Complex Physics

Skills

The aim is to learn how to rephrase a complex phenomenon into a mathematical equation or computer algorithm.

At the conclusion of the course students should be able to develop computer programs that implement and analyse simple quantitative models of stochastic systems with many parts.

The student will learn to implement agent based models, and learn about the advantages of this type of approach to a range of phenomena.

Students will learn to appreciate that the joint dynamics of a many body system often is both quantitatively and qualitatively different from the simple sum of its parts.

Knowledge

The student is expected to gain basic knowledge on contemporary research in complex systems.
In particular the course emphasize the concept of universality and that the behaviour in many large dynamical systems share common features.

This includes the ability to use fundamental concepts from statistical mechanics, non-linear dynamics, time series analysis, stochastic dynamics and self-organizing systems. These topics give understanding of scaling and scale-invariant phenomena, including fractals and scale-free networks.

The course show many examples on non-equilibrium systems that self-organize to a steady state dynamics that is characterized by fractals and power laws.

Competences

How to model and analyse systems with many components in terms of equations and computer programs.

Write computer models of systems with many interacting parts, including the Ising model, Monte-Carlo simulations, percolation, networks, stochastic dynamical systems, and models of disease spreading.

Implement models to describe self-organized dynamics of structures, for example within network theory and for systems that behave similar across a wide range of scales.

The course will provide the students with tools from physics that have application in a range of fields within and beyond physics.