Teaching language: English
Course module 

Credit distribution 

Examination dates 
Sp1 
Sp2 
Sp3 
Sp4 

No Sp 
0199 
Examination 
5,0 c 
Grading: TH 



5,0 c

0,0 c





In programs
FNMAS MSc PROGRAMME IN NANOSCALE SCIENCE AND TECHNOLOGY, Year 1 (elective)
TTFYA ENGINEERING PHYSICS, Year 4 (elective)
TKEFA CHEMICAL ENGINEERING WITH ENGINEERING PHYSICS, Year 4 (elective)
Examiner:
Professor
Göran Wahnström
Eligibility:
For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.
Course specific prerequisites
Basic undergraduate physics, some numerical analysis and computing. Some familiarity with MATLAB is recommended.
Aim
Computational Physics is physics done by means of computational methods and it has become an integral part of contemporary basic and applied physics. The ability to exploit effectively the power offered by computers is essential to a working physicist. The proper modelling of physical systems using computational techniques is far more than blind number crunching and the successful computational physicist draws on a balanced mix of analytically soluble examples, physical intuition, and numerical work to solve problems that are otherwise intractable.
The course is aimed at refining computational skills by providing direct experience in using a computer to solve computational problems in physics. A large number of different numerical techniques are applied to problems taken from quantum, classical, and statistical physics. These problems exemplify many basic and important concepts in physics which the students may have encountered in other courses. Special emphasis is directed to computer simulation methods, the Monte Carlo method and the moleculardynamics technique, but also more traditional numerical methods are included. The course is designed to bridge the gap between undergraduate level physics and computational research.
Content
The course gives an introduction to three important computational methods in physics: stochastic, finite element, and particle methods.
The stochastic methods, often called Monte Carlo methods, are a collection of techniques where random numbers play an essential role. We will introduce the powerful Metropolis algorithm and apply it to problems in material science and in statistical and quantum mechanics. Highdimensional problems can be treated which are intractable with other methods. We will show how the methods can be used to solve kinetic and diffusion problems. In particular, reaction kinetics on nanoparticles will be considered which are of industrial interest in connection to catalysis.
Finite element and finite difference methods are used to solve partial differential equations. These are central in physics and of key importance in engineering. We will introduce the finite element method and similar techniques and show how they can be used to solve various partial differential equations. The wave equation will be used as an illustrative example and Maxwell s equations are being treated in some detail. Modelling of radio antennae connected to complex platforms in 3 dimensions will be performed, of interest for the car industry.
Particle methods can be used to solve both fewbody and manybody problems. They are based on the solution of ordinary differential equations and are used e.g. for modelling plasmas and in galaxy simulations. We will demonstrate how they are used as powerful tools in molecular modelling in materials and biosciences. The technique is then known as the molecular dynamics simulation and it gives much insight into the behaviour of interacting many particle systems and the dynamics of complex proteins and biomolecules.
Organisation
The different numerical techniques and the physical problems are presented in a series of lectures. An important part in the course is the students own activity in applying the methods, solving a set of exercises, and preparing and presenting a computational physics project. Scheduled computer laboratory work is provided, with instructors available for consultation.
The interactive computing environment MATLAB is used for most of the applications in the course. The software FEMLAB will also be used and in addition, a few applications of the programming languages C and/or Fortran will be included .
Literature
The course is based on lecture notes and articles.
Recommended additional material:
As reference book (for more advanced students): J.M.Thijssen, "Computational Physics" (Cambridge University Press).
For MATLAB: Eva PärtEnander and Anders Sjöberg, "The MATLAB Handbook" (Addison Wesley Longman).
For numerical methods: Willliam H. Press et al., "Numerical Recipes; The Art of Scientific Computing" (Cambridge), and Michael T. Heath, "Scientific Computing: An Introductory Survey", (McGrawHill).
Examination
The examination will be based on homework assignments (50%), oral presentation of a project (25%) and a final exam (25%).