News
Course Info
Syllabus
Lectures
- Wednesday, 11:10 am - 2:00 pm in UA 3130
Office hours
- Friday, 12:00 pm - 1:00 pm or by appointment
- in-person in in UA4032
- online at https://meet.google.com/qta-qyuk-aja
- Or by appointment
Lab times and locations are available here.
Canvas (requires login)
Labs and inclass exercises will be submitted through course canvas site.
Course notes
Check out these course notes here.
Labs
Lab handouts are available through course canvas site.
Description
This is a survey course on simulation methodologies, techniques, and applications.
Constructing computer simulations is perhaps one of the funnest things one can do with a computer. Imagine the thrill of simulating an entire planet inhabited with life-like beings going about their business, pondering life’s big questions? Ok, we aren’t quite there yet, but already we have access to countless games that simulate one phenomenon or another for the purposes of entertainment. Think SimCity that simulates a metropolis, or Factorio that simulates, what can only be described as, a logistics nightmare. We have games that simulate driving cars, flying airplanes, playing soccer, hunting big game, and fighting in wars, etc. Similarly we have games that simulate entire worlds populated with dinosaurs and robots and everything in-between: Xenoblade, any one.
Within this context, this course aims to introduce students to computer simulations. We will not be using simulation packages rather we will explore the mathematical models and programming practices that underpin systems that can be used to create computer simulations.
Entertainment and games are not the primary use of computer simulations however. Designers and engineers rely heavily on simulations when designing and implementing complex systems, e.g., airplanes, bridges, highways, drugs, nuclear reactors, etc. Simulations enable us to ask the what if question, which is especially useful when we do not have the access to the actual system or when it is simply too dangerous to run the experiments on the actual system. E.g., how many cars before a bridge collapses? Clearly, we cannot pile cars on a bridge and wait for it to collapse! Many a times simulation is the only mechanism through which we can study a phenomenon.
Another use of simulations is in education and training sphere where it is sometimes easier, cheaper, less dangerous to use a simulation for training. Think how pilots are routinely trained on high-fidelity flight simulators.
Within this context, we will discuss the mathematics, physics, and statistics theory plus programming practices that underpin modern computer simulations. The focus is not to use existing computer simulation tools rather the course aims at developing competency needed to implement computer simulations. By necessity we will focus on setting up simulations for toy problems, such as a ball bouncing on an inclined plane, a factory floor, nuclear decay, random walks, etc.
Grading
- Class participation, quizzes, and exercises 10%
- Lab and assignment participation and completion 15%
- Midterm exams 60%
- Course project 15%
A student must get 50% in the midterm exams to pass the course.
Important dates
- Midterm 1, Wednesday, February 5, in class
- Study break during the week of February 17
- Midterm 2, Wednesday, March 19, in class
- Project selection due by March 3
You may loose up to 10% of the course project grade if project selection isn’t finalized by Mar 4. You may loose up to an additional 20% of the course project grade if the project selection isn’t finalized by Mar 11. If the project isn’t selected by Mar 11, you’ll be asked to provide a written explanation for the delay. - Project topics presentations on March 5 (tentative)
- Project report due on April 6, 11:59 pm
You may be asked to record a 3 minute long project presenation that will be submitted before the last week of lectures.
Ontario Tech University’s academic calendar that lists important dates (and deadlines) is available at here.
Course Calendar
Week 1
Topics
- Why simulations?
- Validate a model or a theory
- Perform experiments
- Support model-based design
- Education and training
- Building simulations
- Requirements
- Modeling
- Data collection
- Implementation
- Validation
- Use
Notes
- Introduction and building simulations
- Some of the videos in the lecture notes sit on youtube. These you can play directly. Others you can find here.
Lab
Labs start from the second week. Labs will be available on the course canvas.
Week 2
Topics
- Continuous systems
- Variables: state, input, and output
- Time
- Ordinary Differential Equations (ODEs)
- Reducibility
- Mass-Spring system
- Ball falling under gravity
- Bouncing balls
- Energy calculations
- Potential and kinetic energy
- Projectile motion
- Terminal Velocity
- Modelling drag
Notes
Code examples
Activity
Lab
Week 3
Topics
- Continue our discussion of continuous systems
- 2D Mass-Spring System Implementation
- Solving ODEs in Python
- Euler method
- Runga-Kutta method
- Many body simulations
Notes
Code examples
Activity
Lab
Week 4
Topics
- Coordinate frames
- Change of basis
- Rigid body dynamics
- Particles vs. rigid bodies
- Position and Orientation
- Linear and angular velocities
- Forces and Torques
- Center of mass
Notes
- Rigid body dynamics
- Deriving equations of motion for unconstrained rigid bodies
- Jan 29 in-class-notes
Code examples
Activity
Lab
Week 5
Midterm 1
Topics
- Rigid body dynamics (continued from last week)
- Inertia tensor
- Equations of motions
- Shape representation
Activity
Lab
- No new labs this week. Labs will still take place and all of you are encouraged to use these times to prepare for the midterm and catch up on the material.
Week 6
Topics
- Collision detection
- Collisions with a static object
- Collision between moving targets
- Efficiency considerations
- Spatial partitioning
Notes
Code examples
Activity
Lab
Reading week break
Week 7
Topics
- Collision response
- Rigid body collisions
- Conservation of momentum
- Newton’s Law of Restitution for Instantaneous Collision with no Friction
- Empirical model of frictionless collision
Notes
Lab
Week 8
Topics
- Random processes
- Monte Carlo simulations
- Random walks
Notes
Code examples
Activity
Week 9
Topics
- Generating Random numbers
- Linear Congruential Method (LCM)
- Chi-Square test
- Kolmogorov-Smirnov test
- Generating random numbers from uniform and non-uniform discrete distributions
- Generating random numbers from Gaussian distribution
Activity
Week 10
Midterm 2
Topics
- Discrete event systems
- Anatomy of a DES
- Entity
- Variable
- Queue
- Resources
- Statistics
- Gathering data for DES
Notes
Lab
Week 11
Topics
- Discrete Event Systems (DES)
Activity
Week 12
Topics
- Many particle systems
- Molecular dynamics
- Boundary conditions
- Setting up initial conditions
- Pressure and temperature
- Ensemble
- Microcanonical ensemble
- Quasi-ergodic hypothesis
- Demon algorithm
- Ising model
- Validation and verification
Notes
Activity
Course project (Slides)
The course project is an independent exploration of a specific problem within the context of this course. The topic of the project will be decided in consultation with the instructor.
Project grade will depend on the ideas, how well you present them in the report, how well you position your work in the related literature, how thorough are your experiments and how thoughtful are your conclusions.
Teams of up to two students are allowed.
Below, you will find a list of projects that students have done in the previous iterations of this course:
- Angry birds;
- Flappy birds;
- Balancing an inverted pendulum on a moving platform;
- Billiard;
- Rocket simulation;
- Stock market simulation;
- High-performance collision detection;
- Simulating a waving flag;
- The attack of zombies;
- Rigibu puzzle;
- Modeling storms;
- Fireworks;
- An analysis of customer service in call centres;
- Crowd simulation;
- A vehicle rental network;
- Golf;
- A leaf blowing in the wind; and
- Simulating waves.
Final report and a three-minutes video
For your final project write-up you must use the VCLab course project template available at Overleaf. Project report is expected to be between 4 to 8 pages.
Additionally, you may submit a 3 minutes video for your project.
Resources
Reading material
No single textbook covers all the material that we will discuss in this course. Still the following two books are useful for a deeper study of most of the topics that we will cover in this course.
- Harvey Gould, Jan Tobochnik, and Wolfgang Christian, “An Introduction to Computer Simulation Methods: Applications to Physical Systems,” Third Edition, Addison Wesley, 2007.
- Wolfgang Christian, “Open Source Physics: A User’s Guide with Examples,” Addison Wesley, 2007.
Students are strongly encouraged to take their own notes during lectures.
Programming resources
Course labs will use Python3.
In the past, we have also used the OSP Java Package and Arena Simulation Software.