…”

mentioning

confidence: 99%

Supernormal conduction in cardiac tissue promotes concordant alternans and action potential bunching

et al. 2011

View full text Add to dashboard Cite

Supernormal conduction (SNC) in excitable cardiac tissue refers to an increase of pulse (or action potential) velocity with decreasing distance to the preceding pulse. Here we employ a simple ionic model to study the effect of SNC on the propagation of action potentials (APs) and the phenomenology of alternans in excitable cardiac tissue. We use bifurcation analysis and simulations to study attraction between propagating APs caused by SNC that leads to AP pairs and bunching. It is shown that SNC stabilizes concordant alternans in arbitrarily long paced one-dimensional cables. As a consequence, spiral waves in two-dimensional tissue simulations exhibit straight nodal lines for SNC in contrast to spiraling ones in the case of normal conduction. Propagation of pulse trains in excitable media is usually characterized by a so-called dispersion curve that gives the velocity of a pulse in a periodic train as a function of its wavelength [1]. In cardiac tissue the dispersion properties are often summarized in the conduction velocity (CV) restitution curve that relates the velocity of an action potential (AP) to its diastolic interval (DI), that is, the time between two consecutive APs (see, e.g., Ref.[2]).Since a pulse typically is followed by a refractory zone of decreased excitability, the pulse velocity monotonically increases with increasing wavelength (=normal dispersion). In the context of excitable cardiac tissue, normal dispersion corresponds to normal conduction. In this paper we focus on the alternative situation where the velocity of a pulse is decreasing with increasing wavelength. In generic excitable media this case is known as anomalous dispersion. For excitable cardiac tissue it corresponds to supernormal conduction (SNC) [3]. Normal and supernormal conduction may appear for a different wavelength in the same systems, then the dispersion curve has to be nonmonotonic.The simplest case of a nonmonotonic dispersion relation is a curve with a single maximum separating anomalous dispersion at long wavelength from normal dispersion at short wavelength. Such behavior has been discovered in various experiments in chemical reaction-diffusion systems [4,5]. It has been found to coincide with attractive long-range interaction between pulses that may lead to stable bound states [6] merging or bunching of pulses [7]. While most excitable cardiac tissues and related models exhibit normal conduction, nevertheless examples of SNC are frequent (for a short review see, e.g., Ref.[8]). SNC is found, for example, in the Iyer-Mazhari-Winslow [9] or in the Drouhard-RobergeBeeler-Reuter (DRBR) model [10,11] employed in the study here, and it is often observed under conditions of low extracellular potassium concentration [12]. Recently, it has been shown to potentiate the onset of alternans in cultured cardiac cell strands [13] and also in generic models of spiral wave formation [14].Alternans is an oscillation in the duration of the AP that usually occurs at short stimulation periods [15]. In a paced cable or tissue alternans ...

show abstract

“…The dispersion relation in the classic BZ reaction is monotonically increasing, whereas the CHD-BZ system shows anomalous dispersion over a wide range of reactant concentrations. 34,35 For the parameter space investigated here, we could not find any evidence for anomalous dispersion. However, it is possible that in the CHD-BZ reaction meandering tip motion exists under conditions that show nonmonotonic dispersion relations.…”

Section: Discussionmentioning

confidence: 60%

Meandering Spiral Waves in the 1,4-Cyclohexanedione Belousov−Zhabotinsky System Catalyzed by Fe[batho(SO₃)₂]₃^4-/3-

2003

Self Cite

View full text Add to dashboard Cite

Meandering spiral waves are observed in the 1,4-cyclohexanedione Belousov-Zhabotinsky (CHD-BZ) reaction at very low concentrations (3-35 mM) of the organic substrate. The spiral tips describe hypocycle-like trajectories indicating the presence of two main rotation periods and radii. The ratio of these periods approaches 1 for decreasing concentrations of CHD. In this limit, we find Z-shaped trajectories with approximately two lobes. The use of Fe[batho(SO 3 ) 2 ] 3 4-/3-as the BZ catalyst gives rise to extremely long rotation periods (1000-4000 s), and the tip trajectories span large areas of up to 40 mm 2 . As a result of the absence of gaseous products and the high absorption of the catalyst, this particular system is ideally suited for the investigation of spiral waves in closed, thin-layer systems, such as nonuniformly curved and micropatterned media.

show abstract

Anomalous Dispersion and Attractive Pulse Interaction in the 1,4-Cyclohexanedione Belousov−Zhabotinsky Reaction

Cited by 66 publications

References 49 publications

CO₂ production in the bromate‐1,4‐cyclohexanedione oscillatory reaction

CO₂ production in the bromate‐1,4‐cyclohexanedione oscillatory reaction

Supernormal conduction in cardiac tissue promotes concordant alternans and action potential bunching

Meandering Spiral Waves in the 1,4-Cyclohexanedione Belousov−Zhabotinsky System Catalyzed by Fe[batho(SO₃)₂]₃^4-/3-

Contact Info

Product

Resources

About

Anomalous Dispersion and Attractive Pulse Interaction in the 1,4-Cyclohexanedione Belousov−Zhabotinsky Reaction

Cited by 66 publications

References 49 publications

CO2 production in the bromate‐1,4‐cyclohexanedione oscillatory reaction

CO2 production in the bromate‐1,4‐cyclohexanedione oscillatory reaction

Supernormal conduction in cardiac tissue promotes concordant alternans and action potential bunching

Meandering Spiral Waves in the 1,4-Cyclohexanedione Belousov−Zhabotinsky System Catalyzed by Fe[batho(SO3)2]34-/3-

Contact Info

Product

Resources

About

CO₂ production in the bromate‐1,4‐cyclohexanedione oscillatory reaction

CO₂ production in the bromate‐1,4‐cyclohexanedione oscillatory reaction

Meandering Spiral Waves in the 1,4-Cyclohexanedione Belousov−Zhabotinsky System Catalyzed by Fe[batho(SO₃)₂]₃^4-/3-