Mode transitions in a model reaction-diffusion system driven by domain growth and noise

Pattern formation in many biological systems takes place during growth of the underlying domain. We study a specific example of a reaction–diffusion (Turing) model in which peak splitting, driven by domain growth, generates a sequence of patterns. We have previously shown that the pattern sequences which are presented when the domain growth rate is sufficiently rapid exhibit a mode-doubling phenomenon. Such pattern sequences afford reliable selection of certain final patterns, thus addressing the robustness problem inherent of the Turing mechanism. At slower domain growth rates this regular mode doubling breaks down in the presence of small perturbations to the dynamics. In this paper we examine the breaking down of the mode doubling sequence and consider the implications of this behaviour in increasing the range of reliably selectable final patterns

Global existence for semilinear reaction-diffusion systems on evolving domains

We present global existence results for solutions of reaction-diffusion systems on evolving domains. Global existence results for a class of reaction-diffusion systems on fixed domains are extended to the same systems posed on spatially linear isotropically evolving domains. The results hold without any assumptions on the sign of the growth rate. The analysis is valid for many systems that commonly arise in the theory of pattern formation. We present numerical results illustrating our theoretical findings.Comment: 24 pages, 3 figure

Housing metadata for the common physicist using a relational database

SAM was developed as a data handling system for Run II at Fermilab. SAM is a collection of services, each described by metadata. The metadata are modeled on a relational database, and implemented in ORACLE. SAM, originally deployed in production for the D0 Run II experiment, has now been also deployed at CDF and is being commissioned at MINOS. This illustrates that the metadata decomposition of its services has a broader applicability than just one experiment. A joint working group on metadata with representatives from ATLAS, BaBar, CDF, CMS, D0, and LHCB in cooperation with EGEE has examined this metadata decomposition in the light of general HEP user requirements. Greater understanding of the required services of a performant data handling system has emerged from Run II experience. This experience is being merged with the understanding being developed in the course of LHC experience with data challenges and user case discussions. We describe the SAM schema and the commonalities of function and service support between this schema and proposals for the LHC experiments. We describe the support structure required for SAM schema updates, the use of development, integration, and production instances. We are also looking at the LHC proposals for the evolution of schema using keyword-value pairs that are then transformed into a normalized, performant database schema