Dynamic computer simulations

If we wish to know the number of (VpV)-collisions that actually take place in this small time interval, we need to know exactly where each particle is located and then follow the motion of all the particles from time tto time t+ bt. In fact, this is what is done in computer simulated molecular dynamics. We wish to avoid this exact specification of the particle trajectories, and instead carry out a plausible argument for the computation of r To do this, Boltzmann made the following assumption, called the Stosszahlansatz, which we encountered already in the calculation of the mean free path ... 

From SCRP spectra one can always identify the sign of the exchange or dipolar interaction by direct exammation of the phase of the polarization. Often it is possible to quantify the absolute magnitude of D or J by computer simulation. The shape of SCRP spectra are very sensitive to dynamics, so temperature and viscosity dependencies are infonnative when knowledge of relaxation rates of competition between RPM and SCRP mechanisms is desired. Much use of SCRP theory has been made in the field of photosynthesis, where stnicture/fiinction relationships in reaction centres have been connected to their spin physics in considerable detail [, Mj. 

Kremer K 1996 Computer simulation methods for polymer physics Monte Carlo and Molecular Dynamics of Condensed Matter Systems vol 49, ed K Binder and G Ciccotti (Bologna Italian Physical Society) pp 669-723... 

Gain G and Pasquarello A 1993 First-principles molecular dynamics Computer Simulation in Chemioal Physios vol 397 NATO ASI Series C ed M P Allen and D J Tildesley (Dordrecht Kluwer) pp 261-313... 

Hilbers P A J and Esselink K 1993 Parallel computing and molecular dynamics simulations Computer Simulation In Chemloal Physios /o 397 NATO ASI Series Ced M P Allen and D J Tlldesley (Dordrecht Kluwer) pp 473-95... 

The complexity of polymeric systems make tire development of an analytical model to predict tlieir stmctural and dynamical properties difficult. Therefore, numerical computer simulations of polymers are widely used to bridge tire gap between tire tlieoretical concepts and the experimental results. Computer simulations can also help tire prediction of material properties and provide detailed insights into tire behaviour of polymer systems. A simulation is based on two elements a more or less detailed model of tire polymer and a related force field which allows tire calculation of tire energy and tire motion of tire system using molecular mechanisms, molecular dynamics, or Monte Carlo teclmiques 1631. 

Northrup S H and Erickson H P 1992 Kinetics of protein-protein association explained by Brownian dynamics computer simulation Proc. Natl Acad. Sci. USA 89 3338-42... 

Creveld, L., Amadei, A., Van Schaik, C., Pepermans, R., De Vlieg, J., Berendsen, H.J.C. Identification of functional and unfolding motions of cutinase as obtained from molecular dynamics computer simulations. Submitted (1998). 

Elamrani et al. 1996] Elamrani, S., Berry, M.B., Phillips Jr., G.N., McCammon, J.A. Study of Global Motions in Proteins by Weighted Masses Molecular Dynamics Adenylate Kinase as a Test Case. Proteins 25 (1996) 79-88 [Elcock et al. 1997] Elcock, A.H., Potter, M.J., McCammon, J.A. Application of Poisson-Boltzmann Solvation Forces to Macromolecular Simulations. In Computer Simulation of Biomoleeular Systems, Vol. 3, A.J. Wilkinson et al. eds., ESCOM Science Publishers B.V., Leiden... 

Such a free energy is called a potential of mean force. Average values of Fs can be computed in dynamics simulations (which sample a Boltzmann distribution), and the integral can be estimated from a series of calculations at several values of s. A third method computes the free energy for perturbing the system by a finite step in s, for example, from si to S2, with... 

E. Barth, M. Mandziuk, and T. Schlick. A separating framework for increasing the timestep in molecular dynamics. In W. F. van Gunsteren, P. K. Weiner, and A. J. Wilkinson, editors. Computer Simulation of Biomolecular Systems Theoretical and Experimental Applications, volume III, chapter 4, pages 97-121. ESCOM, Leiden, The Netherlands, 1997. 

P. A. J Hilbers and K. Esselink, Parallel computing and molecular dynamics simulations , Computer Simulations in Chemical Physics, Proc. of the NATO advanced study institute on new perspectives in computer simulations in chemical physics, 473-95, 1993. 

T.P. Lybrand, Computer simulations of biomolecular systems using molecular dynamics and free energy perturbation methods, in Reviews in Computational Chemistry, Vol. 1, K.B. Lipkowitz, D.B. Boyd (Eds.), VCH, New York, 1990, pp. 295-320. 

Gunsteren W F and H J C Berendsen 1990. Computer Simulation of Molecular Dynamics Methodology, Applications and Perspectives in Chemistry. Angewandte Chemie International Edition in English 29 992-1023. 

See van Gunsteren, W.F. Berendsen, H.J.C. Computer simulation of molecular dynamics-methodology, applications, and perspectives in chemistry Angewandre Chemie, International Edition in English, 29 992-1023, 1990, and Karplus, M. Petsko, G.A. Molecular dynamics simulations in biology Nature 347 631-639, 1990. 

Simulations. In addition to analytical approaches to describe ion—soHd interactions two different types of computer simulations are used Monte Cado (MC) and molecular dynamics (MD). The Monte Cado method rehes on a binary coUision model and molecular dynamics solves the many-body problem of Newtonian mechanics for many interacting particles. As the name Monte Cado suggests, the results require averaging over many simulated particle trajectories. A review of the computer simulation of ion—soUd interactions has been provided (43). 

Various equations of state have been developed to treat association ia supercritical fluids. Two of the most often used are the statistical association fluid theory (SAET) (60,61) and the lattice fluid hydrogen bonding model (LEHB) (62). These models iaclude parameters that describe the enthalpy and entropy of association. The most detailed description of association ia supercritical water has been obtained usiag molecular dynamics and Monte Carlo computer simulations (63), but this requires much larger amounts of computer time (64—66). 

FIG. 6-56 Computational fluid dynamic simulation of flow over a square cylinder, showing one vortex shedding period. (From Choudliuty, et al., Trans. ASME Fluids Div, TN-076[1994].)... 

Although dynamic responses of microbial systems are poorly understood, models with some basic features and some empirical features have been found to correlate with actual data fairly well. Real fermentations take days to run, but many variables can be tried in a few minutes using computer simulation. Optimization of fermentation with models and reaf-time dynamic control is in its early infancy however, bases for such work are advancing steadily. The foundations for all such studies are accurate material Balances. 

COMPUTER SIMULATION OF DYNAMIC PROCESSES IN COMPLEX ELECTROLYTIC MEDIA... 

An important issue, the significance of which is sometime underestimated, is the analysis of the resulting molecular dynamics trajectories. Clearly, the value of any computer simulation lies in the quality of the information extracted from it. In fact, it is good practice to plan the analysis procedure before starting the simulation, as the goals of the analysis will often detennine the character of the simulation to be performed. 

Computer simulation is an experimental science to the extent that calculated dynamic properties are subject to systematic and statistical errors. Sources of systematic error consist of size dependence, poor equilibration, non-bond interaction cutoff, etc. These should, of course, be estimated and eliminated where possible. It is also essential to obtain an estimate of the statistical significance of the results. Simulation averages are taken over runs of finite length, and this is the main cause of statistical imprecision in the mean values so obtained. 

WF van Gunsteren. Molecular dynamics and stochastic dynamics simulations A primer. In WF van Gunsteren, PK Weiner, AJ Wilkinson, eds. Computer Simulations of Biomolecular Systems. Leiden ESCOM, 1993, pp 3-36. 

G Galh, A Pasquarello. Eirst-prmciple molecular dynamics. In MP Allen, DJ Tildesley, eds. Proceedings of the NATO ASI on Computer Simulation in Chemical Physics. Dordrecht Kluwer, 1993, pp 261-313. 

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