Google Scholar profile
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. (2003) Hydrodynamic stability, the Chebyshev tau method and spurious eigenvalues. Contin. Mech. Thermodyn., 15, 571-579. DVI
- Ph.D. Thesis: (2007) The Taylor-Couette Problem for Flow in a Deformable Cylinder. The University of Maryland, College Park, USA.
- Bourne, D.P. & Antman, S.S. (2009) A non-self-adjoint quadratic eigenvalue problem describing a fluid-solid interaction Part I : Formulation, analysis, and computations. Commun. Pure Appl. Anal., 8, 123-142. PDF
- Bourne, D.P., Elman, H. & Osborn, J.E. (2009) A non-self-adjoint quadratic eigenvalue problem describing a fluid-solid interaction Part II : Analysis of convergence. Commun. Pure Appl. Anal., 8, 143-160. PDF
- Antman, S.S. & Bourne, D.P. (2010) Rotational symmetry vs. axisymmetry in shell theory. International Journal of Engineering Science, 48, 991-1005. 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
- 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
Bourne, D.P., Fatima, T., Meurs, P.J.P. van & Muntean, A. (2014) Is adding charcoal to soil a good method for CO2 sequestration? - Modeling a spatially homogeneous soil. Applied Mathematical Modelling, 38, 2463-2475.
- 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.
- Antman, S.S. & Bourne, D.P. Steady bifurcating solutions
of the Couette-Taylor problem for flow in a deformable cylinder. To appear in Journal of Dynamics and Differential Equations.
Published online Feb. 2014: DOI 10.1007/s10884-013-9344-z. PDF
- Bourne, D.P., Peletier, M.A. & Roper, S.M. Hexagonal patterns in a simplified model for block copolymers. To appear in SIAM Journal on Applied Mathematics. PDF
- Bourne, D.P. & Roper, S.M. Centroidal power diagrams, Lloyd's algorithm and applications to optimal location problems. Submitted. PDF
- Bourne, D.P., Conti S. & Müller, S. Folding patterns in thin semiconductor films. In preparation.
Projects with Industry
Through the Study Groups Mathematics 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