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All Outputs (8)

Controlling Fragment Competition on Pathways to Addressable Self-Assembly (2018)
Journal Article
Madge, J., Bourne, D., & Miller, M. A. (2018). Controlling Fragment Competition on Pathways to Addressable Self-Assembly. Journal of Physical Chemistry B (Soft Condensed Matter and Biophysical Chemistry), 122(42), 9815-9825. https://doi.org/10.1021/acs.jpcb.8b08096

Addressable self-assembly is the formation of a target structure from a set of unique molecular or colloidal building-blocks, each of which occupies a defined location in the target. The requirement that each type of building-block appears exactly on... Read More about Controlling Fragment Competition on Pathways to Addressable Self-Assembly.

Ollivier-Ricci idleness functions of graphs (2018)
Journal Article
Bourne, D., Cushing, D., Liu, S., Muench, F., & Peyerimhoff, N. (2018). Ollivier-Ricci idleness functions of graphs. SIAM Journal on Discrete Mathematics, 32(2), 1408-1424. https://doi.org/10.1137/17m1134469

We study the Ollivier--Ricci curvature of graphs as a function of the chosen idleness. We show that this idleness function is concave and piecewise linear with at most three linear parts, and at most two linear parts in the case of a regular graph. W... Read More about Ollivier-Ricci idleness functions of graphs.

Energy Bounds for a Compressed Elastic Film on a Substrate (2016)
Journal Article
Bourne, D., Conti, S., & Mueller, S. (2017). Energy Bounds for a Compressed Elastic Film on a Substrate. Journal of Nonlinear Science, 27(2), 453-494. https://doi.org/10.1007/s00332-016-9339-0

We study pattern formation in a compressed elastic film which delaminates from a substrate. Our key tool is the determination of rigorous upper and lower bounds on the minimum value of a suitable energy functional. The energy consists of two parts, d... Read More about Energy Bounds for a Compressed Elastic Film on a Substrate.

Scheduling the repair of aircraft components - a case study (2016)
Journal Article
Avelino, C., Bourne, D., Ferreira, F., Rasteiro, D., & Santos, J. (2016). Scheduling the repair of aircraft components - a case study. Mathematics-in-industry case studies, 7(1), Article 5. https://doi.org/10.1186/s40929-016-0007-2

In aircraft components maintenance shops, components are distributed amongst repair groups and their respective technicians based on the type of repair, on the technicians skills and workload, and on the customer required dates. This distribution pla... Read More about Scheduling the repair of aircraft components - a case study.

Folding Patterns in Partially Delaminated Thin Films (2016)
Book Chapter
Bourne, D., Conti, S., & Mueller, S. (2016). Folding Patterns in Partially Delaminated Thin Films. In K. Weinberg, & A. Pandolfi (Eds.), Innovative numerical approaches for multi-field and multi-scale problems : in honor of Michael Ortiz's 60th birthday (25-39). Springer Verlag. https://doi.org/10.1007/978-3-319-39022-2_2

Michael Ortiz and Gustavo Gioia showed in the 90s that the complex patterns arising in compressed elastic films can be analyzed within the context of the calculus of variations. Their initial work focused on films partially debonded from the substrat... Read More about Folding Patterns in Partially Delaminated Thin Films.

Centroidal power diagrams, Lloyd's algorithm and applications to optimal location problems (2015)
Journal Article
Bourne, D., & Roper, S. (2015). Centroidal power diagrams, Lloyd's algorithm and applications to optimal location problems. SIAM Journal on Numerical Analysis, 53(6), 2545-2569. https://doi.org/10.1137/141000993

In this paper we develop a numerical method for solving a class of optimization problems known as optimal location or quantization problems. The target energy can be written either in terms of atomic measures and the Wasserstein distance or in terms... Read More about Centroidal power diagrams, Lloyd's algorithm and applications to optimal location problems.

Hexagonal Patterns in a Simplified Model for Block Copolymers (2014)
Journal Article
Bourne, D., Peletier, M., & Roper, S. (2014). Hexagonal Patterns in a Simplified Model for Block Copolymers. SIAM Journal on Applied Mathematics, 74(5), 1315-1337. https://doi.org/10.1137/130922732

In this paper we study a new model for patterns in two dimensions, inspired by diblock copolymer melts with a dominant phase. The model is simple enough to be amenable not only to numerics but also to analysis, yet sophisticated enough to reproduce h... Read More about Hexagonal Patterns in a Simplified Model for Block Copolymers.

Optimality of the Triangular Lattice for a Particle System with Wasserstein Interaction (2014)
Journal Article
Bourne, D., Peletier, M., & Theil, F. (2014). Optimality of the Triangular Lattice for a Particle System with Wasserstein Interaction. Communications in Mathematical Physics, 329(1), 117-140. https://doi.org/10.1007/s00220-014-1965-5

We prove strong crystallization results in two dimensions for an energy that arises in the theory of block copolymers. The energy is defined on sets of points and their weights, or equivalently on the set of atomic measures. It consists of two terms;... Read More about Optimality of the Triangular Lattice for a Particle System with Wasserstein Interaction.