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Domain wall network model for theory of plastic deformations in van der Waals crystals

   Department of Mathematics

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  Prof Vladimir Falko, Prof O Jensen, Dr Vladimir Enaldiev  Applications accepted all year round  Funded PhD Project (UK Students Only)

About the Project

This project aims to develop mathematical models describing plasticity of two-dimensional materials: crystals where the intra-layer covalent bonding of atoms coexists with weak van der Waals (vdW) coupling between the layers. Initially, the project will address the formulation of a two-dimensional network model for domain walls in marginally twisted bilayers of such materials, where the existence of domain structure has been both theoretically predicted [1] and experimentally observed [2] by researchers at the National Graphene Institute in Manchester and worldwide. In those studies, the relation of domain walls with dislocations (generic topological defects in the structure of solids) in layered crystals with relevant symmetries has been identified, and their energies computed using ab initio density functional theory, combined with mesoscale elasticity theory. It has also been suggested that dynamical control of domain structure in bilayers of vdW materials has potential for memristor applications [3], which demands computationally efficient modelling of mesoscale real-time dynamics of multi-connected webs of domain wall networks. We aim to develop such a modelling tool using the vertex-based approach [4] recently developed for network models in cell biology [5]. With such a modelling tool in hand, we will further develop theory of dislocations networks in multilayer films of vdW crystals and apply it to the description of their plasticity. 

This project is part of the Manchester Mathematical Modelling in Science and Industry (MMMSI) PhD Training Centre, which is a community of PhD students at the University of Manchester using mathematical modelling for multi-disciplinary collaborations across the University campus and beyond.   Student appointed to this position will be expected to play an active role in MMMSI. They will also engage in activities of UK’s Henry Royce Institute for Advanced Materials and collaborate with partners of the European Graphene Flagship project.  

Academic background of candidates

This project will suit a candidate with a strong background in applied mathematics or theoretical physics, with excellent analytical, computational and communication skills.  Applicants are expected to hold, or be about to obtain, a minimum upper second class undergraduate degree (or equivalent) in either Mathematics or Physics, or a closely related subject. A Masters degree in a relevant subject and/or experience in either applied mathematics or theoretical condensed matter physics is desirable. 

Contact for further Information

Vladimir Falko: [Email Address Removed]

Oliver Jensen: [Email Address Removed]

Funding Notes

This is a 3.5 year PhD Studentship funded by MMMSI, which will cover fees and stipend £15,609 in 2021-22.
Open to UK applicants only.
The studentship must be taken up before July 2022.


[1] V. Enaldiev, V. Zólyomi, C. Yelgel, S. J. Magorrian, V. Fal’ko, Phys. Rev. Lett. 124, 206101 (2020).
[2] A. Weston, Y. Zou, V. Enaldiev, et al. Nature Nanotechnology 15, 592 (2020)
[3] V. Enaldiev, F. Ferreira, S. Magorrian, V. Fal'ko, 2D Mater 8, 025030 (2020)
[4] A. Nestor-Bergmann, G. Goddard, S. Woolner, O. Jensen, Math. Med. Biol. 35, i1 (2018)
[5] O. Jensen, E. Johns, S. Woolner, Proc. Roy. Soc. A476, 2237 (2020)
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