Reaktiodiffuus

Reaktiodiffuus is a class of systems in which chemical reactions are coupled to the diffusion of reacting species, leading to spatiotemporal patterns. These systems are commonly described by partial differential equations that track the concentrations of two or more chemical species in space and time.

A typical two-species formulation uses concentrations u(x,t) and v(x,t) with equations of the form ∂u/∂t = D_u ∇^2 u + f(u,v) and ∂v/∂t = D_v ∇^2 v + g(u,v), where D_u and D_v are diffusion coefficients and f, g represent nonlinear reaction kinetics. Pattern formation often arises from a diffusion-driven, or Turing, instability: a uniform steady state becomes unstable to small spatial perturbations when the diffusion rates and reaction terms meet certain conditions, producing persistent patterns rather than homogeneous mixtures.

Patterns observed in reaktiodiffuus systems include spots, stripes, and labyrinthine structures. Their appearance depends on kinetic functions, the ratio of diffusion coefficients, boundary conditions, and the size and shape of the domain. The field combines theory, experiment, and computation to understand how simple local rules yield complex global structures.

Historically, the concept was introduced by Alan Turing in 1952 as a potential mechanism for biological morphogenesis. Experimental realizations include chemical oscillators such as the Belousov-Zhabotinsky reaction and catalytic reaction–diffusion systems. Variants of the models, such as the Gray-Scott or FitzHugh–Nagumo systems, are widely used in simulations to study pattern formation in chemistry, biology, and materials science.

See also: Turing pattern, Belousov-Zhabotinsky reaction, reaction-diffusion model.