Theory of conservation laws and critical phenomena (MAGIC097)
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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.
Autumn 2019 (Monday, October 7 to Friday, December 13)
No specific requirements. Standard undergraduate courses in analysis, mathematical methods and partial differential equations are desirable.
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
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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
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