2000/07/06 by Nadav M. Shnerb, N. M. Shnerb, E. Bettelheim +6 · 39 citations
Chemistry · Mathematics · Physics and Astronomy · #Autocatalysis #Autocatalytic reaction #Biological system #Biology #Catalysis #Chemical physics #Chemistry #Classical mechanics #Complex Network Analysis Techniques #Computer science #Condensed matter physics #Coupling (piping) #Extinction (optical mineralogy) #Growth rate #Kinetic energy #Kinetics #Materials science #Mathematics #Noise (video) #Opinion Dynamics and Social Influence #Optics #Phase (matter) #Phase transition #Physics #Quantum mechanics #Reaction rate #Statistical physics #Theoretical and Computational Physics #cond-mat.soft
paper · pdf · doi:10.1103/physreve.63.021103
published in Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 63(2), 021103 (American Physical Society) · 6 pages 6 figure
arxiv created 2000/07/06 · openalex publication_date 2001/01/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Evolution of a system of diffusing and proliferating mortal reactants is analyzed in the presence of randomly moving catalysts. While the continuum description of the problem predicts reactant extinction as the average growth rate becomes negative, growth rate fluctuations induced by the discrete nature of the agents are shown to allow for an active phase, where reactants proliferate as their spatial configuration adapts to the fluctuations of the catalyst density. The model is explored by employing field theoretical techniques, numerical simulations, and strong coupling analysis. For d< or =2, the system is shown to exhibits an active phase at any growth rate, while for d>2 a kinetic phase transition is predicted. The applicability of this model as a prototype for a host of phenomena that exhibit self-organization is discussed.