43 citations · 103 across the 13 of their papers we have counts for
6 papers · 1 filter
Semi-discrete optimal transport methods for the semi-geostrophic equations
David P. Bourne, Charlie P. Egan, Beatrice Pelloni +1
We give a new and constructive proof of the existence of global-in-time weak solutions of the 3-dimensional incompressible semi-geostrophic equations (SG) in geostrophic coordinate…
Energy Bounds for a Compressed Elastic Film on a Substrate
David P. Bourne, Sergio Conti, Stefan Müller
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 valu…
Folding patterns in partially delaminated thin films
David Bourne, Sergio Conti, Stefan Müller
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. Th…
Hexagonal patterns in a simplified model for block copolymers
D. P. Bourne, M. A. Peletier, S. M. Roper
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…
Optimality of the triangular lattice for a particle system with Wasserstein interaction
D. P. Bourne, M. A. Peletier, F. Theil
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…
Is adding charcoal to soil a good method for CO2 sequestration? - Modeling a spatially homogeneous soil
David Bourne, Tasnim Fatima, Patrick van Meurs +1
Carbon sequestration is the process of capture and long-term storage of atmospheric carbon dioxide (CO2) with the aim to avoid dangerous climate change. In this paper, we propose a…