Research

Google Scholar profile

Research Interests

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.


Publications

  1. Bourne, D.P. (2003) Hydrodynamic stability, the Chebyshev tau method and spurious eigenvalues. Contin. Mech. Thermodyn., 15, 571-579. DVI
  2. Ph.D. Thesis: (2007) The Taylor-Couette Problem for Flow in a Deformable Cylinder. The University of Maryland, College Park, USA.
  3. 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
  4. 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
  5. Antman, S.S. & Bourne, D.P. (2010) Rotational symmetry vs. axisymmetry in shell theory. International Journal of Engineering Science, 48, 991-1005. PDF
  6. 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
  7. 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
  8. 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. PDF
  9. 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
  10. 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
  11. 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
  12. Bourne, D.P. & Roper, S.M. Centroidal power diagrams, Lloyd's algorithm and applications to optimal location problems. Submitted. PDF
  13. 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, R. Brussee, T. Fatima, F. Irzal, J. Rademacher, B. Rink, F. Veerman, S. Verpoort.
Read more about the project here