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**Computer simulation of liquids.**
*(English)*
Zbl 0703.68099

Oxford: University Press. XIX, 385 p. (1987).

Computer simulation of liquids has developed rapidly in the last years. The book presented by M. P. Allen and D. J. Tildesley in 1987 and now available in paperback provides a comprehensive introduction and an excellent survey of the state of the art in this complex field.

The book can be divided into four parts: Introduction and fundamental simulation methods, programming tricks and error analysis, topics and advanced simulation techniques and finally applications and case-studies.

The first part consists of four chapters. After a short introduction into motivation and application of simulation, the modelling problem is discussed. Model systems, interaction potentials and boundary conditions are considered. Those aspects of statistical mechanics which are of interest for computer simulation are summarized. The “molecular dynamics” are investigated by solving the classical equations of motion for a set of molecules. The results are obtained by numerical solution of the differential equations. Two integration methods are described: Gears predictor corrector method and the verlet algorithm. The Monte Carlo method is explained and then applied to computer simulation. Fortran program segments for the kernel routines are given.

In the second part (chapter five and six) tricks and special programming techniques are provided. The starting-up-problem is investigated. Analysis of the results and error estimation is considered.

In Chapters 7 to 10 advanced techniques such as stochastic simulation and extensions of the Monte Carlo method are described. Non-equilibrium, Brownian dynamics and quantum simulations are investigated.

In last part (chapter 11) the methods are illustrated by case-studies such as the liquid drop, molten salts and liquid crystals.

Technical details (e.g. computer hardware, Fourier-Transform and generating random numbers) are presented in appendices.

The book is recommended to all research workers in this field.

The book can be divided into four parts: Introduction and fundamental simulation methods, programming tricks and error analysis, topics and advanced simulation techniques and finally applications and case-studies.

The first part consists of four chapters. After a short introduction into motivation and application of simulation, the modelling problem is discussed. Model systems, interaction potentials and boundary conditions are considered. Those aspects of statistical mechanics which are of interest for computer simulation are summarized. The “molecular dynamics” are investigated by solving the classical equations of motion for a set of molecules. The results are obtained by numerical solution of the differential equations. Two integration methods are described: Gears predictor corrector method and the verlet algorithm. The Monte Carlo method is explained and then applied to computer simulation. Fortran program segments for the kernel routines are given.

In the second part (chapter five and six) tricks and special programming techniques are provided. The starting-up-problem is investigated. Analysis of the results and error estimation is considered.

In Chapters 7 to 10 advanced techniques such as stochastic simulation and extensions of the Monte Carlo method are described. Non-equilibrium, Brownian dynamics and quantum simulations are investigated.

In last part (chapter 11) the methods are illustrated by case-studies such as the liquid drop, molten salts and liquid crystals.

Technical details (e.g. computer hardware, Fourier-Transform and generating random numbers) are presented in appendices.

The book is recommended to all research workers in this field.

Reviewer: R.Tracht

### MSC:

68U20 | Simulation (MSC2010) |

68-02 | Research exposition (monographs, survey articles) pertaining to computer science |