Spatiotemporal motions due to global interaction

Abstract

The global interaction between the spatial average of the autocatalytic variable in a reactive (catalytic, electrochemical, gel) medium and a surrounding mixed fluid in a continuously fed vessel may induce a rich structure of spatiotemporal patterns that would not exist otherwise. Patterns may form when the local kinetics are either excitable, oscillatory, or bistable and the reaction rate ascends with reactant concentration. Thus, a local change in the surface reaction rate may affect the reactant concentration in the surrounding well-mixed vessel, so that it arrests moving fronts on the surface. External control of the average temperature (or rate) of a catalytic ribbon by electrical heating is another form of interaction between a spatial average of a local oscillator and a space-independent variable that induces pattern formation. We study various patterns and bifurcations that can develop in a ring or a ribbon due to global interaction using a simple cubic kinetic expression. The predominant pattern on a catalytic ring is a rotating pulse. Other patterns, such as antiphase oscillations and crossing pulses, similar to those found previously on a controlled catalytic ribbon, may coexist for a sufficiently strong interaction. Several of the transitions between regions with qualitatively different patterns are via global bifurcation.

Turing patterns and solitary structures under global control

“…The basic three-variable model with cubic nonlinearity is formulated in Section II, and the equation of motion of a bent kink is derived in Section III. We proceed with the construction of various stationary structures in Section IV, and the analysis of their stability in Section V. The combined picture of the existence and stability regions of solitary band and disk solutions, as discussed in the last Section, is in qualitative agreement with the results of the computer experiment by Middya and Luss [15].…”

“…Global interaction through the gas phase is usually detrimental to pattern formation, as it tends to synchronize the reaction on the entire surface. Recent computations by Middya and Luss [15] demonstrated a sequence of transitions from striped to spotted patterns and, eventually, to restoration of spatial homogeneity with an increased level of global control.…”

“…In recent years, novel experimental techniques were applied to obtain a variety of complex chemical patterns in gel reactors [9][10][11][12] and on catalytic surfaces [13]. A parallel progress in computing and visualization is evident in 2d patterns obtained in recent computer experiments [14,15].…”

Pattern formation in homogeneous reactor models

“…In a system with r ™0 the pattern may T Ž be constructed analytically, similar to patterns on a ring see . Mikhailov, 1991;Middya et al, 1994 . Moreover, patterns will not emerge even in a recycle reactor, since pattern formation of the proposed mechanism requires feedback from the reactor inlet to its exit, contrary to the feedback in the recycled reactor.…”

Non‐Linear Dynamics: Oscillatory Kinetics and Spatio‐Temporal Pattern Formation

“…This is because the decisive effects are thermokinetic in nature and can be approximated by a heat-balance equation in which the chemistry of the reaction is reduced to a single variable and the surface diffusion of the adsorbates is neglected [213][214][215][216][217][218]. Coupling through the gas phase may also be mostly neglected, although its inclusion may give rise to quantitative changes [213].…”