Research
Google Scholar profile
Scopus profile
Preprints on CVGMT
Preprints on HeriotWatt Research Portal
Preprints on the arXiv
Research Interests
Applied analysis (optimal transportation theory, calculus of variations, partial differential equations), numerical analysis, and discrete and computational geometry, with applications in materials science and continuum mechanics. I am particularly interested in energydriven pattern formation problems in materials science. I also enjoy applying mathematics to problems in industry.
Selected Publications

Bourne, D.P. & Cristoferi, R. (2020) Asymptotic optimality of the triangular lattice for a class of optimal location problems,
submitted. PDF

Bourne, D.P., Egan, C., Pelloni, B. & Wilkinson, M. (2020)
Existence for the semigeostrophic equations in geostrophic coordinates via semidiscrete optimal transport,
submitted. PDF. Seminar on this paper

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
 Bourne, D.P., Schmitzer, B. & Wirth, B. (2018)
Semidiscrete unbalanced optimal transport and quantization, submitted.
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

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:
 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:
 Mason Pearce (cosupervised with John Pearson and 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 )
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,
to appear in the Philosophical Magazine. PDF

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:
Study Groups with Industry
Through the Study Groups with Industry I have collaborated with
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.
MathematicsinIndustry 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, 3969. 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, 83116. PDF