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PYU33P06 Dynamical Systems

Michaelmas Term – 30 lectures/tutorials – 5 credits (G Cross, J Pethica)

Part I: Statistical Thermodynamics
Part II: Mechanics of Matter

Learning Outcomes
On successful completion of this module, students should be able to:

  • Apply the concepts of inter-atomic potentials and forces to solid media
  • Distinguish between elastic and non-elastic solid media
  • Describe liquids and gases in terms of fluid flow mechanics
  • Outline the basic concepts of equilibrium statistical thermodynamics
  • Describe mathematically the behaviour of physical systems governed by Fermi-Dirac, Bose-Einstein and Maxwell-Boltzmann statistics
  • Determine the partition functions of simple quantum systems


Part I: Statistical Thermodynamics
The purpose of this course is to introduce Statistical Thermodynamics, which provides a microscopic understanding of the macroscopic thermodynamic properties of materials. A simple assumption of equal statistical weights allows the properties of individual quantum particles to be combined together properly to calculate macroscopic thermodynamic quantities, which can be compared with experiment. Topics covered (1) Counting states in classical and quantum systems (2) Fundamental assumption of statistical physics; ensembles (3) Model system of 2-state components (4) Two systems in equilibrium: entropy, temperature and chemical potential (5) Partition functions and their relation to thermodynamic quantities (6) Third Law of Thermodynamics (7) Fermi-Dirac and Bose-Einstein Statistics (8) Quasi-classical statistics: equipartition of energy (9) Application of quantum statistics to photons, gases, and solids.

Part II: Mechanics of Matter
Atomic origins: inter-atomic potentials and forces, virial expansion, deformation. Elasticity: Young's modulus, stress and strain, hydrostatic and shear components. Beyond elasticity: Breakdown of Hooke’s law, plasticity, dislocations, work hardening, energy dissipation and friction. Liquids: Fluid flow, boundary layers, atomic and molecular characteristics. Gases. Mechanics in practice at different scales.