TY - JOUR
T1 - Consequences of imperfect mixing the Gray-Scott model
AU - Zorzano, M.-P.
AU - Hochberg, D.
AU - Morán, F.
PY - 2006
Y1 - 2006
N2 - We study an autocatalytic reaction-diffusion scheme, the Gray-Scott model, when the mixing processes do not homogenize the reactants. Starting from the master equation, we derive the resulting coupled, nonlinear, stochastic partial differential equations that rigorously include the spatiotemporal fluctuations resulting from the interplay between the reaction and mixing processes. The fields are complex and depend on correlated complex noise terms. We implement a method to solve for these complex fields numerically and extract accurate information about the system evolution and stationary states under different mixing regimes. Through this example, we show how the reaction-induced fluctuations interact with the temporal nonlinearities, leading to results that differ significantly from the mean-field (perfectly mixed) approach. This procedure can be applied to an arbitrary nonlinear reaction diffusion scheme.
AB - We study an autocatalytic reaction-diffusion scheme, the Gray-Scott model, when the mixing processes do not homogenize the reactants. Starting from the master equation, we derive the resulting coupled, nonlinear, stochastic partial differential equations that rigorously include the spatiotemporal fluctuations resulting from the interplay between the reaction and mixing processes. The fields are complex and depend on correlated complex noise terms. We implement a method to solve for these complex fields numerically and extract accurate information about the system evolution and stationary states under different mixing regimes. Through this example, we show how the reaction-induced fluctuations interact with the temporal nonlinearities, leading to results that differ significantly from the mean-field (perfectly mixed) approach. This procedure can be applied to an arbitrary nonlinear reaction diffusion scheme.
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-33751178397&partnerID=MN8TOARS
U2 - 10.1103/PhysRevE.74.057102
DO - 10.1103/PhysRevE.74.057102
M3 - Article
SN - 1539-3755
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
ER -