Kedma Bar‐Eli

A modified Oregonator model exhibiting complicated limit cycle behavior in a flow system

A reversible Oregonator model has been used to simulate recent experimental measurements by Schmitz, Graziani, and Hudson of complicated oscillations by a Belousov–Zhabotinsky system in a stirred tank reactor. The experimental observations indicate chaotic behavior of the small amplitude oscillations occurring between major excursions, but our computer simulation with a small error parameter apparently generates a true limit cycle with six relative maxima before the pattern repeats. The differences between experiment and simulation suggest the chaotic behavior observed experimentally may result from fluctuations too small to measure in any other way. The computations also indicate that reversibility of the reaction of bromate with bromide is important in a continuously stirred tank reactor under conditions such that the (unstable) steady state has a very low concentration of bromide ion.

Relevance of a two‐variable Oregonator to stable and unstable steady states and limit cycles, to thresholds of excitability, and to Hopf vs SNIPER bifurcations

A stiffly‐coupled Oregonator model based on the two independent variables Y and Z has been examined in detail with the use of the stoichiometric factor as a single disposable parameter. The trajectories and periods of the stable limit cycles can be generated with unanticipated accuracy from simple linear differential equations. Transitions between stable limit cycles and stable steady states takes place by means of subcritical Hopf bifurcations. Unstable limit cycles and thresholds of excitability can be recovered by integrating the equations of motion backward in time; such procedures cannot be applied so easily for models based on more than two independent variables. We have examined claims of experimental evidence for saddle‐node infinite period (SNIPER) bifurcations and have concluded that all currently available evidence is equivocal. Until unambiguous criteria can be established for identifying SNIPER bifurcations in real systems, and until chemical mechanisms have been proposed which generate such ...

Unstable supersaturated solutions of gases in liquids and nucleation theory

Limiting supersaturations for dissolved gases manifested by gas evolution oscillators and by direct experiments cannot be accounted for by the application of classical nucleation theory (CNT). The theory predicts bubbles containing 104–105 molecules at nucleation, with Helmholtz energies of ca. 104kT per bubble, much too high for homogeneous nucleation to occur spontaneously in a finite time. We investigate alternative unstable structures (‘blobs’) which do not have well-defined interfaces, which may exist transiently at the point of nucleation as the precursors of true bubbles and which circumvent the need for a large Helmholtz energy for their formation. Effects due to global or local depletion of the solution concentration at nucleation are also considered.

A model for imperfect mixing in a CSTR

When a chemical reaction is carried out in a continuously stirred tank reactor, the behavior may be significantly affected by the efficiency with which the entering chemicals are mixed with the main contents of the reactor. We have developed a model for this effect which assumes that a feed of premixed chemicals remains for a while in totally segregated packets before they are rapidly and perfectly mixed with the rest of the system. The time of this initial segregation is affected by the efficiency of stirring in the reactor. The model has been tested by computations on a mechanism developed by Roelofs et al. for a reaction which would oscillate even in a closed system. It has also been tested by computations on the rapid autocatalytic oxidation of cerous ion by bromate in the presence of a small amount of bromide. The results are qualitatively consistent with effects observed experimentally and in computations with other models including a somewhat similar one by Kumpinsky and Epstein. More quantitative ...

Computations simulating experimental observations of complex bursting patterns in the Belousov–Zhabotinsky system

A model based on five independent composition variables has been tested by simulating the complex bursting patterns observed experimentally for a Belousov–Zhabotinsky system in a flow reactor. If the system is in a region of constraint space where all stationary states are locally unstable, and if malonic acid concentration in the feed is decreased at constant flow of bromide ion, simple limit‐cycle oscillations persist until the system reaches the Hopf bifurcation which generates a stable stationary state with low concentration of bromide ion. If bromide ion concentration in the feed is increased at constant flow of malonic acid, more and more small‐amplitude oscillations are interspersed between trains of fewer and fewer large‐amplitude excursions until a Hopf bifurcation leads to a stable stationary state with a high concentration of bromide ion. Patterns may be quite complex but usually repeat regularly. If a firing number is defined as ΣS/(ΣS+ΣL), where the summations represent the numbers of small‐ ...