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MA9M3 Topics in Applied Mathematics

Lecturer: Shreyas Mandre

Term: Term 2

Commitment: Lectures 30 sessions 1 hour

Timetable: Tu 10-11 (D1.07), Fr 10-12 (D1.07)

Assessment: Oral Examination 100%

Module aims

To give breadth of training in applied/industrial Mathematics, closer to the norm in Germany, France and Italy, for example.

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

  1. Continuum and microscopic theories of capillarity and wetting ,
  2. Models for intermolecular adhesive forces,
  3. Force balance on curved interfaces,
  4. Pairwise balance between surface tension, gravity, inertia and elasticity (static-menisci, capillary-gravity waves, deforming spheres),
  5. Dynamic, geometric and topological singularities in the interface ,
  6. Stress singularities at moving contact lines and models for their resolution,
  7. Surfactant and Marangoni phenomena (Evaporation, convection, tears of wine, fingering),
  8. Dynamics of lipid membranes (mathematical formulation and observed dynamics).

Learning outcomes

By the end of the module, students should be able to:

  • Ability to incorporate mechanics on a curved interface with a variable surface tension into a mathematical framework of the mechanics of bulk material.

Indicative reading list

  1. Capillarity and Wetting Phenomena, P-G de Gennes, F. Brochard-Wyart, David Quéré, Springer
  2. Capillary flows with forming interfaces, Y. Shikhmurzaev, Chapman and Hall/CRC
  3. Intermolecular and Surface Forces, J. Israelachvili, Academic Press
  4. Molecular theory of capillarity, Rowlinson and Widom, Dover.
  5. Interfacial Phenomena: Equilibrium and Dynamic Effects, Miller and Neogi, CRC Press.

Subject specific skills

Develop a deep understanding of an array of topics in Applied/Industrial Mathematics.

As a sample for the module taught in 2022:

-Derivation and solution of partial differential equations for liquid interface geometry and composition

  • Application of thermodynamic principles to derive boundary conditions
  • Solutions of partial differential equations for specific applications
  • Interpretation of solution and implications for applications

Transferable skills

  • sourcing research material
  • prioritising and summarising relevant information
  • absorbing and organizing information
  • presentation skills (both oral and written)