MAGIC097: Theory of conservation laws and critical phenomena

Details Description Lecturer Bibliography Assessment Files Lectures

Course details

A specialist MAGIC course

Semester

Autumn 2019: Monday, October 7th to Friday, December 13th

Hours

Live lecture hours: 10

Recorded lecture hours: 0

Total advised study hours: 40

Timetable

Tuesdays: 13:05 - 13:55 (UK)

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.

Prerequisites

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

Related courses

MAGIC021
MAGIC058

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

Lecturer

AM

Dr Antonio Moro

University

Northumbria University

Bibliography

Follow the link for a book to take you to the relevant Google Book Search page

You may be able to preview the book there and see links to places where you can buy the book. There is also link marked 'Find this book in a library' - this sometimes works well, but not always - you will need to enter your location, but it will be saved after you do that for the first time.

Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory (B A Dubrovin and S P Novikov, )
Hyperbolic systems of conservation laws (Alberto Bressan, )
Singularity Theory and an introduction to Catastrophe Theory (Yung-Chen Lu, )
Catastrophe theory (V.I. Arnold, )
Dispersive and diffusive-dispersive shock waves for non-convex conservation laws (G.A. El, M.A. Hoefer, M.Shearer, )
Introduction to phase transitions and critical phenomena (H.E. Stanley, )

Assessment

The assessment for this course will be released on Monday 6th January 2020 at 00:00 and is due in before Sunday 19th January 2020 at 23:59.

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

Please note that you are not registered for assessment on this course.

Files

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Lectures

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