Research

Google Scholar profile
Scopus profile
Preprints on CVGMT
Preprints on Heriot-Watt Research Portal
Preprints on the arXiv

Research Interests

My research areas are optimal transport theory, the calculus of variations, and applied analysis. In the last few years one of my main interests has been semi-discrete optimal transport theory and its applications to materials science (geometric modelling of polycrystalline microstructures), weather modelling (the semi-geostrophic equations), pattern formation (crystallization), and optimal quantization.

Selected Publications

Bourne, D.P., Pearce, M. & Roper, S.M. (2023) Geometric modelling of polycrystalline materials: Laguerre tessellations and periodic semi-discrete optimal transport, Mechanics Research Communications 127, 104023. PDF software
Egan, C.P., Bourne, D.P., Cotter, C.J., Cullen, M.J.P., Pelloni, B., Roper, S.M. & Wilkinson, M. (2022) A new implementation of the geometric method for solving the Eady slice equations, Journal of Computational Physics 469, 111542. PDF software
Bourne, D.P., Egan, C.P., Pelloni, B. & Wilkinson, M. (2022) Semi-discrete optimal transport methods for the semi-geostrophic equations, Calculus of Variations and Partial Differential Equations, 61, 39. PDF
Bourne, D.P. & Cristoferi, R. (2021) Asymptotic optimality of the triangular lattice for a class of optimal location problems, Communications in Mathematical Physics, 387, 1549-1602. PDF
Bourne, D.P., Kok, P.J.J., Roper, S.M. & Spanjer, W.D.T. (2020) Laguerre tessellations and polycrystalline microstructures: A fast algorithm for generating grains of given volumes, Philosophical Magazine, 100, 2677-2707. PDF software
Bourne, D.P., Schmitzer, B. & Wirth, B. (2018) Semi-discrete unbalanced optimal transport and quantization, submitted. PDF
Bourne, D.P., Cushing, D., Liu, S., Münch F. & Peyerimhoff, N. (2018) Ollivier-Ricci idleness functions of graphs. SIAM Journal on Discrete Mathematics, 32, 1408-1424. PDF
Bourne, D.P., Conti, S. & Müller, S. (2017) Energy bounds for a compressed elastic film on a substrate. Journal of Nonlinear Science, 27, 453-494. PDF
Bourne, D.P. & Roper, S.M. (2015) Centroidal power diagrams, Lloyd's algorithm and applications to optimal location problems. SIAM Journal on Numerical Analysis, 53, 2545-2569. PDF
Bourne, D.P., Peletier, M.A. & Roper, S.M. (2014) Hexagonal patterns in a simplified model for block copolymers. SIAM Journal on Applied Mathematics, 74, 1315-1337. PDF
Bourne, D.P., Peletier, M.A. & Theil, F. (2014) Optimality of the triangular lattice for a particle system with Wasserstein interaction. Communications in Mathematical Physics, 329, 117-140. PDF

Full list

Grants

EPSRC grant EP/V00204X/1 Mathematical Theory of Polycrystalline Materials, £576,848, 1 April 2021 - 31 March 2025, Co-I (with John Ball PI and Lucia Scardia Co-I)
EPSRC First grant EP/R013527/1, EP/R013527/2 Designer Microstructure via Optimal Transport Theory, £101,152, 1 Jan 2018 - 31 May 2020, PI

Supervision

Postdocs:

Maciej Buze (co-supervised with John Ball, Lucia Scardia & Steven Roper, funded by EP/V00204X/1, Feb 2023 -)
Charlie Egan (co-supervised with Beatrice Pelloni, funded by a Maxwell Institute Research Fellowship, Nov 2022 -)
Myrto Galanopoulou (co-supervised with John Ball & Lucia Scardia, funded by EP/V00204X/1, Sept 2021 -)
Riccardo Cristoferi (funded by Heriot-Watt University and EP/R013527/2, Oct 2018 - July 2020)
David Cushing (co-supervised with Norbert Peyerimhoff, funded by an EPSRC Doctoral Prize, Durham University, Jan 2017 - May 2018)

PhD students:

Théo Lavier (co-supervised with Beatrice Pelloni, funded by the Maxwell Institute Graduate School in Mathematical Modelling, Analysis and Computation, Sept 2021 -)
Mason Pearce (co-supervised with Steven Roper, funded by the Maxwell Institute Graduate School in Mathematical Modelling, Analysis and Computation, Sept 2019 -)
Charlie Egan (co-supervised with Beatrice Pelloni and Mark Wilkinson, funded by the Maxwell Institute Graduate School in Analysis & its Applications, Sept 2018 - October 2022)

Collaboration with Tata Steel

I have an ongoing collaboration with Tata Steel Europe. In particular I work with the Plasticity & Tribology Knowldge Group based in IJmuiden, which is part of the Application & Engineering (R&D) department. You can find out more about our work here:

Bourne, D.P., Kok, P.J.J., Roper, S.M. & Spanjer, W.D.T. (2020) Laguerre tessellations and polycrystalline microstructures: A fast algorithm for generating grains of given volumes, Philosophical Magazine, 100, 2677-2707 PDF
Watch my seminar on an application of optimal transport theory in the steel industry at the workshop Mathematical design of new materials, 11-15 March 2019:

Study Groups with Industry

Through the Study Groups with Industry I have collaborated with

Atom Bank
MARIN (Maritime Research Institute Netherlands)
TAP Maintenance & Engineering
Teknova
Thales Nederland

Here is a short film about a project I did with MARIN (Maritime Research Institute Netherlands):

This was also in collaboration with M. Apri, N. Banagaaya, J. B. van den Berg, R. Brussee, T. Fatima, F. Irzal, J. Rademacher, B. Rink, F. Veerman, S. Verpoort.
Read more about the project here

Study Group proceedings and publications:

Bourne, D.P., Broadfoot, K., Caiado, C., Charlesworth, H., Feier, R., Hilton, J., Huntley, N., Piwarska, K., Rowinska, P., Shatil, N. & Ying, F. (2016) Optimizing the diffusion of innovations in saturated markets. Proceedings of the 116th European Study Group with Industry.
Avelino, C., Bourne, D.P., Ferreira, F., Rasteiro, D. & Santos, J. (2016) Scheduling the repair of aircraft components - a case study. Mathematics-in-Industry Case Studies, 7. PDF
Bourne, D.P., Jones, G., Whittaker, R. & Zagórowska, M. (2015) Slag Interface Instability. Proceedings of the 107th European Study Group with Industry.
Bansal, N., Bourne, D.P., Firat, M., Graaf, M. de, Kapodistria, S., Kumar, K., Meerman, C., Mitici M., Nardi, F.R., de Rijk, B., Sarwat, S. & Scardia, L. (2012) Optimization of lifetime in sensor networks. Proceedings of the 84th European Study Group Mathematics with Industry, 39-69. PDF
Apri, M., Banagaaya, N., Berg, J.B. van den, Brussee, R., Bourne, D.P., Fatima T., Irzal, F., Rademacher, J., Rink, B., Veerman, F. & Verpoort, S. (2011) Analysis of a model for ship maneuvering. Proceedings of the 79th European Study Group Mathematics with Industry, 83-116. PDF