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Introduction to Computer Simulation Methods
Applications to sandpiles, fluids, earthquakes, and other areas are discussed. Some of the basic ideas of equilibrium statistical mechanics and kinetic theory are introduced.
Metthods for an Introduction to Computer Simulation Methods. The generation of random number sequences also is discussed. We will find that the use of the computer to do numerical experiments will help us gain insight into the nature of chaos. A simple algorithm for solving first-order differential tobocnnik numerically also is discussed.
Applications to the Ising model and various particle systems are discussed and more efficient Monte Carlo algorithms are introduced. We study simple nonlinear deterministic models that exhibit chaotic behavior.
The nature of object-oriented programming and various computer languages also is considered. This material has 23 associated documents. We emphasize that the methods we have discussed can be applied to a wide variety of natural phenomena and contexts. We introduce cellular automata, neural networks, genetic algorithms, and growing networks to explore the concepts of self-organization and complexity.
We compute how objects appear at relativistic speeds and in the vicinity of a large spherically symmetric mass. Simple classical and Monte Carlo methods including importance sampling are illustrated in the context of the cojputer evaluation of definite integrals. We study affine transformations in order to visualize objects in three dimensions.
We introduce the concept of fractal dimension and discuss several processes that generate fractal objects. We discuss how to simulate thermal systems using simulafion variety of Monte Carlo methods including the traditional Metropolis algorithm. This file is included in the full-text index.
We introduce several geometrical concepts associated with percolation, including the percolation threshold, clusters, and cluster finding algorithms. Download Updates and corrections to the third edition.
An Introduction to Computer Simulation Methods
We explore the behavior of oscillatory systems, including the simple harmonic oscillator, a simple pendulum, electrical circuits, and introduce the concept of phase space. We discuss the physics of wave phenomena and the motivation and use of Fourier transforms. Random processes are introduced in the context ccomputer several simple physical systems, including random walks on a lattice, polymers, and diffusion controlled chemical reactions.
We introduce some of the core syntax of Java in the context of simulating the motion of falling particles near the Earth’s surface.
The importance of computers in physics and the nature of computer simulation is discussed. This file has previous versions. Select a document title to view a document’s information. We simulate the dynamical behavior of many particle systems such as dense gases, liquids, and solids and observe their qualitative features.
We discuss several numerical methods needed to simulate the motion of particles using Newton’s laws and introduce interfaces, an important Java construct that makes it possible for unrelated objects to declare that they perform the same methods. We also introduce the ideas of critical phenomena in the context of the percolation transition, including critical comluter, scaling relations, and the renormalization group.
We discuss numerical solutions of the time-independent and time-dependent Schroedinger equation and describe several Monte Carlo methods for estimating the ground state of quantum systems.
We then solve Euler’s equation of motion for rigid body dynamics using the quaternion representation of rotations. We compute the electric fields due to static and moving charges, describe methods for computing the electric potential in boundary value problems, and solve Maxwell’s equations numerically.
We apply Newton’s laws of motion to planetary motion and other systems of a few particles and explore some of the counter-intuitive consequences of Newton’s laws.