Simple Simulation Algorithms and Sample Applications

Abstract

This section offers basic recipes and sample applications which allow the reader to immediately start his/her own simulation project on topics we dealt with in this book. Concerning molecular dynamics and Monte Carlo simulation there are, of course, several useful books already available which describe the ‘art of simulation‘ [141, 156, 256] in an exhaustive way. The reason we print some simple codes is that we skipped algorithmic details in the foregoing chapters. Simulations are always performed using dimensionless numbers, and all dimensional quantities can be expressed in terms of reduced units, cf. Sect. 4.3 for conventional Lennard–Jones units. In this chapter, we concentrate on the necessary, and skip anything more sophisticated. Codes have been used in classrooms, they are obviously open for modifications and extensions, and offer not only an executable, but all necessary formulas for doing simulations in the correct (which is often essential) order. The overall spirit is as follows: codes are short, run without changes, demonstrate the main principle in a modular fashion, and are thus in particular open regarding efficiency issues and extensions. Algorithms are presented in the Matlab^TM language, which is mostly directly portable to programming languages like fortran, c, or Mathematica^TM. For an introduction we refer to [423]. Additional commands needed to visualize the results are given in the figure title for each application. Simulation codes, in a less modular fashion, are also available online at www.complexfluids.ethz.ch. Functions are shared over sections, for that reason we begin with an alphabetic list of all (nonbuiltin) functions in this chapter.