Abutting faults: a case study of the evolution of strain at Courthouse branch point, Moab Fault, Utah

Slip planes and slip directions of subsequent generations of faults were measured in the interaction damage zone two abutting faults in porous sandstones, to understand the evolution of paleostress/paleostrain evolution. The Courthouse branch point, of the Moab Fault in SE Utah, is a much-studied spectacular outcrop of two abutting faults. It shows a wide range of deformation structures and fault related diagenesis: striated slip planes, deformation bands, veins, Liesegang bands and copper-rich mineralization. By combining our own measurements with published results on the relative age of these structures, we classified our data in four sets. Using the Numeric Dynamic Analysis (NDA) to calculate the orientation of the kinematic axes we found three different paleo-extension directions in the four sets, recording the evolution of stress/strain axes during the abutting process. The first phase of deformation direction is the regional extension in the NE-SE direction. As the second fault approached the main fault from its footwall side and the two faults start to become kinematically linked, the extension direction changed so that the overall extension became perpendicular to the approaching fault (NW-SE). Finally, the extension direction changed back to perpendicular to the first segment (NE-SW), when the two faults become geometrically-linked and regional extension dominates.

Regularization of the Ostwald supersaturation model for Liesegang bands

In a previous paper, we analysed the Keller–Rubinow formulation of Ostwald's supersaturation theory for the formation of Liesegang rings or Liesegang bands, and found that the model is ill-posed, in the sense that after the termination of the first crystal front growth, secondary bands form, as in the experiment, but these are numerically found to be a single grid space wide, and thus an artefact of the numerical method. This ill-posedness is due to the discontinuity in the crystal growth rate, which itself reflects the supersaturation threshold inherent in the theory. Here we show that the ill-posedness can be resolved by the inclusion of a relaxation mechanism describing an impurity coverage fraction, which physically enables the transition in heterogeneous nucleation from precipitate-free impurity to precipitate-covered impurity.

Spatial Dissipative Structures in Excitable Media (Plankton, Soil Bacteria. . . .)

A general, the simplest model of a spatial dissipative structure arising in an excitable medium is constructed, containing at least two components interacting with each other with their own mobility. One of these components (active) uses the other component as food. It is shown that such a model leads to a stationary stable spatial distribution of the components in the form of Liesegang bands. As specific examples of the formation of spatial dissipative structures, structures arising in plankton consisting of phytoplankton and zooplankton and in the soil containing the bacterial population and the nutrient substrate are considered. Bifurcation diagrams are constructed in the parameter space, characteristic for each of the considered excitable media, which determine the conditions for the formation of dissipative structures in these media. The existence in the plankton of a strange attractor of a previously unknown shape in four-dimensional phase space has been discovered.

Self-organization in precipitation reactions far from the equilibrium

Far from the thermodynamic equilibrium, many precipitation reactions create complex product structures with fascinating features caused by their unusual origins. Unlike the dissipative patterns in other self-organizing reactions, these features can be permanent, suggesting potential applications in materials science and engineering. We review four distinct classes of precipitation reactions, describe similarities and differences, and discuss related challenges for theoretical studies. These classes are hollow micro- and macrotubes in chemical gardens, polycrystalline silica carbonate aggregates (biomorphs), Liesegang bands, and propagating precipitation-dissolution fronts. In many cases, these systems show intricate structural hierarchies that span from the nanometer scale into the macroscopic world. We summarize recent experimental progress that often involves growth under tightly regulated conditions by means of wet stamping, holographic heating, and controlled electric, magnetic, or pH perturbations. In this research field, progress requires mechanistic insights that cannot be derived from experiments alone. We discuss how mesoscopic aspects of the product structures can be modeled by reaction-transport equations and suggest important targets for future studies that should also include materials features at the nanoscale.

Self-organized rhythmic patterns in geochemical systems

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.

Liesegang-like patterns of Toll crystals grown in gel

Generating high-quality crystals remains a bottleneck in biological and materials sciences. Here a counter-diffusion method was used to improve the X-ray diffraction quality of the N-terminal domain ofDrosophila melanogasterToll receptor crystals. It was observed that crystallization occurred with a peculiar pattern along the capillary resembling Liesegang bands; this phenomenon is described at both macroscopic and atomic levels. It was found that bands appeared for native protein as well as for co-crystals of magic triangle (I3C)-bound protein even though they crystallize in different space groups. Crystallization occurred with a linear recurrence independent of the precipitant concentration and a protein-specific spacing coefficient. Bandwidth varied along the capillary, oscillating between large precipitation areas and single crystals. The reported data suggest that repetitive patterns can be generated with biological macromolecules in the presence of sodium malonate as a crystallization agent. A comparison with typical Liesegang patterns and the possible mechanism underlying this phenomenon are discussed.