Syllabus for Statistical Thermodynamics: Theory and Simulation Methods

Learning outcomes

On completion of the course, the student should be able to:

• discuss the physical interpretation and justify the use of different ensembles and partition functions as well as to calculate thermodynamic properties in model systems using Boltzmann, Fermi-Dirac, and Bose-Einstein statistics
• justify and interpret interaction potentials as well as calculate thermodynamic properties using corresponding configuration integrals for different model systems
• analyse and apply distribution function theory on fluids
• analyse problems concerning adsorption and phase equilibria with the help of lattice models and carry out calculations with the help of the corresponding theories.
• evaluate and analyse the usefulness and limitations of both models and simulations methods
• describe and analyse different simulations methods and apply these to the modelling of dynamics and structure of molecules, liquids and solids as well as present the results orally and in writting

Content

Boltzmann-, Fermi-Dirac-, och Bose-Einstein statistics. Ensembles. Classical statistical thermodynamics. Distribution functions. Virial expansions. Lattice based models for liquids. The Bragg-William approximation. Molecular dynamics. Monte Carlo simulations - rare events and extended sampling methods. The random walk and Brownian dynamics. Random number generation, Lagrangian and Hamiltonian functions. Extended Lagrangian methods. Simulations in different ensembles. Partition functions and free energy. Force fields for molecules, liquids, and solid materials. Many-body and polarisation models. Diffusion limited and reaction limited aggregation.

Instruction

Lectures, tutorials, seminars, project and laboratory exercises.

Assessment

Written examination and the end of the course (7 credits), laboratory exercises (3 credits), seminars (1 credit) and oral and written presentation of project (4 credits). The final grade represents and weighed sum of the results from the written examination, project and laboratory exercises.

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.

Other directives

The course cannot be counted towards a degree together with 1KB354 Statistical Thermodynamics, 1KB359 Molecular Modelling and Simulation, or 1KB362 Statistical thermodynamics: Theory and simulation methods.