MA4SMA-Statistical Mechanics and Applications

Module Provider: Mathematics and Statistics
Number of credits: 10 [5 ECTS credits]
Level:7
Terms in which taught: Spring term module
Pre-requisites: MA2MPH Mathematical Physics or MA2MOD Mathematical Modelling
Non-modular pre-requisites:
Co-requisites:
Modules excluded: MA3SMA Statistical Mechanics and Applications
Current from: 2023/4

Module Convenor: Prof Valerio Lucarini
Email: v.lucarini@reading.ac.uk

Type of module:

Summary module description:
This module will introduce the concepts of statistical mechanics and their mathematical formulation.

Aims:
To introduce the concepts of statistical mechanics and their mathematical formulation; to apply these concepts in studying the equilibrium properties of simple physical systems.

Assessable learning outcomes:

By the end of the module students are expected to be able to:

• acquire basic concepts of statistical mechanics, including entropy, ensemble, partition function and free energy, and their mathematical formulation;


• solve problems related to the equilibrium properties of simple physical systems.

This module will be assessed to a greater depth than the excluded module MA3SMA.

Additional outcomes:

Solve real world problems, such as understanding the properties of non-ideal gases.

Outline content:

Statistical mechanics applies the mathematical tools of calculus and probability theory to study the macroscopic properties of large physical systems from the properties of their individual components. In a self-contained manner, this module covers:

• background knowledge of mathematics, probability distributions and thermodynamics;


• basic concepts in statistical mechanics, such as entropy, free energy, ensembles and partition functions, and their mathematical formulation;


• application of statistical mechanics in studying the equilibrium properties of some model systems, such as ideal gas and simple van der Waals liquids and Ising model;


• (optional) Investigation of simple out-of-equilibrium forced and dissipative systems.

Brief description of teaching and learning methods:
Lectures supported by problem sheets.

Contact hours:

Ìý	Autumn	Spring	Summer
Lectures		20
Tutorials		10
Guided independent study:		70
Ìý	Ìý	Ìý	Ìý
Total hours by term	0		0
Ìý	Ìý	Ìý	Ìý
Total hours for module	100

Summative Assessment Methods:

Method	Percentage
Written exam	100

Summative assessment- Examinations:

2 hours.

The examination for this module will require a narrowly defined time window and is likely to be held in a dedicated exam venue.

Summative assessment- Coursework and in-class tests:

Formative assessment methods:
Problem sheets.

Penalties for late submission:

The Support Centres will apply the following penalties for work submitted late:

• where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for that piece of work will be deducted from the mark for each working day (or part thereof) following the deadline up to a total of five working days;
• where the piece of work is submitted more than five working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.

The University policy statement on penalties for late submission can be found at: /cqsd/-/media/project/functions/cqsd/documents/cqsd-old-site-documents/penaltiesforlatesubmission.pdf
You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Assessment requirements for a pass:
A mark of 50% overall.

Reassessment arrangements:

One examination paper of 2 hours duration in August/September.

Additional Costs (specified where applicable):

1) Required text books:Ìý

2) Specialist equipment or materials:Ìý

3) Specialist clothing, footwear or headgear:Ìý

4) Printing and binding:Ìý

5) Computers and devices with a particular specification:Ìý

6) Travel, accommodation and subsistence:Ìý

Last updated: 30 March 2023