Book contents
- Frontmatter
- Contents
- Acknowledgments
- 1 Introduction
- 2 Elements of probability and combinatorial theory
- 3 Phase spaces, from classical to quantum mechanics, and back
- 4 Ensemble theory
- 5 Canonical ensemble
- 6 Fluctuations and other ensembles
- 7 Molecules
- 8 Non-ideal gases
- 9 Liquids and crystals
- 10 Beyond pure, single-component systems
- 11 Polymers – Brownian dynamics
- 12 Non-equilibrium thermodynamics
- 13 Stochastic processes
- 14 Molecular simulations
- 15 Monte Carlo simulations
- 16 Molecular dynamics simulations
- 17 Properties of matter from simulation results
- 18 Stochastic simulations of chemical reaction kinetics
- Appendices
- Index
- References
17 - Properties of matter from simulation results
Published online by Cambridge University Press: 05 December 2011
- Frontmatter
- Contents
- Acknowledgments
- 1 Introduction
- 2 Elements of probability and combinatorial theory
- 3 Phase spaces, from classical to quantum mechanics, and back
- 4 Ensemble theory
- 5 Canonical ensemble
- 6 Fluctuations and other ensembles
- 7 Molecules
- 8 Non-ideal gases
- 9 Liquids and crystals
- 10 Beyond pure, single-component systems
- 11 Polymers – Brownian dynamics
- 12 Non-equilibrium thermodynamics
- 13 Stochastic processes
- 14 Molecular simulations
- 15 Monte Carlo simulations
- 16 Molecular dynamics simulations
- 17 Properties of matter from simulation results
- 18 Stochastic simulations of chemical reaction kinetics
- Appendices
- Index
- References
Summary
The output of simulations is a list of microscopic states in phase space. These are either a sample of points generated with Metropolis Monte Carlo, or a succession of points in time generated by molecular dynamics. Particle velocities, as well as higher time derivatives of particle positions, can also be saved during a molecular dynamics simulation.
This information is periodically recorded on computer disks during the simulation for subsequent analysis. Minimal analysis can be conducted during the actual simulation, primarily in order to ensure that equilibrium is reached and the simulation is numerically stable. Usually most of the analysis is conducted off-line, after the simulation is completed. The drawback is that large files must be stored and processed. Furthermore, saving positions and velocities does not occur for every integration time step. Instead, positions and velocities are saved infrequently, which results in some information being thrown away. It is more convenient, however, to analyze results off-line, developing and using analysis algorithms as needed. It is also important to maintain an archival record of simulation results.
Structural properties
The pair distribution function, g(r), can be computed from stored particle positions. A program to compute it is given below and can be found in http://statthermo.sourceforge.net/. It computes the distance between all pairs of particles, and counts the number of particle pairs that are in a specific distance range, defined by a parameter delr.
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- Information
- Statistical Thermodynamics and Stochastic KineticsAn Introduction for Engineers, pp. 287 - 294Publisher: Cambridge University PressPrint publication year: 2011