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Forces along Equidistant Particle Paths 总被引:1,自引:1,他引:0
Two particles on the sphere leave the equator moving due south and travel at a constant and equal speed along a geodesic colliding
at the south pole. An observer who is unaware of the curvature of the space will conclude that there is an attractive force
acting between the particles. On the other hand, if particles travel at the same speed (initially parallel) along geodesics
in the hyperbolic plane, then the particle paths diverge. Imagine two particles in the hyperbolic plane that are bound together
at a constant distance with their center of mass traveling along a geodesic path at a constant velocity, then the force due
to the curvature of the space acts to break the bond and increases as a quadratic function of the velocity. We consider this
problem for the sphere and the hyperbolic plane and we give the exact formula for the apparent force between the particles.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
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Ladlow M Legge CH Neudeck T Pipe AJ Sheppard T Yang LL 《Chemical communications (Cambridge, England)》2003,(16):2048-2049
A method to effect photo-mediated differential release of bead-based compound libraries using a tuneable laser in combination with chromatically orthogonal photolabile linkers is described. 相似文献
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Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87)for analysing the time discretization error and assuming moreregularity on the initial data, we improve on the error boundderived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,257-287) for a fully practical piecewise linear finite elementapproximation with a backward Euler time discretization of amodel for phase separation of a multi-component alloy. 相似文献
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We consider totally complex submanifolds of the Cayley projective plane with estimates on the length squared of the second fundamental form. We determine those bounds for which the second fundamental form is parallel and for which the submanifold is totally geodesic. The case of totally real submanifolds is also included. 相似文献
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