represents the vector of chemical concentrations or state variables. Dbold cap D is the diagonal matrix of diffusion coefficients. represents the nonlinear reaction kinetics.
No discussion of pattern formation in nonequilibrium systems can begin anywhere other than with the landmark review article by Michael C. Cross and Pierre C. Hohenberg, published in Reviews of Modern Physics in 1993. This 262-page tour de force (occupying pages 851–1112 of volume 65) remains the most cited and influential single work in the field, with over 6,000 citations. PDF copies of this review are widely available through academic repositories such as Semantic Scholar, Bohrium, and institutional library systems. pattern formation and dynamics in nonequilibrium systems pdf
: Stationary in time, periodic in space (e.g., stripes, hexagons). : Periodic in time, uniform in space (oscillations). : Periodic in both space and time (waves). University of Cambridge Key Physical Examples represents the vector of chemical concentrations or state
represent the concentrations of an activator and an inhibitor. Ducap D sub u Dvcap D sub v are their respective diffusion coefficients. represent the nonlinear reaction terms. No discussion of pattern formation in nonequilibrium systems