Equations of motion integration

The reader is referred to this paper for the details of the structure annealing procedure , equation of motion integration, and so forth. 

Now we are able to substitute B/t) in Eq. 8 from Eq. 9. After replacing the acceleration Rj (t) with the force F/ (t) we finally obtain Eq. 6. There are several others algorithms to integrate the equations of motion (e.g., leapfrog, Verlet). The consequences of different equation of motion integration schemes with regard to AMD are discussed in the excellent review of Remler and Madden (54). 

Introduction. - Technical improvements in molecular simulation have continued to be made over recent years. A number of old themes are still very popular, especially the important issue of how to deal with long-range forces. Interest on equation of motion integration algorithms ( integrators ) has incidentally grown dramatically in recent years, with the establishment of objective measures. In the next sections we summarise some of the main advances and new approaches. 

Using these results and the definition of T, it is easily shown that dp/dt = 0 in Eq. (Ill) provided that g = Ndf. This shows that the extended-system phase-space density pe,r(i , p, y) is a stationary (equilibrium) solution of Eq. (111) corresponding to the Nose-Hoover equations of motion. Integrating out the y variable leads to the real-system phase-space probability density for the Nosd-Hoover thermostat (realtime sampling)... 

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See also in sourсe #XX -- [ , ]

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