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The Swift–Hohenberg equation (named after Jack B. Swift and Pierre Hohenberg) is a partial differential equation noted for its pattern-forming behaviour. It takes the form
where u = u(x, t) or u = u(x, y, t) is a scalar function defined on the line or the plane, r is a real bifurcation parameter, and N(u) is some smooth nonlinearity.
The equation is named after the authors of the paper,[1] where it was derived from the equations for thermal convection.
The webpage of Michael Cross[2] contains some numerical integrators which demonstrate the behaviour of several Swift–Hohenberg-like systems.
Applications
Geometric Measure Theory
The equation has been used for finding a solution to the Kelvin Problem on minimal surfaces.
References
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Summary
Structure of Fiber Bragg Gratings (FBGs). 1) a uniform FBG, where the refractive index change has a fixed period, . 2) a chirped FBG, where the refractive index change is graded to give a larger bandwidth, . 3) a tilted FBG, where the change in refractive index occurs are an angle to the optical axis of the fiber. 4) a superstructure FBG.
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 18:04, 15 July 2007 | | 600 × 600 (14 KB) | wikimediacommons>Grahamwild |
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