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Computational methods pertaining to many branches of science, such as physics, physical chemistry and biology, are presented. The text is primarily intended for third-year undergraduate or first-year graduate students. However, active researchers wanting to learn about the new techniques of computational science should also benefit from reading the book. It treats all major methods, including the powerful molecular dynamics method, Brownian dynamics and the Monte-Carlo method. All methods are treated equally from a theroetical point of view. In each case the underlying theory is presented and then practical algorithms are displayed, giving the reader the opportunity to apply these methods directly. For this purpose exercises are included. The book also features complete program listings ready for application.

Inhaltsverzeichnis

Frontmatter

1. Introductory Examples

Abstract
A problem lending itself almost immediately to a computer-simulation approach is that of percolation. Consider a lattice, which we take, for simplicity, as a two-dimensional square lattice. Each lattice site can be either occupied or unoccupied. A site is occupied with a probability p ∈ [0, 1] and unoccupied with a probability 1-p. For p less than a certain probability pc, there exist only finite clusters on the lattice. A cluster is a collection of occupied sites connected by nearest-neighbour distances. For p larger than or equal to pc there exists an infinite cluster (for an infinite lattice, i.e., in the thermodynamic limit) which connects each side of the lattice with the opposite side. In other words, for an infinite lattice the fraction of sites belonging to the largest cluster is zero below pc and unity at and above pc.
Dieter W. Heermann

2. Computer-Simulation Methods

Abstract
Computer-simulation methods are by now an established tool in many branches of science. The motivations for computer simulations of physical systems are manifold. One of the main motivations is that one eliminates approximations. Usually, to treat a problem analytically (if it can be done at all) one needs to resort to some kind of approximation; for example, a mean-field-type approximation. With a computer simulation we have the ability to study systems not yet tractable with analytical methods. The computer simulation approach allows one to study complex systems and gain insight into their behaviour. Indeed, the complexity can go far beyond the reach of present analytic methods.
Dieter W. Heermann

3. Deterministic Methods

Abstract
The kind of systems we are dealing with in this chapter are such that all degrees of freedom are explicitly taken into account. We do not allow stochastic elements representing, for example, an interaction of the system with a heat bath. The starting point is a Newtonian, Lagrangian or Hamiltonian formulation within the framework of classical mechanics. What we are interested in is to compute quantities for such systems, for example, thermodynamic variables, which appear as ensemble averages. Due to energy conservation the natural ensemble is the microcanonical one. However, sometimes it is desirable to compute a quantity in a different ensemble. To allow such calculations within the framework of a Newtonian, Lagrangian or Hamiltonian description, the formulation has to be modified. In any case, the formulation leads to differential equations of motion. These equations will be discretized to generate a path in phase space, along which the properties are computed.
Dieter W. Heermann

4. Stochastic Methods

Abstract
This chapter is concerned with methods which use stochastic elements to compute quantities of interest. These methods are not diametrically opposed to the deterministic ones. Brownian dynamics provides an example where the two methods are combined to form a hybrid technique. However, there are also inherently stochastic methods, such as the Monte-Carlo technique. An application of this simulation method was presented in the introductory chapter.
Dieter W. Heermann

Backmatter

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