Computer modeling of physical phenomena

Cellular automata and discrete media:

Wolfram’s 1D automata; Game of Life and other 2D models

Networks and collective dynamics:

network science and social networks; neural networks and the Hopfield model, river network formation

Games and evolution:

game theory; Nash equilibria; genetic algorithms

Active matter

swarm models (birds and ant trails), tissue and membrane growth models

Mesoscopic hydrodynamics:

lattice Boltzmann method; Stokesian dynamics

Learning outcomes

After completing the course, students will be able to

formulate simple models of physical and natural phenomena using discrete (cellular automata, networks, agent-based) and mesoscopic (lattice Boltzmann, Stokesian dynamics) descriptions;

implement these models in Python, choosing appropriate data structures, numerical schemes and algorithms;

analyse and visualise simulation results, identify pattern formation and collective behaviour, and relate them to underlying physical mechanisms;

compare different modelling approaches (e.g. cellular automata vs. continuum, networks vs. agent-based models) and justify the choice of method for a given problem;

design and carry out a small simulation project, from problem formulation through implementation and testing to interpretation of results;

critically assess the limitations, numerical artefacts and sources of error in computer simulations;

communicate their findings clearly in written form and short oral presentations, using reproducible code and graphical output.

The course is a combination of review-like lectures and computer labs. The students are asked to prepare a short presentation summarizing one topic from the lectures. They are also required to complete a number of computer based projects in the lab.