Simon Fraser University
Engaging the World

Course Outlines

Spring 2022 - PHYS 846 G100

Nonlinear Physics (3)

Class Number: 7949

Delivery Method: In Person

Overview

  • Course Times + Location:

    Jan 10 – Apr 11, 2022: Mon, Wed, Fri, 12:30–1:20 p.m.
    Burnaby

  • Exam Times + Location:

    Apr 26, 2022
    Tue, 7:00–10:00 p.m.
    Burnaby

  • Prerequisites:

    PHYS 384 or equivalent.

Description

CALENDAR DESCRIPTION:

Nonlinear dynamics and chaos. Pattern formation and an introduction to turbulence.

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:

Text:  We will primarily draw on two excellent textbooks.  They are available online at the SFU library and for purchase at the SFU bookstore and various online sellers.

  1. Nonlinear Dynamics and Chaos, 2nd ed., Stephen H. Strogatz.  Taylor & Francis / CRC Press, 2015.
  2. Pattern Formation and Dynamics in Nonequilibrium Systems, Michael Cross and Henry Greenside, Cambridge Univ. Press, 2009.   

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.

Graduate Studies Notes:

Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

SFU’s Academic Integrity web site http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating.  Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the University community.  Academic dishonesty, in whatever form, is ultimately destructive of the values of the University. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the University. http://www.sfu.ca/policies/gazette/student/s10-01.html

TEACHING AT SFU IN SPRING 2022

Teaching at SFU in spring 2022 will involve primarily in-person instruction, with safety plans in place.  Some courses will still be offered through remote methods, and if so, this will be clearly identified in the schedule of classes.  You will also know at enrollment whether remote course components will be “live” (synchronous) or at your own pace (asynchronous).

Enrolling in a course acknowledges that you are able to attend in whatever format is required.  You should not enroll in a course that is in-person if you are not able to return to campus, and should be aware that remote study may entail different modes of learning, interaction with your instructor, and ways of getting feedback on your work than may be the case for in-person classes.

Students with hidden or visible disabilities who may need class or exam accommodations, including in the context of remote learning, are advised to register with the SFU Centre for Accessible Learning (caladmin@sfu.ca or 778-782-3112) as early as possible in order to prepare for the spring 2022 term.