Google Scholar profile
Preprints on CVGMT
Applied analysis (calculus of variations, partial differential equations, optimal transportation theory), numerical analysis, and discrete and computational geometry, with applications in materials science and continuum mechanics. Currently I am particularly interested in crystallization and energy-driven pattern formation problems in materials science. In recent years I have also enjoyed applying mathematics to problems in industry.
- Bourne, D.P., Schmitzer, B. & Wirth, B. (2018)
Semi-discrete unbalanced optimal transport and quantization, submitted.
- Madge, J., Bourne, D. & Miller, M.A. (2018) Controlling fragment competition on pathways to addressable self-assembly, accepted in Journal of Physical Chemistry B. 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.
- 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.
- Bourne, D.P., Conti, S. & Müller, S. (2016)
Folding patterns in partially delaminated thin films. In
Innovative Numerical Approaches for Multi-Field and Multi-Scale Problems,
Pandolfi, A. & Weinberg, K. (eds.), Springer, 25-39.
- 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
- Antman, S.S. & Bourne, D.P. (2015) Steady bifurcating solutions
of the Couette-Taylor problem for flow in a deformable cylinder. Journal of Dynamics and Differential Equations, 27, 457-483.
- 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.
EPSRC First grant EP/R013527/1, Designer Microstructure via Optimal Transport Theory, £101,152, Jan 2018-Dec 2019
Projects 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,
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.
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