Master projects
List of suggested bachelor’s projects supervised by the research group Mathematical Modeling for the master program in Mathematical Modelling and quantum technologies (alphabetically by supervisor). Updated: April 2025.
For more projects suggestions and details on each project, see the list of Proposed projects on the ACIT Master Canvas page (ACIT Master class).
| Tittel | Beskrivelse | Fagfelt | Veileder(e) |
|---|---|---|---|
| Efficient GPU-based hydrological or hydrodynamic modeling for estimation of local risk exposure from stormwater runoff | With the projected increase in frequency of extreme rainfall there is a need to understand the flow of water on the terrain after the rain has hit the ground. Different numerical models, both physics-based and more simplified discrete models, are being employed by urban planners, property developers and insurance companies in order to predict and mitigate the risk of damage to buildings. In the project. we build a dynamic hydrological model taking into account meteorological factors and underground processes and employ high performance computing techniques, using Python and CUDA to take advantage of the GPU, possibly by building on the GPU Ocean model. | Mathematical modelling, Programming | Martin Lilleeng Sætra |
| Quantum groups and quantum computing | Quantum groups can be considered as generalized symmetries inspired by quantum mechanics. Like (classical) groups can be considered as symmetries of (classical) spaces, quantum groups can be regarded as generalized symmetries of quantum spaces. In this context, spaces get replaced by algebras of observables which, upon quantization, become non-commutative as in quantum mechanics. In this project we want to explore some applications to quantum computing. An important problem in the context of quantum information theory is the following: find subspaces of large relative dimension in a tensor product such that all states are highly entangled. While this problem has been widely studied using random techniques, this does not provide much insight into constructing examples explicitly. In recent years, it has been shown that the problem can be studied using the representation theory of free orthogonal quantum groups. | Mathematics | Marco Matassa |
| Quantum groups and integrable systems | In this project we want to explore how quantum groups can be used to obtain solutions to certain (integrable) systems arising in statistical mechanics. Here the main role is played by the Yang-Baxter equation, whose solutions allow for an ingenious way of studying such systems, as first shown by Baxter. It turns out that such solutions can be generated from quantum groups, which historically was one of the reasons for their introduction. A useful reference here is the book by Baxter. | Mathematics | Marco Matassa |
| Methods for solving dynamical equations in quantum physics | In order to understand quantum phenomena and exploit them in quantum technology, theoretical studies and simulations are vital. In the case of dynamical quantum systems, the relevant numerical equations are often solved using specific methods such as Runge-Kutta methods or Crank-Nicolson. However, methods based Krylov-subspaces have proven a to be a very efficient alternative – not just to the Schrödinger equation, but also to other dynamical quantum equations such as Master equations. In this project we will implement such methods for rather generic systems which may conveniently be described as time-dependent matrices. We will compare the accuracy and efficiency of the Krylov method with more standard ones. | Quantum physics | Sølve Selstø |
| Visualization of quantum phenomena | In this assignment we will develop interactive visualization tools demonstrating basic quantum phenomena – such as interference, tunneling, spin flip, measurement and quantization. In the general case, this will involve implementing numerical solutions to the underlying dynamical equations. Both the Python library Pyplot and MATLAB are adequate tools for achieving this. Other tools and platforms could also be considered. It is, however, an advantage if the final application can run independently of these environments, e.g., through a web-based interface. The functionality of the applications should be as simple as possible – and graphical. Numerical inputs should be tunable by using slider, knobs or similar. While numerical solutions to differential equations will be part of the implementation, the emphasis will be on the graphical user interface. When it comes to the numerics, relevant source code may be provided – depending on the background and the interest of the candidate. | Quantum physics | Sølve Selstø, Frode Eika Sandnes |
| Computational investigation of a tripartite synapse network model | Information propagation in the brain is mediated by neurons. However, astrocytes – brain cells that are at least as numerous as neurons – also contribute to signaling, mostly by providing a sound environment around the neurons. This project studies the dynamics of the so called tripartite synapse – the unit consisting of the neuron, the astrocyte that ensheaths the neuron and the extracellular space that separates the cells. The aim of this project is to develop, analyse and simulate a tripartite synapse network model based on an existing model which describes ion concentration and membrane potential dynamics in the tripartite synapse. This model will be duplicated and the two resulting models will be assumed to be coupled via ions diffusing through the extracellular space. | Mathematical modelling, Numerical mathematics | Leiv Øyehaug |
| Fire-diffuse-fire models of calcium dynamics in heart cells | Fire–diffuse–fire models typically consist of a regular array of point-source release sites embedded in a continuum in which a chemical substance diffuses. When the substance reaches a threshold concentration at the release site, large quantities of the substance are released. This type of model can be used to describe calcium spatiotemporal dynamics in the cytoplasm of cardiomyocytes (heart cells), where large quantities of calcium are released from sites called ryanodine receptors during the so-called excitation-contraction coupling. Characteristic of many fire-diffuse-fire models is the simplicity that allows them to be analytically solved. However, this simplicity puts severe restrictions on how we describe mathematically key actors and mechanisms of the model. Thus there is a need for computational methods that can handle models with e.g. nonlinearities and complex geometries, see Øyehaug et al. (2013). | Mathematical modelling, Numerical mathematics | Leiv Øyehaug |