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General


Description

The aim of this course is to provide an introduction to the theory of hyperbolic conservation laws and their perturbations with emphasis on integrability aspects, singularity of their solutions in relation to catastrophe theory and phase transitions.
Specific application of conservation laws methods to mean field models in statistical thermodynamics will be also discussed.

Semester

Autumn 2019 (Monday, October 7 to Friday, December 13)

Hours

  • Live lecture hours: 10
  • Recorded lecture hours: 0
  • Total advised study hours: 40

Timetable

  • Tue 13:05 - 13:55

Prerequisites

No specific requirements. Standard undergraduate courses in analysis, mathematical methods and partial differential equations are desirable.

Syllabus

1) Introduction to hyperbolic conservation laws of hydrodynamic type
2) Integrability and generalised hodograph method
3) Singularities and catastrophes
4) Viscous and dispersive regularisations
5) Critical asymptotics and Universality
6) Mean field models and equations of state

Other courses that you may be interested in:

Bibliography


Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theoryB A Dubrovin and S P Novikov
Hyperbolic systems of conservation lawsAlberto Bressan
Singularity Theory and an introduction to Catastrophe TheoryYung-Chen Lu
Catastrophe theoryV.I. Arnold
Dispersive and diffusive-dispersive shock waves for non-convex conservation lawsG.A. El, M.A. Hoefer, M.Shearer
Introduction to phase transitions and critical phenomenaH.E. Stanley


Note:

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Assessment



Exam paper consisting of FOUR mandatory questions.
Marks for each question part are indicated after each part. Total marks per question are shown below each question.
Each question is worth 25 marks.
Exam paper is marked out of 100 marks.
Pass mark is 50

No assignments have been set for this course.

Files


Files marked L are intended to be displayed on the main screen during lectures.

Week(s)File
1MAGIC097_Lecture1.pdfL
2MAGIC097_Lecture2.pdfL
3MAGIC097_Lecture3.pdfL
4MAGIC097_Lecture4.pdfL
6MAGIC097_Lecture6.pdfL
7MAGIC097_Lecture7.pdfL
8MAGIC097_Lecture8.pdfL
9MAGIC097_Lecture9.pdfL
10MAGIC097_Lecture10.pdfL


Recorded Lectures


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