Self-organization with traveling waves: A case for a convective torus

A traveling wave of BaSO4 in the chlorite-thiourea reaction has shown concentric precipitation patterns upon being triggered by the autocatalyst HOCl. The precipitation patterns show circular rings of alternate null and full precipitation regions. This self-organization appears to be the result of the formation of a convective torus. The formation of the convective torus can be described as a Benard-Marangoni instability with lateral heating

Validity of threshold-crossing analysis of symbolic dynamics from chaotic time series

A practical and popular technique to extract the symbolic dynamics from experimentally measured chaotic time series is the threshold-crossing method, by which an arbitrary partition is utilized for determining the symbols. We address to what extent the symbolic dynamics so obtained can faithfully represent the phase-space dynamics. Our principal result is that such practice leads to a severe misrepresentation of the dynamical system. The measured topological entropy is a Devil's staircase-like, but surprisingly nonmonotone, function of a parameter characterizing the amount of misplacement of the partition.Comment: 8 pages + 4 figures in .pd

Kinetics and Mechanism of Oxidation of Methimazole by Chlorite in Slightly Acidic Media

The kinetics and mechanism of the oxidation of methimazole (1-methyl-3H-imidazole), MMI, by chlorite in mildly acidic environments were studied. It is a complex reaction that gives oligo-oscillations in chlorine dioxide concentrations in excess chlorite conditions. The stoichiometry is strictly 2:1, with the sulfur center being oxidized to sulfate and the organic moiety being hydrolyzed to several indeterminate species. In excess MMI conditions over chlorite, the sulfinic acid and sulfonic acid were observed as major intermediates. The sulfenic acid, which was observed in the electrochemical oxidation of MMI, was not observed with chlorite oxidations. Initial reduction of chlorite produced HOCl, an autocatalytic species in chlorite oxidations. HOCl rapidly reacts with chlorite to produce chlorine dioxide, which, in turn, reacts rapidly with MMI to produce more chlorite. The reaction of chlorine dioxide with MMI is competitive, in rate, with the chlorite–MMI and HOCl–ClO2– reactions. This explains the oligo-oscillations in ClO2concentrations

Practical error analysis of the quasi-steady-state approximation

The Quasi-Steady-State Approximation (QSSA) is a method of getting approximate solutions to differential equations, developed heuristically in biochemistry early this century. It can produce acceptable and important results even when formal analytic and numerical procedures fail. It has become associated with singular perturbation theory [1], which provides a means of assessing the accuracy and validity of the QSSA, but this involves rather complicated mathematics. In contrast, it is shown here how the necessary safeguards against misuse can be based on a simpler intuitive approach to singular perturbation theory, allied to the powerful numerical mathematical packages which have become available in recent years. This approach has been subjected to rigorous analysis and has been applied to problems in transport theory and chemical kinetics. In this note, examples are restricted to the case of ordinary differential equation systems involving only a few dependent variables. Use of the QSSA is described ab initio. Quaestiones Mathematicae 23(2000), 129–15