SC740 SEMINAR REPORT 06 for Frederick L. Jones
PRESENTER: Dr. Dexuan Xie
TOPIC: SHAKE Analysis in the Framework of Nonlinear SOR Theory
OVERVIEW
After first explaining why molecular dynamics was chosen to model the behavior of bimolecules, then Dr. Dexuan Xie explained exactly how to do molecular dynamics simulation modeling of bimolecules. Next, Dr. Xie described some of the challenges of molecular dynamics simulation modeling of bimolecules.
Dr. Xie then described SHAKE, a widely used scheme for molecular dynamics. Then a variation of SHAKE known as SHAKE-SOR, which uses the Successive Over-Relaxation (SOR) iterative PDE solution technique, was introduced and its performance was explained.
WHY MOLECULAR DYNAMICS MODELS ARE USED
Dr. Xie began his seminar by asking the question: "Why Molecular Dynamics?" To answer this question, Dr. Xie reviewed the assumptions of molecular dynamics models. Some of the assumptions of molecular dynamics models given by Dr. Xie are the following:
(1)For a molecule with N atoms, the model is a mechanical system with N particles. The atoms are the particles and the bonds between atoms are springs.
(2)The motion of the molecules is determined by the Newtonian vector equation of motion, i.e. M d2r/dt2 = F(r(t)), where M is the molecular mass, r is position, t is time, and F is a given force field.
HOW TO DO MOLECULAR DYNAMICS SIMULATION MODELING OF BIMOLECULES
Then, Dr. Dexuan Xie explained exactly how to do molecular dynamics simulation modeling of bimolecules. Dr. Xie’s description of exactly how to do molecular dynamics simulation modeling included the following:
(1)Determine how to define the force field F(r(t)).
(2)Determine how to define the bond energy between particles, as well as the non-bonded energy.
(3)Determine how to define the angle energy between particles.
(4)Determine how to compute the force field F(r(t)).
(5)Determine the numerical system equations. This usually involves determining the finite difference equations to use.
THE CHALLENGES OF MOLECULAR DYNAMICS SIMULATION MODELING OF BIMOLECULES
Next, Dr. Xie described some of the challenges of molecular dynamics simulation modeling of bimolecules. The challenges primarily have to do with the fact that the time change D t is very small, since the bond frequency is approximately 10-13/sec. This means that the grid size of the finite difference equations is very large. Thus the number of steps in a solution technique will be extremely large, say more than 109 steps.
Concerning the challenges of having a very small time change D t and thus a very large finite difference grid to use in any PDE solution technique, Dr. Xie suggested two alternative solutions. The two alternative solutions to the challenges are: (a) find faster summation algorithms or (b) make the D t larger.
Dr. Xie chose the latter alternative of making the D t larger for his research, i.e., Dr. Xie used the SHAKE method. Thus, Dr. Xie also chose a PDE solution technique for finite difference equations that inceased D t , i.e., the SHAKE – SOR method.
THE SHAKE-SOR METHOD
Finally, Dr. Xie briefly described a variation of SHAKE known as SHAKE-SOR, which uses the Successive Over-Relaxation (SOR) iterative PDE solution technique. The topics Dr. Xie briefly covered included the following:
(1)The general SHAKE method, which traditional uses the Gauss-Seidel PDE solution method.
(2)SHAKE-SOR as an alternative to the traditional SHAKE method.
(3)Convergence analysis.
SUMMARY AND CONCLUSIONS
After first explaining why molecular dynamics was chosen to model the behavior of bimolecules, Dr. Dexuan Xie explained exactly how to do molecular dynamics simulation modeling of bimolecules. Next, Dr. Xie described some of the challenges of molecular dynamics simulation modeling of bimolecules.
Dr. Xie then described SHAKE, a widely used scheme for molecular dynamics. Then a variation of SHAKE known as SHAKE-SOR, which uses the Successive Over-Relaxation (SOR) iterative PDE solution technique, was introduced and its performance was explained.
The explanation of the molecular dynamics field and its assumptions in detail was more in depth than Dr. Xie had planned. However, the material provided a background to better be able to understand Dr. Xie's specific application of PDE solution techniques. The brief coverage of the SHAKE-SOR PDE solution method will need to be supplemented by individual reading and research.