| 21. | For instance, one might study solutions of the heat equation in an idealised semi-infinite metal bar.
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| 22. | In probability theory, the heat equation is connected with the study of Brownian motion via the Fokker Planck equation.
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| 23. | He was the first mathematician to apply heat equation methods to the proof of the Index Theorem for elliptic operators.
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| 24. | Recall too that solutions of the heat equation can be found by assuming a scaling " Ansatz ".
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| 25. | The Heat equation is very useful in this . talk ) 21 : 32, 25 August 2007 ( UTC)
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| 26. | For example, consider the following initial / boundary value problem for the heat equation on the spatial interval and times:
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| 27. | In history, the heat equation proposed by Fourier in 1822 has been applied to investigating a temperature distribution in materials.
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| 28. | With a constant diffusion coefficient, the anisotropic diffusion equations reduce to the heat equation which is equivalent to Gaussian blurring.
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| 29. | The formula for the Ricci flow is an imitation of the heat equation which describes the way heat flows in a solid.
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| 30. | Joseph Fourier introduced the transform in his study of heat transfer, where Gaussian functions appear as solutions of the heat equation.
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