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Translated hyperplane

Similar in spirit is the Milestoning [90] method by Fiber and coworkers, who assume that the diffusion of interest occurs through a tube in configuration space, and translate the rare process into a non-Markovian hopping between configuration space hyperplanes, the so-called milestones (which are in fact rather similar to the TIS interfaces, except that they do not form a foliation). The kinetics is obtained from starting an equilibrium ensemble on a milestone, and measuring the time distribution needed to reach the next milestone. The distribution can subsequently be used to construct the kinetics. The assumption is that there is an equilibrium (Boltzmann) distribution on each milestone. [Pg.421]

Candidate AR construction via bounding hyperplanes (either via translation or rotation) may be extended to allow for constructions involving a parameter that may affect the direction of the rate vector. A system involving temperature-dependent kinetics is a well-known example of this. In Figure 8.26(b), the rotated hyperplanes method is used to compute an AR with temperature-dependent kinetics. At each point of evaluation, a temperature range between 300 and 1000 K is generated and rate vectors are checked for tangency with the hyperplane. This allows for... [Pg.266]

Once the complex is embedded into R", a usual way to define the link of a vertex v is to place a sphere of sufficiently small radius with its center in v. The intersection of this sphere with the complex is the link. To see that this is actually a polyhedral complex, it is enough to notice that up to face-preserving homeomorphism, the intersection of a small sphere with the polytope can be replaced by the intersection with a hyperplane. This hyperplane can be foimd as follows take the hyperplane H whose intersection with our poljdope is equal to the considered vertex, and consider the parallel translation of this hyperplane by a sufficiently small number in the direction of the poljdope. [Pg.28]


See other pages where Translated hyperplane is mentioned: [Pg.293]    [Pg.181]    [Pg.199]    [Pg.256]    [Pg.266]    [Pg.234]    [Pg.146]    [Pg.151]    [Pg.320]   


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