Module Information
Course Delivery
Delivery Type | Delivery length / details |
---|---|
Lecture | 8 x 1 hour lectures |
Practical | 11 x 2 hour |
Workload Breakdown | Lectures and tutorials 8 hours Practical programming workshops (2 x 11 hours) 22 hours Worksheets 10 hours Project 10 hours |
Assessment
Assessment Type | Assessment length / details | Proportion |
---|---|---|
Semester Assessment | Exercises set in semester week 8 comprising a portfolio drawn from coursework. | 40% |
Semester Assessment | Mini project set in semester week 8 for Completion by the end of term. | 60% |
Supplementary Assessment | 2 Hours Supplementary two hour examination | 100% |
Learning Outcomes
On successful completion of this module students should be able to:
1. Demonstrate a familiarity with various techniques for scientific computing and analysis
2. Devise and implement numerical codes to perform the relevant analysis
Aims
Numerical solutions to mathematical and physics problems is a cornerstone of both physics and applied mathematics research. This module is a an applied, numerical course designed to introduce three important techniques that are applied to condensed matter physics, fluid dynamics and the solid state. These are Monte Carlo, Lattice-Boltzmann and finite element.
Brief description
Computational physics provides an alternative approach for the solution of practical and theoretical problems. The module will developed further the Monte Carlo technique introduced in the third year making a more explicit connection between MC and statistical mechanics and developing this technique further by introducing quantum Monte Carlo methods. Lattice-gas automata are used to model fluid dynamics and increasingly form part of the canon of computational physics, and are applied for example to fluid flow in porous media and even quantum mechanical systems. The finite element method is a further discretised method with applications both to fluids and solids This section of the course follows directly from the finite differences encountered in the solution to partial differential equations this is the method of choice for solving structural mechanical problems and is also used in computational fluid dynamics. The Fortran programming environment will be used, building on the techniques used in the earlier modules. A step-by-step guide to the implementation of these numerical methods forms part of the programming workshops.
Content
Simple Monte Carlo methods
Importance sampling
Importance sampling for lattice systems
Off-lattice models
Quantum Monte Carlo methods
The Finite element method
The structural element
The Galerkin weighted residual
Convergence
Elasticity
Field problems and fluid flow
The Lattice Boltzmann equation
Lattice gas cellular automata
Lattice Boltzmann models with microdynamics
Flows in disordered media
Turbulent flows.
Complex fluids.
Module Skills
Skills Type | Skills details |
---|---|
Application of Number | Throughout the module. |
Communication | Students will be expected to submit written reports as a portfolio and a written project detailing the implementation of a numerical method to an applied physics problem. |
Improving own Learning and Performance | Feedback in workshops and from programming exercises will enable students to improve their own learning. |
Information Technology | Extensive use of programming language, example codes will and can be obtained from on-line resources, include practice questions and text book tie-ins. |
Personal Development and Career planning | Students will be exposed to areas of application of numerical methods for solution of physical problems, using the most robust and universal programming language, Fortran. This will enable students to adapt to other languages. This module is directly aligned to future careers in physics research. |
Problem solving | All situations considered are problem-based. |
Research skills | Students will be encouraged to consult various books and journals for examples of application of numerical methods. The project background will also need to be researched. |
Subject Specific Skills | Ability to solve numerical problems using script based programming languages. |
Team work | Working in groups to solve numerical problems is encouraged. |
Notes
This module is at CQFW Level 7