Nonlinear Resonance Artifacts in Molecular Dynamics Simulations

Journal of Computational Physics

Volumn 140, Issue 1, 1998, Pages 1-29

  Schlick, Tamar ^a   Mandziuk, Margaret ^a   Skeel, Robert D ^b   Srinivas, K ^b  

^a NEW YORK UNIVERSITY   (United States)

^b UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EQUATIONS OF MOTION; LENNARD-JONES POTENTIAL; MOLECULAR DYNAMICS; MORSE POTENTIAL; NONLINEAR ANALYSIS; NONLINEAR EQUATIONS;

CLASSICAL EQUATION; DYNAMICS SIMULATION; IMPLICIT SCHEMES; MOLECULAR SYSTEMS; NONLINEAR RESONANCE; SIMPLE++; SYMPLECTIC; SYSTEM DYNAMICS; THIRD ORDER; TIME STEP;

AMINO ACIDS;

EID: 0001310692     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1998.5879     Document Type: Article

References (30)

1. Arnold V. I. Mathematical Methods of Classical Mechanics. 1989.
2. Barth E., Mandziuk M., Schlick T. A separating framework for increasing the timestep in molecular dynamics. Computer Simulation of Biomolecular Systems: Theoretical and Experimental Applications. 3:1997;97.
3. E. Barth, T. Schlick, Overcoming stability limitations in biomolecular dynamics: Combining force splitting via extrapolation with Langevin dynamics, 1997.
4. Bishop T., Skeel R. D., Schulten K. Difficulties with multiple timestepping and the fast multipole algorithm in molecular dynamics. J. Comput. Chem. 18:1997;1785.
5. Brooks B. R., Bruccoleri R. E., Olafson B. D., States D. J., Swaminathan S., Karplus M. A program for macromolecular energy, minimization, and dynamics calculations. J. Comput. Chem. 4:1983;187.
6. Derreumaux P., Schlick T. Long-time integration for peptides by the dynamics driver approach. Proteins: Struc. Func. Gen. 21:1995;282.
7. Elber R. Novel methods for molecular dynamics simulations. Curr. Opin. Struc. Biol. 6:1996;232.
8. García-Archilla B., Sanz-Serna J. M., Skeel R. D. Long-time-step methods for oscillatory differential equations. SIAM J. Sci. Comput. 1996/7.
9. Gonzalez O., Simo J. On the stability of symplectic and energy-momentum algorithms for nonlinear Hamiltonian systems with symmetry. Comput. Methods Appl. Mech. Eng. 134:1996;197.
10. Grubmüller H., Heller H., Windemuth A., Schulten K. Generalized Verlet algorithm for efficient molecular dynamics simulations with long-range interactions. Molecular Simulation. 6:1991;121.
11. Hao M. H., Pincus M. R., Rackovsky S., Scheraga H. A. Unfolding and refolding of the native structure of bovine pancreatic trypsin inhibitor studied by computer simulations. Biochemistry. 32:1993;9614.
12. Janezic D., Merzel F. An efficient symplectic integration algorithm for molecular dynamics simulations. J. Chem. Inf. Comput. Sci. 35:1995;321.
13. B. J. Leimkuhler, S. Reich, R. D. Skeel, Integration methods for molecular dynamics, Mathematical Approaches to Biomolecular Structure and Dynamics, J. P. MesirovK. SchultenD. W. Sumners, 82, IMA Volumes in Mathematics and its Applications, 161, Springer-Verlag, 1996.
14. M. López-Marcos, J. M. Sanz-Serna, R. D. Skeel, Cheap enhancement of symplectic integrators, Numerical Analysis 1995, D. F. GriffithsG. A. Watson, 107, Longman Group, London, 1996.
15. Mandziuk M., Schlick T. Resonance in the dynamics of chemical systems simulated by the implicit midpoint scheme. Chem. Phys. Letters. 237:1995;525.
16. McLachlan R. I., Atela P. The accuracy of symplectic integrators. Nonlinearity. 5:1992;541.
17. Peskin C. S., Schlick T. Molecular dynamics by the backward Euler method. Comm. Pure and Appl. Math. 42:1989;1001.
18. Rahman A. Correlation in the motion of atoms in liquid argon. Phys. Rev. A. 136:1964;405.
19. Sanz-Serna J., Calvo M. Numerical Hamiltonian Problems. 1994.
20. J. M. Sanz-Serna, Two topics in nonlinear stability, Advances in Numerical Analysis, W. Light, Clarendon Press, Oxford, 1991.
21. Schlick T., Barth E., Mandziuk M. Biomolecular dynamics at long timesteps: Bridging the timescale gap between simulation and experimentation. Ann. Rev. Biophys. Biomol. Struc. 26:1997;179.
22. Schlick T., Fogelson A. TNPACK - A truncated Newton minimization package for large-scale problems. I. Algorithm and usage. ACM Trans. Math. Software. 18:1992;46.
23. Simo J. C., Tarnow N. The discrete energy-momentum method. Conserving algorithms for nonlinear elastodynamics. ZAMP. 43:1992;757.
24. Simo J. C., Tarnow N. A Review of Conserving Algorithms for Nonlinear Dynamics. 1992.
25. Skeel R. D., Zhang G., Schlick T. A family of symplectic integrators: Stability, accuracy, and molecular dynamics applications. SIAM J. Sci. Comput. 18:1997;203.
26. Tuckerman M., Berne B. J., Martyna G. J. Reversible multiple time scale molecular dynamics. J. Chem. Phys. 97:1992;1990.
27. Wisdom J., Holman M. Symplectic maps for then. Astr. J. 104:1992;2022.
28. Zhang G., Schlick T. LIN: A new algorithm to simulate the dynamics of biomolecules by combining implicit-integration and normal mode techniques. J. Comput. Chem. 14:1993;1212.
29. Zhang G., Schlick T. Implicit discretization schemes for Langevin dynamics. Mol. Phys. 84:1995;1077.
30. Zhang M., Skeel R. D. Cheap implicit symplectic integrators. Appl. Num. Math. 25:1997.