# Interdisciplinary Applied Mathematics

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</j</jerfc(/c|rjj + n|)

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^    Iru + n

=0 i=1 j = 1    1 1J

The value of к is chosen such that only terms corresponding to n = 0 (i.e., interactions involving charges in the central box only) make a contribution. Because of this, Vreal can be computed using the usual cutoff method. In the second step, another charge distribution is imposed to counteract exactly the neutralizing distribution. The contribution of this charge distribution to the potential energy is called a

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The Fast Multipole Method (FMM): The traditional particle-particle, particle-mesh, or a combination of these methods commonly benefit

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Cut-Off Scheme. The most expensive part of energy and force calculations is the nonbonded interactions, since there are N(N — 1)/2 such interactions to calculate in an N -atom system. To save computer time, it is usual practice to neglect nonbonded interactions that occur between atoms separated by more than a given distance (say 10 A). This use of a cut-off scheme in potential/force calculation is justified for potentials like the Lennard-Jones potential. However,

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Storing the Simulation Results. MD simulation generates the trajectories of each atom in the simulation system. The properties of the system can be obtained by analyzing these trajectories. The common practice is to save the system trajectories at certain intervals during the simulation, and analyze the trajectories when the simulation is finished. For most measurables, e.g., density, this is sufficient. Because the trajectories of neighboring time steps are usually highly

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