Abdul Hadi Asfarangga, The University of Adelaide
Professor Matthew Simpson, Queensland University of Technology
This four-week course will introduce students to a range of lattice-based stochastic transport models that have applications in a range of areas including biology, ecology and traffic flow. Taking a hands-on approach, we will build and explore a range of lattice-based interacting random walk models that will include unbiased migration, biased migration, birth-death phenomena and models of complex populations with interactions between different subpopulations. Students will learn how to build simple simulation tools, to visualise a range of computational experiments, and to extract averaged data from simulations to characterise the expected outcomes of these simulations.
To provide mathematical insight into the stochastic simulations we will introduce coarse-graining methods to extract approximate differential equation descriptions of the mean behaviour of the simulations. These differential equations will involve both ordinary differential equations and partial differential equations and we will use a range of exact and numerical solutions of these differential equations to explore how well the stochastic models can be modelled using simpler differential equations.
This course will proceed by presenting information about how we build and analyse simulation together with plenty of time for assignment-based assessment where students will build and explore stochastic simulation tools, as well as using mathematical descriptions of these simulations. The assessment can be undertaken in small groups or individually.
This syllabus will be sported by a series of four weekly assignments to reinforce these concepts.
This will be a foundational course that requires basic skills in programming.
Students should be confident in programming (e.g. MATLAB, C++, Python, Julia or equivalent). Students will not be required to work in a particular programming language, but students will be expected to build relatively simple algorithms with plenty of hands-on help. Sample code will be provided to get students started.
Some background knowledge of ordinary differential equations and partial differential equation will be an advantage. We will work with a mixture of exact solutions of simple differential equations (logistic equation, linear heat equation) but we will also develop numerical solutions of some nonlinear partial differential equations (Fisher’s equation). Skills in numerical methods will be developed during the course.
Take this quiz and look at some of the expected foundational skills in this topic