Publications
133 results found
Vire A, Xiang J, Piggott M, et al., 2013, Towards the fully-coupled numerical modelling of floating wind turbines, 10th Deep Sea Offshore Wind R and D Conference (DeepWind), Publisher: ELSEVIER SCIENCE BV, Pages: 43-51, ISSN: 1876-6102
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- Citations: 12
Cotter CJ, Holm DD, 2012, On Noether's Theorem for the Euler-Poincaré equation on the diffeomorphism group with advected quantities, Foundations of Computational Mathematics, ISSN: 1615-3375
Aston JAD, Buck D, Coleman J, et al., 2012, Phylogenetic inference for function-valued traits: speech sound evolution, Trends Ecol Evol, Vol: 27, Pages: 160-166, ISSN: 0169-5347
Phylogenetic models have recently been proposed for data that are best represented as a mathematical function (i.e. function valued). Such methods can be used to model the change over time in function-based descriptions of various data of interest to evolutionary biologists, including the sound of speech. This approach to phylogenetic inference and analysis is challenging, both in terms of modeling the phylogenetics of functions and in engaging with previously existing evidence for character-state change. Nevertheless, it is both a real and exciting prospect. Our approach could provide those interested in investigating a greater range of evolutionary processes with the ability to use statistical hypothesis-testing procedures and to create estimates of the states of function-valued characteristics (e.g. speech sounds) at earlier historical times.
Clark A, Peiró J, Cotter CJ, 2012, A reparameterisation based approach to geodesic constrained solvers for curve matching, International Journal of Computer Vision
Vialard F-X, Rissier L, Cotter CJ, et al., 2012, Diffeomorphic 3D image registration via geodesic shooting using an efficient adjoint calculation, International Journal of Computer Vision
In the context of large deformations by diffeomorphisms, we propose a new diffeomorphic registration algorithm for 3D images that performs the optimization directly on the set of geodesic flows. The key contribution of this work is to provide an accurate estimation of the so-called initial momentum, which is a scalar function encoding the optimal deformation between two images through the Hamiltonian equations of geodesics. Since the initial momentum has proven to be a key tool for statistics on shape spaces, our algorithm enables more reliable statistical comparisons for 3D images.Our proposed algorithm is a gradient descent on the initial momentum, where the gradient is calculated using standard methods from optimal control theory. To improve the numerical efficiency of the gradient computation, we have developed an integral formulation of the adjoint equations associated with the geodesic equations.We then apply it successfully to the registration of 2D phantom images and 3D cerebral images. By comparing our algorithm to the standard approach of Beg et al. (Int. J. Comput. Vis. 61:139–157, 2005), we show that it provides a more reliable estimation of the initial momentum for the optimal path. In addition to promising statistical applications, we finally discuss different perspectives opened by this work, in particular in the new field of longitudinal analysis of biomedical images.
Thuburn J, Cotter CJ, 2012, A framework for mimetic discretization of the rotating shallow-water equations on arbitrary polygonal grids, SIAM Journal on Scientific Computing
Cotter CJ, Shipton J, 2012, Mixed finite elements for numerical weather prediction, J. Comp. Phys.
Weller H, Thuburn J, Cotter CJ, 2012, Computational modes and grid imprinting on five quasi-uniform spherical C-grids, Monthly Weather Review
Cotter CJ, Holm DD, Ivanov RI, et al., 2011, Waltzing peakons and compacton pairs in a cross-coupled Camassa-Holm equation, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 44, ISSN: 1751-8113
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- Citations: 13
Cotter CJ, Ham DA, 2011, Numerical wave propagation for the triangular P1DG-P2 finite element pair, Journal of Computational Physics
Maddison JR, Cotter CJ, Farrell PE, 2011, Geostrophic balance preserving interpolation in mesh adaptive linearised shallow-water ocean modelling, Ocean Modelling
Cotter CJ, Holm DD, Percival JR, 2010, The square root depth wave equations, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol: 466, Pages: 3621-3633, ISSN: 1364-5021
We introduce a set of coupled equations for multi-layer water waves that removes the ill-posedness of the multi-layer Green–Naghdi (MGN) equations in the presence of shear. The new well-posed equations are Hamiltonian and in the absence of imposed background shear, they retain the same travelling wave solutions as MGN. We call the new model the square root depth (Inline Formula) equations from the modified form of their kinetic energy of vertical motion. Our numerical results show how the Inline Formula equations model the effects of multi-layer wave propagation and interaction, with and without shear.
Cotter C, Bokhove O, 2010, Variational water-wave model with accurate dispersion and vertical vorticity, JOURNAL OF ENGINEERING MATHEMATICS, Vol: 67, Pages: 33-54, ISSN: 0022-0833
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- Citations: 8
Cotter CJ, Holm DD, 2010, Geodesic boundary value problems with symmetry, J. Geom. Mech., Vol: 2, Pages: 51-68
Kramer SC, Cotter CJ, Pain CC, 2010, Solving the Poisson equation on small aspect ratio domains using unstructured meshes, OCEAN MODELLING, Vol: 35, Pages: 253-263, ISSN: 1463-5003
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- Citations: 13
Cotter CJ, Pavliotis GA, 2009, Estimating eddy diffusivities from noisy Lagrangian observations, Communications in Mathematical Sciences, Vol: 7, Pages: 805-838, ISSN: 1539-6746
Markose G, Cotter CJ, Hislop WS, 2009, Facial atrophy following accidental subcutaneous extrusion of sodium hypochlorite, BRITISH DENTAL JOURNAL, Vol: 206, Pages: 263-264, ISSN: 0007-0610
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- Citations: 10
Cotter CJ, Ham DA, Pain CC, 2009, A mixed discontinuous/continuous finite element pair for shallow-water ocean modelling, Ocean Modelling, Vol: 26, Pages: 86-90, ISSN: 1463-5003
We introduce a mixed discontinuous/continuous finite element pair for ocean modelling, with continuous quadratic layer thickness and discontinuous velocity. We investigate the finite element pair applied to the linear shallow-water equations on an f-plane. The element pair has the property that all geostrophically balanced states which strongly satisfy the boundary conditions have discrete divergence equal to exactly zero and hence are exactly steady states of the discretised equations. This means that the finite element pair has excellent geostrophic balance properties. We also show that the element pair applied to the non-rotating linear shallow-water equations does not have any spurious small eigenvalues. We illustrate these properties using numerical tests and provide convergence calculations which show that the numerical solutions have errors which decay quadratically with element edge length for both velocity and layer thickness.
Cotter CJ, Holm DD, 2009, Momentum Maps for Lattice EPDiff, SPECIAL VOLUME: COMPUTATIONAL METHODS FOR THE ATMOSPHERE AND THE OCEANS, Vol: 14, Pages: 247-278, ISSN: 1570-8659
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- Citations: 1
Cotter CJ, Holm DD, 2009, Discrete momentum maps for lattice EPDiff, Handbook of Numerical Analysis, Editors: Temam, Tribbia, Publisher: North-Holland, Pages: 247-278, ISBN: 978-0-444-51893-4
Cotter CJ, Ham DA, Pain CC, et al., 2009, LBB stability of a mixed Galerkin finite element pair for fluid flow simulations, Journal of Computational Physics, Vol: 228, Pages: 336-348
We introduce a new mixed finite element for solving the 2- and 3-dimensional wave equations and equations of incompressible flow. The element, which we refer to as P1D–P2, uses discontinuous piecewise linear functions for velocity and continuous piecewise quadratic functions for pressure. The aim of introducing the mixed formulation is to produce a new flexible element choice for triangular and tetrahedral meshes which satisfies the LBB stability condition and hence has no spurious zero-energy modes. The advantage of this particular element choice is that the mass matrix for velocity is block diagonal so it can be trivially inverted; it also allows the order of the pressure to be increased to quadratic whilst maintaining LBB stability which has benefits in geophysical applications with Coriolis forces. We give a normal mode analysis of the semi-discrete wave equation in one dimension which shows that the element pair is stable, and demonstrate that the element is stable with numerical integrations of the wave equation in two dimensions, an analysis of the resultant discrete Laplace operator in two and three dimensions on various meshes which shows that the element pair does not have any spurious modes. We provide convergence tests for the element pair which confirm that the element is stable since the convergence rate of the numerical solution is quadratic.
Cotter CJ, Holm DD, 2009, Continuous and discrete Clebsch variational principles, Foundations of Computational Mathematics, Vol: 9
Percival JR, Cotter CJ, Holm DD, 2008, A Euler–Poincaré framework for the multilayer Green–Nagdhi equations, Meeting held in Honor of Darryl D Holms on Geometry and Analysis in Physical Systems, Publisher: IOP Publishing, Pages: 344018-344031, ISSN: 1751-8113
The Green–Nagdhi equations are frequently used as a model of the wave-like behaviour of the free surface of a fluid, or the interface between two homogeneous fluids of differing densities. Here we show that their multilayer extension arises naturally from a framework based on the Euler–Poincaré theory under an ansatz of columnar motion. The framework also extends to the travelling wave solutions of the equations. We present numerical solutions of the travelling wave problem in a number of flow regimes. We find that the free surface and multilayer waves can exhibit intriguing differences compared to the results of single layer or rigid lid models.
Cotter CJ, 2008, The variational particle-mesh method for matching curves, Pages: 344003-344021
Cotter CJ, Frank J, Reich S, 2007, The remapped particle-mesh semi-Lagrangian advection scheme, QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Vol: 133, Pages: 251-260, ISSN: 0035-9009
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- Citations: 22
Cotter CJ, Holm DD, Hydon PE, 2007, Multisymplectic formulation of fluid dynamics using the inverse map, Proceedings of the Royal Society A, Vol: 463, Pages: 2671-2687
We construct multisymplectic formulations of fluid dynamics using the inverse of the Lagrangian path map. This inverse map, the ‘back-to-labels’ map, gives the initial Lagrangian label of the fluid particle that currently occupies each Eulerian position. Explicitly enforcing the condition that the fluid particles carry their labels with the flow in Hamilton's principle leads to our multisymplectic formulation. We use the multisymplectic one-form to obtain conservation laws for energy, momentum and an infinite set of conservation laws arising from the particle relabelling symmetry and leading to Kelvin's circulation theorem. We discuss how multisymplectic numerical integrators naturally arise in this approach.
Piggott MD, Pain CC, Gorman GJ, et al., 2007, Multi-scale ocean modelling with adapting unstructured grids, CLIVAR Exchanges, Vol: 12, Pages: 21-23, ISSN: 1026-0471
Cotter CJ, Devine JC, 2006, Replacement of nasogastric tubes in patients with cancer of the head and neck, BRITISH JOURNAL OF ORAL & MAXILLOFACIAL SURGERY, Vol: 44, Pages: 411-411, ISSN: 0266-4356
C J Cotter, S Reich, 2006, Time Stepping Algorithms for Classical Molecular Dynamics, Handbook of Theoretical and Computational Nanotechnology, Editors: Reith, Schommers, Publisher: American Scientific Publishers, ISBN: 9781588830425
Cotter CJ, Holm DD, 2006, Discrete momentum maps for lattice EPDiff, Pages: 7-278
We focus on the spatial discretization produced by the VariationalParticle-Mesh (VPM) method for a prototype fluid equation the known as theEPDiff equation}, which is short for Euler-Poincar\'e equation associated withthe diffeomorphism group (of $\mathbb{R}^d$, or of a $d$-dimensional manifold$\Omega$). The EPDiff equation admits measure valued solutions, whose dynamicsare determined by the momentum maps for the left and right actions of thediffeomorphisms on embedded subspaces of $\mathbb{R}^d$. The discrete VPManalogs of those dynamics are studied here. Our main results are: (i) avariational formulation for the VPM method, expressed in terms of a constrainedvariational principle principle for the Lagrangian particles, whose velocitiesare restricted to a distribution $D_{\VPM}$ which is a finite-dimensionalsubspace of the Lie algebra of vector fields on $\Omega$; (ii) a correspondingconstrained variational principle on the fixed Eulerian grid which gives adiscrete version of the Euler-Poincar\'e equation; and (iii) discrete versionsof the momentum maps for the left and right actions of diffeomorphisms on thespace of solutions.
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