CS - Dr Rainer Klages

1. Stochastic modelling of bumblebee movement patterns from experimental data 

Supervisor: Dr Rainer Klages

Project description:

Understanding the movement patterns of organisms by constructing stochastic movement models from data is an important problem of much current interest [1,2]. This topic cross-links the field of movement ecology with stochastic theory, the theory of active matter as well as, to some extent, nonlinear dynamics. In an unpublished new laboratory experiment single bumblebees were tracked in a flight cage. The arrangement of artificial flowers and branches, as well as nectar delivery rates, were manipulated to assess the impact on foraging, scent marking and patrolling. The resulting high resolution data set of movement paths should be analysed in order to construct advanced stochastic models from data reproducing  bumblebee movement strategies [3,4] under variation of environmental conditions. These mathematical models constructed in the form of coupled stochastic differential equations need to be solved numerically in order to compare their predictions with the experimental data. This challenging cross-disciplinary project at the interface between statistical data analysis, advanced stochastic theory and experimental biology will be performed in close collaboration with experimental biologists at QMUL. There is also scope to explore nonlinear properties of bumblebee flights. 

Sound knowledge of statistical data analysis is required, including relevant software packages like R, and familiarity with a programming language like python, or similar. At least basic knowledge of stochastic processes is necessary, and interest to learn more about them [5].

References:

[1] R. Klages, Search for food of birds, fish and insects, in: A.Bunde et al., Diffusive Spreading in Nature, Technology and Society (Springer, Berlin, 2018), p.49

[2] L.Giuggioli and O.Maini (Eds.), The Mathematics of Movement: An Interdisciplinary Approach to Mutual Challenges in Animal Ecology and Cell Biology (Springer, 2025)

[3] F.Lenz et al., Phys. Rev. Lett. 108, 098103 (2012)

[4] F.Lenz, A.V.Chechkin, R.Klages, PLoS ONE 8, e59036 (2013)

[5] R. Klages, G.Radons, I.M.Sokolov (Eds.), Anomalous transport: Foundations and Appplications (Wiley-VCH, 2008)

Funding Notes:

Further information: 
How to apply 
Entry requirements 
Fees and funding

PhD Information Session 2026:
On Wednesday 14 January, we will be holding a short information session about PhD studies in Mathematics at QMUL. For full details about the event, please visit: https://www.qmul.ac.uk/maths/postgraduate/postgraduate-research/phd-information-session-2026/

As one of the UK’s most diverse universities, QMUL fosters an inclusive and supportive academic community.

The School of Mathematical Sciences is committed to the equality of opportunities and to advancing women’s careers. As holders of a Bronze Athena SWAN award, we offer family-friendly benefits and support part-time study.  

2. Weak chaos, fractals and anomalous diffusion

Supervisor: Dr Rainer Klages

Project description:

There is a deep, interesting connection between microscopic chaos in the motion of diffusing particles, the emergence of fractal structures in nonequilibrium steady states, and the generation of macroscopic transport properties like diffusion [1]. Spatially extended chaotic dynamical systems characterised by a positive Lyapunov exponent typically generate normal diffusion similar to the Brownian motion of a particle in a fluid. However, there is a wide class of nonlinear dynamical systems with zero Lyapunov exponent that nevertheless exhibit irregular, random-looking, so-called weakly chaotic dynamics [2] leading to non-Brownian, anomalous diffusion [3]. The goal of this project is to construct and explore a novel class of weakly chaotic dynamical systems exhibiting anomalous deterministic transport. The approach will employ the concept of dissipative, thermostated dynamical systems introduced for nonequilibrium molecular dynamics computer simulations [1]. This approach should be generalised analytically to produce non-Gaussian, weakly chaotic dynamics characterised by Levy-type distributions yielding anomalous diffusion. The resulting dynamics should be implemented numerically by performing computer simulations. The emerging nonequilibrium steady states should be analysed in view of weak chaos properties and fractal structures.

This project requires sound knowledge of nonlinear dynamical systems as well as at least basic knowledge of (nonequilibrium) statistical physics. Familiarity with a programming language like python, or similar, is absolutely necessary, and interest to perform computer simulations. Some knowledge of stochastic processes is a plus.

References:

[1] R.Klages, Microscopic Chaos, Fractals and Transport in Nonequilibrium Statistical Mechanics (World Scientific, 2007) 

[2] R.Klages, Weak chaos, infinite ergodic theory, and anomalous dynamics, invited book chapter in: X.Leoncini and M.Leonetti (Eds.), From Hamiltonian Chaos to Complex Systems (Springer, 2013), p.3-42 

[3] R. Klages, G.Radons, I.M.Sokolov (Eds.), Anomalous transport (Wiley-VCH, 2008) 

Funding Notes:

Further information: 
How to apply 
Entry requirements 
Fees and funding

PhD Information Session 2026:
On Wednesday 14 January, we will be holding a short information session about PhD studies in Mathematics at QMUL. For full details about the event, please visit: https://www.qmul.ac.uk/maths/postgraduate/postgraduate-research/phd-information-session-2026/

As one of the UK’s most diverse universities, QMUL fosters an inclusive and supportive academic community.

The School of Mathematical Sciences is committed to the equality of opportunities and to advancing women’s careers. As holders of a Bronze Athena SWAN award, we offer family-friendly benefits and support part-time study.