Physics – Condensed Matter – Soft Condensed Matter
Scientific paper
2010-07-19
Physics
Condensed Matter
Soft Condensed Matter
32 pages
Scientific paper
Pattern formation in reaction-diffusion systems is of great importance in surface micro-patterning [Grzybowski et al. Soft Matter. 1, 114 (2005)], self-organization of cellular micro-organisms [Schulz et al. Annu. Rev. Microbiol. 55, 105 (2001)] and in developmental biology [Barkai et al. FEBS Journal 276, 1196 (2009)]. In this work, we apply the Lattice Boltzmann method (LBM) to study pattern formation in reaction-diffusion systems. As a first methodological step, we consider the case of a single species undergoing transformation reaction and diffusion. In this case, we perform a third-order Chapman-Enskog multiscale expansion and study the dependence of the Lattice Boltzmann truncation error on the diffusion coefficient and the reaction rate. These findings are in good agreement with numerical simulations. Furthermore, taking the Gray-Scott model as a prominent example, we provide evidence for the maturity of the LBM in studying pattern formation in non-linear reaction-diffusion systems. For this purpose, we perform linear stability analysis of the Gray-Scott model and determine the relevant parameter range for pattern formation. Lattice Boltzmann simulations allow not only to test the validity of the linear stability phase diagram including Turing and Hopf instabilities, but also permit going beyond the linear stability regime, where large perturbations give rise to interesting dynamical behavior such as the so called self replicating spots. We also show that the length scale of the patterns may be tuned by rescaling all relevant diffusion coefficients in the system with the same factor while letting all the reaction constants unchanged.
Ayodele S. G.
Raabe Dierk
Varnik Fathollah
No associations
LandOfFree
Lattice Boltzmann study of pattern formation in reaction-diffusion systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Lattice Boltzmann study of pattern formation in reaction-diffusion systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Lattice Boltzmann study of pattern formation in reaction-diffusion systems will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-62082