Below follows a list of suggested master projects (corresponding to one semester of work roughly). The suggestions could also serve as one year masters projects or bachelor projects after suitable adaptation. I am always open for new ideas, so if you have suggestions for other projects, let me know!
Parameter estimation/curve fitting to ensemble averages. Fitting to time-dependent ensemble averages, i.e., trajectory-based averages of some observable, are of importance in most fields of science. When interpreting such data one commonly fits these averages (for instance, squared displacements at different sampling times) with a function and extract parameters (such as diffusion constants). A commonly overlooked challenge in such fitting procedures is that fluctuations around mean values, by construction, exhibit temporal correlations. We recently introduced a new framework for parameter estimation (fitting) to ensemble averages, which deals with the said correlations in a mathematically correct way, and produce parameter estimations with accurate error estimation. In this project, the aim is to extend these results and introduce a new goodness-of-fit test for fits to ensemble averages. The project involves multi-dimensional integrals of the type encountered in statistical physics and quantum field theory.
Antibody binding. Bacteria and humans have co-evolved during their common existence and therefore developed specific defence and target mechanisms against each. In this project, you will model the binding tendencies (affinities) of antibodies to bacterial surface proteins, with applications for understanding immune responses in humans. The project is joint with experimentalist Pontus Nordenfelt (Division of Infection Medicine, Lund University) which will provide experimental data. The aim of the project is to model (using transfer matrices) and understand experiments using equilibrium statistical physics methods.
DNA barcoding. We have since several years back a well-established collaboration with three experimental groups (Fredrik Westerlund, Chalmers University, Jonas Tegenfeldt Lund University, and Yuval Ebenstein, Tel Aviv), within an EU-project, http://www.beyondseq.eu/ . We help out with very "hands on" things related to analyzing and predicting so called DNA barcodes (optical DNA maps). We do all sorts of things, like image analysis, statistics, statistical physics etc. The field is rapidly evolving, so please contact me for recent challenges.
Single-file diffusion/Rouse chain dynamics using transfer matrices. The dynamics of a chain of harmoncailly coupled beads where each bead has a friction constant which is a random number is to be studied theoretically. Here, we would use simulations/numerics and aim at providing some asymptotic (long time) results for the mean square displacement of a tracer particle (a single bead in the chain). We will use transfer matrices, which you may have encountered in courses on statistical physics (for solving the Ising model, for instance).
Competitive binding of ligands to DNA. A theory challenge is here to study the "car parking problem" of ligands (binding proteins) binding along DNA chain (curb). For the case where all ligands are identical, the associated binding curves are given by the McGhee von Hippel results, but for the case of, say, two types of ligands (as Fredrik Westerlund group uses in their experiments, see above) no simple formula exists. The challenge to be tackled in this project is to derive such a formula, using tools from statistical physics, and validate it using numerics.
General framework for first-passage times, using the independent interval approximation. Applications include modeling of disease extinction.
Fitting of spatial correlation functions, and static structure factors, to time-independent ensemble averages based on simulations. In equilibrium statistical mechanics one often employ Monte Carlo or molecular dynamics simulations. A downstream challenge when interpreting the results of such simulation is to fit associated sample averages to some functional form for the correlation function. Since fluctuations around mean values are correlated, by construction, in such simulations, the error in estimated parameters are affected. In this project, the aim is to derive and test a new way of estimating parameters when fitting simulations to correlation functions. The project will be co-supervised by Anders Irbäck.