Model of the Belousov-Zhabotinsky reaction

The article describes results of the modified model of the Belousov-Zhabotinsky reaction, which resembles rather well the limit set observed upon experimental performance of the reaction in the Petri dish. We discuss the concept of the ignition of circular waves and show that only the asymmetrical ignition leads to the formation of spiral structures. From the qualitative assumptions on the behavior of dynamic systems, we conclude that the Belousov-Zhabotinsky reaction likely forms a regular grid.Comment: 17 pages, 12 figure

Flow-distributed spikes for Schnakenberg kinetics

This is the post-print version of the final published paper. The final publication is available at link.springer.com by following the link below. Copyright @ 2011 Springer-Verlag.We study a system of reaction–diffusion–convection equations which combine a reaction–diffusion system with Schnakenberg kinetics and the convective flow equations. It serves as a simple model for flow-distributed pattern formation. We show how the choice of boundary conditions and the size of the flow influence the positions of the emerging spiky patterns and give conditions when they are shifted to the right or to the left. Further, we analyze the shape and prove the stability of the spikes. This paper is the first providing a rigorous analysis of spiky patterns for reaction-diffusion systems coupled with convective flow. The importance of these results for biological applications, in particular the formation of left–right asymmetry in the mouse, is indicated.RGC of Hong Kon

Geoarchaeological and 3D visualisation approaches for contextualising in-situ fossil bearing palaeokarst in South Africa: A case study from the ∼2.61 Ma Drimolen Makondo

South Africa contains a wealth of palaeokarst deposits that have yielded hominin fossils and Early Stone Age archaeology. Despite the complex nature of deposition within many of these caves there has been a dearth of detailed geoarchaeological studies undertaken on these sites. Many sites in South Africa have been interpreted using an overly simplistic Member System based on simplified sedimentological attributes, rather than chronostratigrahic units. Many of the defined Members thus identify different, but contemporary geological processes occurring in the caves. This has caused serious confusion in reconstructing the life histories of palaeocaves and the ages of the fossil remains interned within them. It is critical to uncover new sites that have not been extensively altered by decades of data collection and destructive mining techniques employed early in their discovery. Although unmined sites present their own problems with regards to extensive colluvium cover and access to fossil-bearing units, analysing strata that is found in-situ enhances overall confidence of interpretations drawn. A wealth of geoarchaeological and 3D visualisation techniques can now be employed to aid in the understanding of cave life histories, as well as their excavation. In this paper we present the first attempt to integrate and publish data from a range of such methods on South African fossil bearing palaeokarst using the newly discovered Drimolen Makondo deposit as a case study. This includes the use of ground penetrating radar, 3D visualisation through photogrammetry and multi-scale 3D scanning, micromophology and petrography, palaeomagnetism, mineral magnetism, synchrotron radiation, electron spin resonance, uranium-lead dating and biochronology. Our analysis has allowed us to successfully uncover the full extent of this new ∼2.61 Ma fossil bearing palaeokarst deposit and to visualise and interpret its chronostratigraphy