What are Simulations?

1.2. What are Simulations?#

Computer simulation is the running of a model on a computer or cluster, where the model is meant to represent the behaviour of either a physical system or a theory. Simulations are complementary methods to experiments and theory, as shown in Fig. 1.1.

Allen Tildesley view on the role of simulations

Fig. 1.1 Flowchart of interplay between experiment, simulation, and theory. Adapted from Allen & Tildesley.#

A model consists of the equations or rules used to encode the behavior of a system or theory. A computer simulation is the actual running of the program that perform algorithms which solve those equations. So, we “design a model” and “run a simulation”.

Here, the focus is on molecular systems, therefore the models usually describe molecules or atoms. The simulations are then representative solutions of these molecular models, that can be used to understand experiments, test theories and make predictions (Fig. 1.1).

We will describe both Molecular Dyamics Simulations(MD) and Monte Carlo Simulations (MC).

1.2.1. History#

The first simulations were of hard spheres using a Monte Carlo algorithm.

Metropolis, Nicholas, Arianna W. Rosenbluth, Marshall N. Rosenbluth, Augusta H. Teller, and Edward Teller. “Equation of state calculations by fast computing machines.” The journal of chemical physics 21, no. 6 (1953): 1087-1092.

The first molecular dynamics simulations of hard spheres were performed in 1957

Alder, Berni Julian, and Thomas Everett Wainwright. “Phase transition for a hard sphere system.” The Journal of chemical physics 27, no. 5 (1957): 1208.

  • Fermi, Pasta, Ulam (1954) experiment on ergodicity

  • Alder, Wainwright (1958) liquid-solid transition in hard spheres. “long time tails” (1970)

  • Vineyard (1960) radiation damage using MD

  • Rahman (1964) liquid argon, water (1971)

  • Verlet (1967) correlation functions, algorithms …

  • Andersen, Rahman, Parrinello (1980) constant pressure MD

  • Nose, Hoover (1983) constant temperature thermostats.

  • Car, Parrinello (1985) ab initio MD.

1.2.2. Problems That Can be Addressed by Simulations#

  • Determine properies of materials at conditions where experiments would be challenging or expensive

  • Gain microscopic insight into macroscopic behavior

  • Investigate phase behavior, transport coefficents, structure-propoerty relationships

  • Discovery/Inverse Design: use simulations to screen/discover/“make” new materials

1.2.3. References#

Allen, Michael P., and Dominic J. Tildesley. “Computer simulation of liquids.”, Oxford (1987).

1.2.4. Additional Resorces & References#

  • “Understanding Molecular Simulation”, Frenkel and Smit

  • “Computational Materials Science”, Richard LeSar

  • “A Guide to Monte Carlo Simulations in Statistical Physics”, David P. Landau, Kurt Binder, Cambridge University Press

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