The Mathematical Theory of Ito Diffusions on Hypersurfaces, with Applications to NMR Relaxation Problems |
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| Authors: | L. Persson U. Cegrell N. Usova P.-O. Westlund |
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| Affiliation: | (1) Division of NBC Defence, Swedish Defence Research Agency, Sweden;(2) Mathematics Department, Umeå University, Sweden;(3) Chemistry Department, Biophysical Chemistry, Umeå University, Sweden;(4) Present address: Institute of Electronics NANB, Logojsky Tract 22, 220090 Minsk, Belarus |
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| Abstract: | A mathematical framework for translational Brownian motion on hypersurfaces is presented, using an imbedding of the surface and Ito diffusions in the ambient space. This includes a survey of Ito calculus and differential geometry. Computational methods for time correlation functions relevant to spin relaxation studies on curved interfaces are given, and explicit calculations of time correlation functions and order parameters for a  Rippled surface are presented. |
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| Keywords: | Ito diffusion Brownian motion hypersurface relaxation theory correlation function |
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