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Soft Matter in Physics & Biology - MAT00070M

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  • Department: Mathematics
  • Module co-ordinator: Dr. Mitya Pushkin
  • Credit value: 10 credits
  • Credit level: M
  • Academic year of delivery: 2020-21

Module summary

Pre-requisite Module(s)

Introduction to Probability and Statistics - see link in Pre-requisite section

Applied Mathematics MAT00034I or equivalent - see link in Pre-requisite section

Physics students can use Thermodynamics and Statistical Mechanics PHY00013H as a pre-requisite if necessary.

Related modules

Co-requisite modules

  • None

Prohibited combinations

  • None

Additional information

Pre-requisite modules: students should have taken Introduction to Probability and Statistics MAT00004C or Thermodynamics and Statistical Mechanics PHY00013H.

Module will run

Occurrence Teaching cycle
A Autumn Term 2020-21

Module aims

The module aims to

  • Introduce students to the major notions and modern applications of statistical mechanics, modelling of the structure and dynamics of biological and soft materials

  • Demonstrate a variety of mathematical techniques, from stochastic to continuous, required to describe the behaviour of materials at widely separated scales

  • Teach students to read, analyse and discuss current scientific literature in the field of soft matter and biological materials

Module learning outcomes

By the end of this module students should


  • Be able to describe a wide variety of phenomena in soft and biological matter using the unifying mathematical language of statistical mechanics

  • Solve problems usingcalculus of variations

  • Have gained experience of working with recently published papers in the field of soft matter and be able to succinctly summarise their results.


  • Develop problem-solving skills and abilities to treat problems using a set of different but complementary approaches

  • Ability to read and analyse interdisciplinary literature

Module content


The following topics will be covered:

  • Soft matter and biological materials as subjects of statistical mechanics (SM).

  • Mechanical equilibrium as energy minimisation problem. Protein buckling as a bifurcation.

  • Introduction to fundamentals of SM. Temperature and probability.

  • Ligand-receptor binding as a statistical mechanical problem.

  • Entropy. The principle of free energy minimisation. Thermodynamic and entropic forces.

  • Canonical formalism of SM and examples of biological systems: optical trap, mechanosensitive ion channel, and phosphorylation of proteins.

  • One-dimensional matter: basic models for protein structure. Random walk and the entropic origin of elasticity.

  • Two-dimensional matter: structure and energetics of bubbles, drops and cell membranes. Surface tension and wetting phenomena.

  • Mixing cocktails: phase transitions. The mean field theory.

  • Topics in nonequilibrium and active matter

In addition to lectures, the students will work with recently published papers and will learn to succinctly summarise and present their results.


Task Length % of module mark
Online Exam
Soft Matter in Physics & Biology
N/A 80
Oral presentation/seminar/exam
45 minute presentation
N/A 20

Special assessment rules



Task Length % of module mark
Re-assessment report
N/A 20
Online Exam
Re-assessment exam - Soft Matter in Physics & Biology
N/A 80

Module feedback

Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy.

Indicative reading

  • R. Phillips et al. The physical biology of the cell. Garland science (2013).

  • S. J. Blundell and K.M. Blundell. Concepts in thermal physics. OUP (2010).

  • M. Doi. Soft matter physics. OUP (2013).

  • D.-G. De Gennes et al. Capillarity and Wetting Phenomena. Springer (2012).

  • P. M. Chaikin, T. C. Lubensky. Principles of condensed matter physics. CUP (2000).

  • T. A. Witten. Structured fluids. OUP (2004).

The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.