Difference between revisions of "Micro-and nanotechnology via reaction–diffusion"

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(New page: == Context == The term reaction-diffusion is used to describe systems in which the components are both reacting with in some way (local production/consumption) and diffusing. The general f...)
 
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== Context ==
 
== Context ==
 
The term reaction-diffusion is used to describe systems in which the components are both reacting with in some way (local production/consumption) and diffusing. The general form of the PDE for these systems is
 
The term reaction-diffusion is used to describe systems in which the components are both reacting with in some way (local production/consumption) and diffusing. The general form of the PDE for these systems is
<math>\partial_t C_i =</math>
+
<math>\partial_t C_i =\nabla \cdot(D_i\nabla C_i)+R_i(\{C_i\},r,t) </math>
 +
 
 +
where <math>C_i </math>is the concentration of the ith component and <math>D_i</math> and <math>R_i</math> the diffusive and reactive constants of the ith component. The reaction-diffusion equation first gained interest after Turing showed that a system obeying this equation could display spontaneous pattern formation. Since then, many

Revision as of 01:29, 30 November 2010

Context

The term reaction-diffusion is used to describe systems in which the components are both reacting with in some way (local production/consumption) and diffusing. The general form of the PDE for these systems is <math>\partial_t C_i =\nabla \cdot(D_i\nabla C_i)+R_i(\{C_i\},r,t) </math>

where <math>C_i </math>is the concentration of the ith component and <math>D_i</math> and <math>R_i</math> the diffusive and reactive constants of the ith component. The reaction-diffusion equation first gained interest after Turing showed that a system obeying this equation could display spontaneous pattern formation. Since then, many