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Laplace's equation |
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Laplace's equationIn mathematics, a partial differential equation whose solutions (harmonic functions) are useful in investigating physical problems in three dimensions involving gravitational, electrical, and magnetic fields, and certain types of fluid motion. Named for Pierre-Simon Laplace, the equation states that the sum of the second partial derivatives (the Laplace operator, or Laplacian) of an unknown function is zero. It can apply to functions of two or three variables, and can be written in terms of a differential operator as ΔF = 0, where Δ is the Laplace operator. How to thank TFD for its existence? Tell a friend about us, add a link to this page, add the site to iGoogle, or visit webmaster's page for free fun content. |
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Since each component of the magnetic field in the trap satisfies Laplace's equation, it might be possible to develop a special function expansion approximation for the potential. Two classic relations resulted describing equilibrium at the contact line solid/liquid/surrounding fluid (contact angle), and relating the local curvature of a static liquid/fluid meniscus to the pressure difference across the interface; these being generally known respectively as Young's and Laplace's equations. |
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