## MA3SMA-Statistical Mechanics and Applications

Module Provider: Mathematics and Statistics
Number of credits: 10 [5 ECTS credits]
Level:6
Terms in which taught: Spring term module
Pre-requisites: MA2MPH Mathematical Physics or MA2MM Mathematical Modelling or MA1MM Mathematical Modelling
Non-modular pre-requisites:
Co-requisites:
Modules excluded: MA4SMA Statistical Mechanics and Applications
Current from: 2018/9

Module Convenor: Prof Valerio Lucarini

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.

Solve real world problems, such as understanding the properties of the 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:
 Autumn Spring Summer Lectures 20 Guided independent study 80 Total hours by term 100.00 Total hours for module 100.00

Summative Assessment Methods:
 Method Percentage Written exam 100

Summative assessment- Examinations:
2 hours.

Summative assessment- Coursework and in-class tests:
One examination paper.

Formative assessment methods:
Problem sheets.

Penalties for late submission:

The Module Convener will apply the following penalties for work submitted late, in accordance with the University policy.
where the piece of work is submitted up to one calendar week after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for the 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: http://www.reading.ac.uk/web/FILES/qualitysupport/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 40% overall.

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