Department of Physics, Unit Catalogue 2008/09 |
PH30055 Computational physics A |
| Credits: 6 |
| Level: Honours |
| Semester: 1 |
| Assessment: CW 100% |
| Requisites: |
| Before taking this unit you must take PH20018 |
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Students should have taken an appropriate selection of year 1 and year 2 physics units, including PH20018 in order to take this unit.
Aims: The aims of this unit are to introduce students to the practical use of computer modelling as a complement to theoretical and experimental solution of physical problems, to introduce a contemporary package available to the modeller, and to explore topics in physics that lend themselves to computational modelling.
Learning Outcomes: After taking this unit the student should be able to: * identify the strengths and weaknesses of a computational approach to modelling; * demonstrate a practical knowledge of the Maple computer algebra system; * construct Maple worksheets to analyse physical problems; * use computational modelling to perform in-depth investigations into selected topics; * explain the methodology, relevant issues and output of the investigations performed. Skills: Written Communication T/F A, Numeracy T/F A, Data Acquisition, Handling, and Analysis T/F A, Information Technology T/F A, Problem Solving T/F A. Content: Introduction to computational modelling as a means of gaining physical insight: Contemporary applications of computer modelling. Computer algebra packages as a scientific computer environment: Problems solved effectively in this environment and those that are not. Practical introduction to Maple: Data structures; constants, variables, expressions, functions, lists, arrays, sets and strings. Basic calculus; integration, differentiation, limits, series, sums. Standard functions. Graphics; x-y plots, parametric plots, 3d plots, plot objects, animation. Data i/o. Solving equations; symbolic, numerical, systems of equations, ordinary differential equations. Linear Algebra; vectors, matrices, addition, subtraction, multiplication, dot & cross products, determinant, trace, eigenvalues, eigenvectors. Programming; logic, loops, procedures. Exercises and projects based upon construction of Maple worksheets: Examples may include: Bound state problems in quantum physics by shooting method, basis set expansion. Coupled oscillators; normal modes, time-series analysis. Planetary dynamics; orbit prediction, three-body problems, chaotic motion. Electrons in molecules and solids; linear combination of atomic orbitals, energy levels/bands, bonding/antibonding. Fractals; generation, characterisation via fractal dimension. Stochastic systems; random walkers, diffusion limited aggregation. Dynamics of non-linear systems; logistic map, Lorentz equations, limit cycles, chaos. Percolation; cluster counting algorithms, percolation threshold. |