43 citations · 103 across the 13 of their papers we have counts for
14 papers
Geometric modelling of polycrystalline materials: Laguerre tessellations and periodic semi-discrete optimal transport
D. P. Bourne, M. Pearce, S. M. Roper
In this paper we describe a fast algorithm for generating periodic RVEs of polycrystalline materials. In particular, we use the damped Newton method from semi-discrete optimal tran…
A new implementation of the geometric method for solving the Eady slice equations
Charlie P. Egan, David P. Bourne, Colin J. Cotter +4
We present a new implementation of the geometric method of Cullen & Purser (1984) for solving the semi-geostrophic Eady slice equations which model large scale atmospheric flows an…
Asymptotic optimality of the triangular lattice for a class of optimal location problems
David P. Bourne, Riccardo Cristoferi
We prove an asymptotic crystallization result in two dimensions for a class of nonlocal particle systems. To be precise, we consider the best approximation with respect to the 2-Wa…
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…
Controlling Fragment Competition on Pathways to Addressable Self-Assembly
Jim Madge, David Bourne, Mark A. Miller
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 targe…
Laguerre tessellations and polycrystalline microstructures: A fast algorithm for generating grains of given volumes
D. P. Bourne, P. J. J. Kok, S. M. Roper +1
We present a fast algorithm for generating Laguerre diagrams with cells of given volumes, which can be used for creating RVEs of polycrystalline materials for computational homogen…
Semi-discrete unbalanced optimal transport and quantization
David P. Bourne, Bernhard Schmitzer, Benedikt Wirth
In this paper we study the class of optimal entropy-transport problems introduced by Liero, Mielke and Savaré in Inventiones Mathematicae 211 in 2018. This class of unbalanced tran…
Ollivier-Ricci idleness functions of graphs
David Bourne, David Cushing, Shiping Liu +2
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 linear pa…
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…
Centroidal power diagrams, Lloyd's algorithm and applications to optimal location problems
David Bourne, Steven Roper
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…
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…