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Reaction–diffusion systems are naturally applied in chemistry. However, the system can also describe dynamical processes of non-chemical nature. Examples are found in biology, geology and physics (neutron diffusion theory) and ecology. Mathematically, reaction–diffusion systems take the form of semi-linear parabolic partial differential ...
The parameters depend on the physical system under consideration. In the context of fish skin pigmentation, the associated equation is a three field reaction–diffusion one in which the linear parameters are associated with pigmentation cell concentration and the diffusion parameters are not the same for all fields. [9]
The theory, which can be called a reaction–diffusion theory of morphogenesis, has become a basic model in theoretical biology. [2] Such patterns have come to be known as Turing patterns. For example, it has been postulated that the protein VEGFC can form Turing patterns to govern the formation of lymphatic vessels in the zebrafish embryo. [3]
The complete morphological diagram can be obtained by using two fields, density of bacteria and nutrient concentration, and taking into account that bacteria can increase motility in response to adverse external conditions. That means that diffusion in the medium and the response of bacteria are the relevant factors in this particular case.
The convection–diffusion equation can be derived in a straightforward way [4] from the continuity equation, which states that the rate of change for a scalar quantity in a differential control volume is given by flow and diffusion into and out of that part of the system along with any generation or consumption inside the control volume: + =, where j is the total flux and R is a net ...
The total reaction may be diffusion controlled (the electron transfer step is faster than diffusion, every encounter leads to reaction) or activation controlled (the "equilibrium of association" is reached, the electron transfer step is slow, the separation of the successor complex is fast). The ligand shells around A and D are retained.
Simulation of the Brusselator as reaction diffusion system in two spatial dimensions Simulation [1] of the reaction-diffusion system of the Brusselator with reflective border conditions. The Brusselator is a theoretical model for a type of autocatalytic reaction.
Hantz reactions are a class of pattern-forming precipitation reactions in gels implementing a reaction–diffusion system. The precipitation patterns are forming as a reaction of two electrolytes : a highly concentrated "outer" one diffuses into a hydrogel , while the "inner" one is dissolved in the gel itself.