Title: Spread of microorganisms through soil
Understanding how microorganisms move in porous media such as soil is an important and fascinating topic relevant to several disciplines. The project will address this question using theoretical approaches based on constructing mathematical models and solving these models by both numerical and analytical methods.
The microorganisms invade or move through the pore space of soil which has a peculiar topological characteristics and, in fact, is a fractal or multifractal (not compact) object. This multifractality brings interesting aspects to dynamics of spreading agents in soil. Different types of microorganisms can be considered in the project, i.e. individual organisms (e.g. insects) or colonies (e.g. mycelium). Spread of individual organisms can be of diffusional type, but the diffusion occurs on a multifractal and this changes significantly the laws of diffusion. Spread of mycelium can be treated as a branching process which differs from diffusion but again occurs in fractal pore space. Fractality imposes certain constrains on branching and results in quite an unusual mycelium growth.
The structure of the pore space is a crucial factor for spreading and it depends on type of soil, soil treatment, presence of water and other factors. Presence of nutrients and competing species in soil can also significantly affect the spreading process. The influence of all these factors on the motion of microorganisms in soil will be investigated in the project. The digitised images of the real-soil samples will be used for the analysis of the void space in soil and its effects on the spreading.
The main objectives of the project are the following:
(i) Develop and solve a diffusion model for spreading of individual microorganisms through the pore space in soil of different types.
(a) the model can be of a lattice coarse-grained type or network model ;
(b) dynamical rules can be of random-walk type with biased transition rates .
(ii) Develop and solve a model for branching process mimicking mycelium growth.
(a) the model can be of epidemiological type describing spread of infection through the network of hosts  or two-state model for avalanches in magnetic materials or capillary condensation ;
(b) both discrete and continuous time dynamics can be analysed.
(iii) Investigate the effect of the pore space topology on the spreading process and specify the main factors which can be used for control of the spread of microorganisms in soil.
1. Francisco J. Perez-Reche, Jonathan J. Ludlam, Sergei N. Taraskin, and Christopher A. Gilligan, Phys. Rev. Lett. 106, 218701 (2011). 2. S.N. Taraskin, Phys. Stat. Solidi B 250, 1029 (2013). 3. Franco M. Neri, Anne Bates, Winnie S. Füchtbauer, Francisco J. Pérez-Reche, Sergei N. Taraskin, Wilfred Otten, Douglas J. Bailey, Christopher A. Gilligan, PLoS Comput Biol 7, e1002174 (2011). 4. T.P. Handford, F.J. Pérez-Reche, S.N. Taraskin, Phys Rev E 88, 012139 (2013).
Requirements for the project: Mathematical Biology IA NST course (Cambridge) or equivalent.
- F.J. Pérez-Reche, S.N. Taraskin, W. Otten, M.P. Viana, L.D.F. Costa, C.A. Gilligan, Phys. Rev. Lett. 109, 098102 (2012).
- Franco M. Neri, Anne Bates, Winnie S. Füchtbauer, Francisco J. Pérez-Reche, Sergei N. Taraskin, Wilfred Otten, Douglas J. Bailey, Christopher A. Gilligan, PLoS Comput Biol 7, e1002174 (2011).
- Francisco J. Perez-Reche, Jonathan J. Ludlam, Sergei N. Taraskin, and Christopher A. Gilligan, Phys. Rev. Lett. 106, 218701 (2011).