Simon Fraser University
Engaging the World

Course Outlines

Fall 2025 - PHYS 484 D100

Nonlinear Physics (3)

Class Number: 5999

Delivery Method: In Person

Overview

  • Course Times + Location:

    Sep 3 – Dec 2, 2025: Tue, Thu, 12:30–2:20 p.m.
    Burnaby

  • Prerequisites:

    PHYS 384 with a minimum grade of C- or permission of the department.

Description

CALENDAR DESCRIPTION:

Nonlinear mechanics, nonlinear lattice dynamics, competition phenomena, applications in optics and chemistry, forced oscillations, chaos. Quantitative.

COURSE DETAILS:

General Description:  Why is the Universe not boring?  Nineteenth-century thermodynamics suggests a picture of a Universe that is continually running down, with entropy increasing towards a uniform, featureless —  boring (and dead) — final state.  But that is not what the world looks like!  Why not?  This course will explore how systems, when forced out of equilibrium, spontaneously develop order and structure.  Such structure is responsible for much of what we see around us, and, ultimately, for life itself.  Our overall goal will be to understand how nonlinearity in the laws of physics can lead to phenomena such as self-sustained periodic motion, chaos, synchronization, and the formation of patterns.  Along the way, we will introduce useful mathematical tools such as the geometric (phase space) approach to dynamical systems, bifurcations, Lyapunov exponents and fractals, time-scale separation and amplitude equations.  Applications and examples will be in part tailored to match the interests of students enrolled.


Outline:

Part 1:  Nonlinear Dynamics

  • review of linear dynamics
  • non-dimensionalization & scaling
  • stability, instability, and bifurcation in 1d flows
  • limit cycles and 2d flows
  • chaos in 3d+ flows &  discrete maps
  • synchronization, from soft modes to collective behaviour

Part 2:  Pattern Formation

  • linear stability analysis of uniform states
  • applications, e.g. reaction-diffusion systems
  • formal tools:  time-scale separation and amplitude equations
  • spatiotemporal chaos and turbulence

 

COURSE-LEVEL EDUCATIONAL GOALS:

Course level:  The course is aimed at final-year undergraduates and graduate students.  The general prerequisites are a good understanding of systems of linear ordinary differential equations and linear algebra.  Physics 384 is good preparation.  Students who have not had that course (or an equivalent at a different institution) are encouraged to contact the instructor to discuss their background. 

Grading

  • Problem Sets 50%
  • Final Project 50%

NOTES:

Note that the grading will be separate for the two courses; undergraduates will NOT be in competition with those enrolled in the graduate version of this course.

Materials

MATERIALS + SUPPLIES:

Required Text: 

Complex Dynamics and Morphogenesis: An Introduction to Nonlinear Science Paperback – July 5 2018, by Chaouqi Misbah (e-copy available here)

Final Project:  Each student will do a final project, with a more extensive project  expected from Phys. 846 students.  I will draw up a list of ideas during the course.

REQUIRED READING NOTES:

Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.

Department Undergraduate Notes:

Students who cannot write their exam during the course's scheduled exam time must request accommodation from their instructor in writing, clearly stating the reason for this request, within one week of the final exam schedule being posted.

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

At SFU, you are expected to act honestly and responsibly in all your academic work. Cheating, plagiarism, or any other form of academic dishonesty harms your own learning, undermines the efforts of your classmates who pursue their studies honestly, and goes against the core values of the university.

To learn more about the academic disciplinary process and relevant academic supports, visit: 


RELIGIOUS ACCOMMODATION

Students with a faith background who may need accommodations during the term are encouraged to assess their needs as soon as possible and review the Multifaith religious accommodations website. The page outlines ways they begin working toward an accommodation and ensure solutions can be reached in a timely fashion.