Self-organized rhythmic patterns in geochemical systems

Abstract

Chemical oscillating patterns are ubiquitous in geochemical systems. Although many such patterns result from systematic variations in the external environmental conditions, it is recognized that some patterns are due to intrinsic self-organized processes in a non-equilibrium nonlinear system with positive feedback. In rocks and minerals, periodic precipitation (Liesegang bands) and oscillatory zoning constitute good examples of patterns that can be explained using concepts from nonlinear dynamics. Generally, as the system parameters exceed some threshold values, the steady (time-independent) state characterizing the system loses its stability. The system then evolves towards other time-dependent solutions (‘attractors’) that may have an oscillatory behaviour or a complex chaotic one. In this review, we describe many of these pattern types taken from a variety of geological environments: eruptive, sedimentary, hydrothermal or metamorphic. One particular example (periodic precipitation of pyrite bands in an evolving sapropel sediment) is presented here for the first time. This will help in convincing the reader that the tools of nonlinear dynamics may be useful to understand the history of our planet.

Pattern formation in the geosciences

“…In other situations, complex interactions can give rise to simple regular patterns. This is the case we focus on here, although often both chaos and patterns may be found in the same system (see [7] on geochemical precipitation patterns). In both cases, the systems are usually dynamical, nonlinear and out of equilibrium: the patterns are dissipative, entropy-producing states, driven by an energy flux between some external energy source and heat sink.…”

“…For example, Petroff et al [3] here demonstrate that springs eroding into a slope will generically split, or bifurcate, at an angle of 2π/5, while I present a crack-ordering mechanism that links columnar joints with polygonal terrain and mud-cracks [4]. There are many other situations where regular patterns are generated, from the largest scales of geomorphology, such as the curving subduction arcs of the Earth's crust [5] or the meanders of river networks, to ripples on the beach [6] and periodic chemical precipitation patterns [7]. The details of such patterns can provide quantitative information about the systems in which they form and the mechanisms underlying them.…”

“…all members of the same universality class share the same behaviour close to a supercritical bifurcation). For example, the transition from a straight to wavy crack [12], and the onset of oscillations during certain chemical reactions [7,8] are Hopf bifurcations and near their transitions these very different problems can be mapped onto each other. Just as critical points are the key to understanding the behaviour of classical thermodynamic phase diagrams, they are generally a very powerful tool for establishing and testing the physics of any pattern-forming system.…”

“…This mechanism directly underlies about a third of the articles in this Theme Issue. L'Heureux [7] applies a form of it, close to its original intent, to show how periodic precipitation patterns are found in a variety of rocks. This banding is thus a permanent chemical record of the dynamical processes of its formation and can be read only with an appropriate understanding of the nonlinear feedbacks and instabilities of the system.…”

“…Finally, L'Heureux [7] reviews a class of geochemical patterns that are related to the case of periodically precipitating Liesegang rings. He shows that the same generic reactiondiffusion instability can lead to the rhythmic banding of precipitates in volcanic, sedimentary and metamorphic rocks, and presents a particularly detailed novel account of this process in sapropels.…”