Research
Google Scholar profile
Scopus profile
Preprints on CVGMT
Preprints on HeriotWatt 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 semidiscrete optimal transport theory and its applications to materials science (geometric modelling of polycrystalline microstructures), weather modelling (the semigeostrophic equations), pattern formation (crystallization), and optimal quantization.
Selected Publications

Bourne, D.P., Pearce, M. & Roper, S.M. (2024) Inverting Laguerre tessellations: Recovering tessellations from the volumes and centroids of their cells using optimal transport, arXiv:2406.00871. PDF
 Buze, M., Feydy, J., Roper, S.M., Sedighiani K. & Bourne, D.P. (2024) Anisotropic power diagrams for polycrystal modelling: efficient generation of curved grains via optimal transport, arXiv:2403.03571. PDF software

Bourne, D.P., Pearce, M. & Roper, S.M. (2023) Geometric modelling of polycrystalline materials: Laguerre tessellations and periodic semidiscrete 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)
Semidiscrete optimal transport methods for the semigeostrophic 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, 15491602. 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, 26772707. PDF
software
 Bourne, D.P., Schmitzer, B. & Wirth, B. (2018)
Semidiscrete unbalanced optimal transport and quantization, submitted.
PDF
 Bourne, D.P., Cushing, D., Liu, S., Münch F. & Peyerimhoff, N. (2018)
OllivierRicci idleness functions of graphs. SIAM Journal on Discrete Mathematics, 32, 14081424.
PDF
 Bourne, D.P., Conti, S. & Müller, S. (2017) Energy bounds for a compressed elastic film on a
substrate. Journal of Nonlinear Science, 27, 453494.
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, 25452569. 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, 13151337. 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, 117140.
PDF
Full list
Grants

EPSRC grant EP/V00204X/1
Mathematical Theory of Polycrystalline Materials, £576,848, 1 April 2021  31 March 2025, CoI (with John Ball PI and Lucia Scardia CoI)

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 (cosupervised with John Ball, Lucia Scardia & Steven Roper, funded by EP/V00204X/1, Feb 2023 )
 Charlie Egan (cosupervised with Beatrice Pelloni, funded by a Maxwell Institute Research Fellowship, Nov 2022  Oct 2023)
 Myrto Galanopoulou (cosupervised with John Ball & Lucia Scardia, funded by EP/V00204X/1, Sept 2021  Oct 2023)
 Riccardo Cristoferi (funded by HeriotWatt University and EP/R013527/2, Oct 2018  July 2020)
 David Cushing (cosupervised with Norbert Peyerimhoff, funded by an EPSRC Doctoral Prize, Durham University, Jan 2017  May 2018)
PhD students:
 Théo Lavier (cosupervised with Beatrice Pelloni, funded by the Maxwell Institute Graduate School in Mathematical Modelling, Analysis and Computation, Sept 2021 )
 Mason Pearce (cosupervised with Steven Roper, funded by the Maxwell Institute Graduate School in Mathematical Modelling, Analysis and Computation, Sept 2019 )
 Charlie Egan (cosupervised with Beatrice Pelloni and Mark Wilkinson, funded by the Maxwell Institute Graduate School in Analysis & its Applications, Sept 2018  Oct 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:
 Buze, M., Feydy, J., Roper, S.M., Sedighiani K. & Bourne, D.P. (2024) Anisotropic power diagrams for polycrystal modelling: efficient generation of curved grains via optimal transport, arXiv:2403.03571. PDF software

Bourne, D.P., Pearce, M. & Roper, S.M. (2023) Geometric modelling of polycrystalline materials: Laguerre tessellations and periodic semidiscrete optimal transport,
Mechanics Research Communications 127, 104023. PDF
software

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, 26772707. PDF
software

Watch my seminar
on an application of optimal transport theory in the steel industry at the workshop
Mathematical design of new materials, 1115 March 2019: