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

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<math>\partial_t C_i =\nabla \cdot(D_i\nabla C_i)+R_i(\{C\},r,t) </math> | <math>\partial_t C_i =\nabla \cdot(D_i\nabla C_i)+R_i(\{C\},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. | + | 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. Solutions to the reaction-diffusion (RD) equation can have some interesting properties; some solutions have traveling waves. Others show spontaneous formation of patterns, which can be quite intricate. The RD equation first gained interest after Alan Turing showed that stable patterns could exist in these systems. Since then, many phenomena in nature have been found to obey RD. Zebra stripes, cave stalactites, and certain chemical reactions are all patterns that can be described as an outcome of RD. |

− | As nature is able to use RD to form intricate patterns, the questions arises whether or not we can utilize this method as a way to fabricate patterns. This paper describes some techniques that were used to controllably engineer micro- and nano-patterns. | + | As nature is able to use RD to form intricate patterns, the questions arises as to whether or not we can utilize this method as a way to fabricate patterns. This paper describes some techniques that were used to controllably engineer micro- and nano-patterns. |

## Revision as of 01:38, 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\},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. Solutions to the reaction-diffusion (RD) equation can have some interesting properties; some solutions have traveling waves. Others show spontaneous formation of patterns, which can be quite intricate. The RD equation first gained interest after Alan Turing showed that stable patterns could exist in these systems. Since then, many phenomena in nature have been found to obey RD. Zebra stripes, cave stalactites, and certain chemical reactions are all patterns that can be described as an outcome of RD.

As nature is able to use RD to form intricate patterns, the questions arises as to whether or not we can utilize this method as a way to fabricate patterns. This paper describes some techniques that were used to controllably engineer micro- and nano-patterns.