This course consists of four projects that must be completed before you may attend the exam. The projects have several aims:
- To provide experience with developing various codes relevant for problems in Statistical Physics
- To use the codes to develop intuition for some of the main concepts in Statistical Physics
- To learn how to measure statistical properties in simulations with many particles
- To provide a deeper insight into the role of fluctuations, finite size effects, and scaling concepts used in modern statistical physics.
The lectures will support the various projects, and will therefore vary from more theoretical when addressing percolation, to more practical when addressing atomic modeling.
Project 1: Atomic modeling of liquids
Project description
You can find a complete description of this project here: Atomic Modeling of Liquids.
Lecture videos:
Week 01: Project 1: Introduction to molecular dynamics of the Lennard-Jones system. Non-dimensional equations. (Norwegian) (English - old)
Week 02: Project 1: Introduction to molecular dynamics of the Lennard-Jones system. Non-dimensional equations. Periodic boundary conditions. Cut-off and optimization methods. Parallel computing.(Norwegian1) (Norwegian2) (English - old)
Week 03: Project 1: Molecular measurements and interpretations. Theory for random walks and self-diffusion. Three-particle interactions. (Norwegian) (English - old)
Week 04: Project 1: Molecular measurements continued. Van der Waals gases, scripting and data collapse plots. Water models. (Norwegian) (English - old)
Additional learning materials
For an introduction to molecular dynamics, see
- chapter 4 in Frenkel and Smit - Understanding Molecular Simulation
- chapters from Thermal and Statistical Physics Using Python (Ch03 provides an introduction to molecular dynamics. The beginning of Ch04 demonstrates how to set up a lammps simulation and extract data. Ch05 provides an example of how to run many lammps simulations and compile the results). The lammps_logfile can be found here .
- Example code for simple molecular dynamics (without forces, just a shell)
- Example code for parallel molecular dynamics and geometries (advanced implementation)
- Files: https://github.com/evenmn/fys4460
Project 2: Atomic modeling of nanoporous media
Project description
You can find a complete description of project 2 here: Atomic modeling of nanoporous media
Lecture videos
Week 05: Project 2: Nanoscale porous media. Simulations with LJ systems. Fluid-dynamics comparisons. Viscous flow in tubes. (Norwegian) (English - old)
Week 06: Project 2: Porosity and permeability. (Norwegian) (English - old)
Addition learning material
- For an introduction to flow in porous media see chapter 4, 6 and 7 in Flow in porous media textbook
Project 3: Percolation
Project description
You can find the complete project description here: Percolation
Lecture videos
Week 07: Project 3: Introduction to percolation theory. Percolation on small lattices. (Norwegian) (English)
Week 08: Project 3: Percolation in one dimension. Introduction of n(s,p). Scaling ansatz and cut-offs. (Norwegian) (English) (English - old)
Week 09: Project 3: Scailng theory and the scaling ansatz.(Norwegian) (English)
Week 10: Project 3: Geometry of the percolation system. (Norwegian) (English) (English - old)
Week 11: Project 3: Finite size scaling. (Norwegian) (English) (English - old)
Week 12: Project 3: Subsets of the spanning cluster. (Norwegian) (English)
Week 13: Project 3: Physics on the percolation system - conductivity. (Norwegian) (English - old)
Week 14: Project 3: Physics on the percolation system - diffusion.(Norwegian) (English - old)
Week 15: Project 3: Diffusion fronts and invasion percolation (Norwegian)
Learning material
- Percolation textbook (Curriculum: Ch. 1,2,4,5,6,8, and 11 or 13.)
- Python versions of the percolation walk scripts are located here: exwalk.py, walk.py, exflow.py, percwalk.py .
Project 4: Final project
For project 4, you select one project that you spend a bit more time on. This should correspond to a few days work. You will present the results from project 4 as the first part of the oral exam. The following document provides ideas for what you can do in project 4: Final Project . You should just select one of the projects/exercises sketched in this document!