Postgraduate research opportunities

Multidimensional Visibility Graphs and Submonolayer Deposition

The project deals with VISIBILITY GRAPHS. It will involve numerical work as well as methods of network and graph theory, primarily spectral analysis of adjacency matrices and Laplacians of the visibility graphs, and centrality and communicability indices of these graphs.

Number of places

1

Funding

Home fee, Stipend

Opens

6 July 2020

Deadline

1 December 2020

Duration

4 years

Eligibility

Applicants should have, or be expecting to obtain in the near future, a first class or good 2.1 honours degree (or equivalent) in mathematics, engineering or a mathematical science.

The studentship is available for UK/EU candidates subject to specific eligibility criteria (see, e.g., https://www.strath.ac.uk/studywithus/scholarships/strathclyderesearchstudentshipscheme-studentexcellenceawardsepsrc/).

Project Details

The project deals with VISIBILITY GRAPHS. It will involve numerical work (kinetic Monte Carlo simulations) as well as methods of network and graph theory, primarily spectral analysis of adjacency matrices and Laplacians of the visibility graphs, and centrality and communicability indices of these graphs, Voronoi cell decompositions, and at a later stage Minkowski functionals and persistent homology. Thus this is a project that applies a variety of analytical, topological, and computational tools to an important industrial problem which we will describe below.

Visibility graphs will be used to allow us better to differentiate between mechanisms of realistic multidimensional extended island Submonolayer Deposition (SD) processes as the first step to a better control of the resulting morphology. For different processes, different morphologies of the resulting surface (substrate covered in islands) are important. For quantum dots, for example, one would like to have islands of particular size and shape periodically spaced on the surface; in other contexts uniform layers of deposition are needed as basis for "sandwich''-like arrangements of materials. The overall aim is to extend the machinery created by Allen, Grinfeld and Mulheran Physica A 532 (2019), 121872) for SD in a one-dimensional setting and point islands to a realistic multidimensional context involving extended islands.

Funding Details

The project is fully funded by the Engineering and Physical Sciences Research Council (EPSRC) for 48 months. The successful recipient of the award will have their full Home/EU fees covered for the 4-year duration of the project, as well as receiving an annual stipend for living costs. The stipend rate for the 2020/21 academic year is £15,285 per annum. 

Additionally, the award provides a Research Training Support Grant (RTSG) of £5,000 over the 4-year duration of the studentship for the purpose of incidental costs associated with conference attendance, travel for research purposes and consumables.

How to apply

Details of how to apply can be found here.