Physique non-linéaire

This is an introductory course in nonlinear physics. It relates in a first part to first and second order differential equations (identification of equilibrium solutions, their stability, phase diagrams and bifurcation diagrams). The analysis of the asymptotic behaviour of solutions calls upon a set of global techniques and finds applications in chemistry, biology, circuit theory, or mechanics. The study of chaos concerns differential systems of at least three dimensions and is the subject of the second part of the course. In this framework, a return map on a hyper-surface leads to iterative systems, the simplest of which take the form of mappings of the unit interval onto itself. We will focus on the attractors of such systems, which describe their asymptotic properties in statistical form. A classic example is the Lorenz attractor which has fractal geometry.

This introduction to the physics of non-linear phenomena and complex systems is part of the MA in Physics program. Its main objective is to introduce students to a broad area of trans-disciplinary contemporary research. It is also aimed at mathematics students with an interest in applied maths.

Required and Corequired knowledge and skills

Familiarity with calculus, linear algebra, numerical programming (python or any other language).

Cours ayant celui-ci comme co-requis

The course is divided into 18 sessions of 2 hours. Exercises are offered on a weekly basis, which count in the assessment. The teaching material is made available via the virtual university.

Contribution to the teaching profile

• Acquire scientific expertise in physics
• Master the scientific thought process and approach
• Learn to communicate appropriately depending on context and target audience

References, bibliography, and recommended reading

• M W Hirsch, S Smale et R L Devaney, Differential equations, dynamical systems, and an introduction to chaos‎ (Elsevier Academic Press 2013)
• S Strogatz, Nonlinear dynamics and chaos with applications to physics, biology, chemistry and engineering (Westview Press 2015)
• D G Schaeffer et J W Cain, Ordinary Differential Equations: Basics and Beyond (Springer  2016)
• J D Meiss, Differential Dynamical Systems‎ (SIAM 2017)

Course notes

• Université virtuelle

Contacts

Email: thomas.gilbert@ulb.be
Campus Plaine, NO building, 5th floor, room P.2.O5.105

Campus

Plaine

Method(s) of evaluation

• written examination
• Oral examination
• Other

written examination

Oral examination

Other

Weekly homework assignments, written (often take-home) and oral exams

 

Mark calculation method (including weighting of intermediary marks)

Homework (1/3), written exam (1/3), oral exam (1/3)

Language(s) of evaluation

• french
• (if applicable english )