Soft Matter in Physics & Biology - MAT00070M

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  • Department: Mathematics
  • Credit value: 10 credits
  • Credit level: M
  • Academic year of delivery: 2022-23

Related modules

Pre-requisite modules

Co-requisite modules

  • None

Prohibited combinations

  • None

Additional information

Pre-requisite Module(s)

Introduction to Probability and Statistics 

Applied Mathematics MAT00034I or equivalent

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

Module will run

Occurrence Teaching period
A Autumn Term 2022-23

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

(Academic)

  • 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.

(Graduate)

  • 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.

Indicative assessment

Task % of module mark
Closed/in-person Exam (Centrally scheduled) 80
Essay/coursework 20

Special assessment rules

None

Indicative reassessment

Task % of module mark
Closed/in-person Exam (Centrally scheduled) 80
Essay/coursework 20

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).