Imperial College London
Alternate

ProfessorDarrylHolm

Faculty of Natural Sciences, Department of Mathematics

Chair in Applied Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8531d.holm Website

 
 
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Location

 

6M27Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
to

335 results found

Gay-Balmaz F, Holm DD, Meier DM, Ratiu TS, Vialard F-Xet al., 2012, Invariant Higher-Order Variational Problems, COMMUNICATIONS IN MATHEMATICAL PHYSICS, Vol: 309, Pages: 413-458, ISSN: 0010-3616

Journal article

Bruveris M, Ellis DCP, Holm DD, Gay-Balmaz Fet al., 2011, UN-REDUCTION, JOURNAL OF GEOMETRIC MECHANICS, Vol: 3, Pages: 363-387, ISSN: 1941-4889

Journal article

Gay-Balmaz F, Holm DD, Ratiu TS, 2011, Higher order Lagrange-Poincar, and Hamilton-Poincar, reductions, BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, Vol: 42, Pages: 579-606, ISSN: 1678-7544

Journal article

Ellis DCP, Gay-Balmaz F, Holm DD, Ratiu TSet al., 2011, Lagrange-Poincare field equations, JOURNAL OF GEOMETRY AND PHYSICS, Vol: 61, Pages: 2120-2146, ISSN: 0393-0440

Journal article

Graham JP, Holm DD, Mininni P, Pouquet Aet al., 2011, The effect of subfilter-scale physics on regularization models, Journal of Scientific Computing, Vol: 49, Pages: 21-34, ISSN: 0885-7474

The subfilter-scale (SFS) physics of regularization models are investigated to understand the regularizations’ performance as SFS models. Suppression of spectrally local SFS interactions and conservation of small-scale circulation in the Lagrangian-averaged Navier-Stokes α-model (LANS-α) is found to lead to the formation of rigid bodies. These contaminate the superfilter-scale energy spectrum with a scaling that approaches k +1 as the SFS spectra is resolved. The Clark-α and Leray-α models, truncations of LANS-α, do not conserve small-scale circulation and do not develop rigid bodies. LANS-α, however, is closest to Navier-Stokes in intermittency properties. All three models are found to be stable at high Reynolds number. Differences between L 2 and H 1 norm models are clarified. For magnetohydrodynamics (MHD), the presence of the Lorentz force as a source (or sink) for circulation and as a facilitator of both spectrally nonlocal large to small scale interactions as well as local SFS interactions prevents the formation of rigid bodies in Lagrangian-averaged MHD (LAMHD-α). LAMHD-α performs well as a predictor of superfilter-scale energy spectra and of intermittent current sheets at high Reynolds numbers. It may prove generally applicable as a MHD-LES.

Journal article

Risser L, Vialard F-X, Wolz R, Murgasova M, Holm DD, Rueckert Det al., 2011, Simultaneous Multi-scale Registration Using Large Deformation Diffeomorphic Metric Mapping, IEEE TRANSACTIONS ON MEDICAL IMAGING, Vol: 30, Pages: 1746-1759, ISSN: 0278-0062

Journal article

Cotter CJ, Holm DD, Ivanov RI, Percival JRet 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

Journal article

Holm D, Ivanov R, 2011, Smooth and peaked solitons of the Camassa-Holm equation and applications, Journal of Geometry and Symmetry in Physics, Vol: 22, Pages: 13-49, ISSN: 1312-5192

The relations between smooth and peaked soliton solutions are reviewed for the Camassa-Holm (CH) shallow water wave equation in one spatial dimension. The canonical Hamiltonian formulation of the CH equation in action-angle variables is expressed for solitons by using the scattering data for its associated isospectral eigenvalue problem, rephrased as a Riemann-Hilbert problem. The momentum map from the action-angle scattering variables T*(TN) to the flow momentum provides the Eulerian representation of the N-soliton solution of CH in terms of the scattering data and squared eigenfunctions of its isospectral eigenvalue problem. The dispersionless limit of the CH equation and its resulting peakon solutions are examined by using an asymptotic expansion in the dispersion parameter. The peakon solutions of the dispersionless CH equation in one dimension are shown to generalize in higher dimensions to peakon wave-front solutions of the EPDiff equation whose associated momentum is supported on smoothly embedded subspaces. The Eulerian representations of the singular solutions of both CH and EPDiff are given by the (cotangent-lift) momentum maps arising from the left action of the diffeomorphisms on smoothly embedded subspaces.

Journal article

Holm DD, Ivanov RI, 2011, Two-component CH system: inverse scattering, peakons and geometry, INVERSE PROBLEMS, Vol: 27, ISSN: 0266-5611

Journal article

Gibbon JD, Holm DD, 2011, Extreme events in solutions of hydrostatic and non-hydrostatic climate models, PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 369, Pages: 1156-1179, ISSN: 1364-503X

Journal article

Benoit S, Holm DD, Putkaradze V, 2011, Helical states of nonlocally interacting molecules and their linear stability: a geometric approach, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 44, ISSN: 1751-8113

Journal article

Bruveris M, Gay-Balmaz F, Holm DD, Ratiu TSet al., 2011, The Momentum Map Representation of Images, JOURNAL OF NONLINEAR SCIENCE, Vol: 21, Pages: 115-150, ISSN: 0938-8974

Journal article

Holm DD, 2011, Geometric mechanics - Part I: Dynamics and symmetry: 2nd edition, ISBN: 9781848167742

This textbook introduces the tools and language of modern geometric mechanics to advanced undergraduates and beginning graduate students in mathematics, physics and engineering. It treats the fundamental problems of dynamical systems from the viewpoint of Lie group symmetry in variational principles. The only prerequisites are linear algebra, calculus and some familiarity with Hamilton’s principle and canonical Poisson brackets in classical mechanics at the beginning undergraduate level. The ideas and concepts of geometric mechanics are explained in the context of explicit examples. Through these examples, the student develops skills in performing computational manipulations, starting from Fermat’s principle, working through the theory of differential forms on manifolds and transferring these ideas to the applications of reduction by symmetry to reveal Lie–Poisson Hamiltonian formulations and momentum maps in physical applications. The many Exercises and Worked Answers in the text enable the student to grasp the essential aspects of the subject. In addition, the modern language and application of differential forms is explained in the context of geometric mechanics, so that the importance of Lie derivatives and their flows is clear. All theorems are stated and proved explicitly. The organisation of the first edition has been preserved in the second edition. However, the substance of the text has been rewritten throughout to improve the flow and to enrich the development of the material. In particular, the role of Noether’s theorem about the implications of Lie group symmetries for conservation laws of dynamical systems has been emphasised throughout, with many applications.

Book

Holm DD, 2011, Geometric mechanics - Part II: Rotating, translating and rolling: 2nd edition, ISBN: 9781848167773

This textbook introduces modern geometric mechanics to advanced undergraduates and beginning graduate students in mathematics, physics and engineering. In particular, it explains the dynamics of rotating, spinning and rolling rigid bodies from a geometric viewpoint by formulating their solutions as coadjoint motions generated by Lie groups. The only prerequisites are linear algebra, multivariable calculus and some familiarity with Euler–Lagrange variational principles and canonical Poisson brackets in classical mechanics at the beginning undergraduate level. The book uses familiar concrete examples to explain variational calculus on tangent spaces of Lie groups. Through these examples, the student develops skills in performing computational manipulations, starting from vectors and matrices, working through the theory of quaternions to understand rotations, then transferring these skills to the computation of more abstract adjoint and coadjoint motions, Lie–Poisson Hamiltonian formulations, momentum maps and finally dynamics with nonholonomic constraints. The organisation of the first edition has been preserved in the second edition. However, the substance of the text has been rewritten throughout to improve the flow and to enrich the development of the material. Many worked examples of adjoint and coadjoint actions of Lie groups on smooth manifolds have also been added and the enhanced coursework examples have been expanded. The second edition is ideal for classroom use, student projects and self-study.

Book

Graham JP, Holm D, Mininni P, Pouquet Aet al., 2011, The effect of subfilter-scale physics on regularization models, 2nd Workshop on Quality and Reliability of Large-Eddy Simulations, Publisher: SPRINGER, Pages: 411-+, ISSN: 1382-4309

Conference paper

Gibbon JD, Holm DD, 2011, The gradient of potential vorticity, quaternions and an orthonormal frame for fluid particles, GEOPHYSICAL AND ASTROPHYSICAL FLUID DYNAMICS, Vol: 105, Pages: 329-339, ISSN: 0309-1929

Journal article

Holm DD, Ivanov RI, 2010, Multi-component generalizations of the CH equation: geometrical aspects, peakons and numerical examples, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 43, ISSN: 1751-8113

Journal article

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.

Journal article

Holm DD, Ivanov RI, 2010, Smooth and peaked solitons of the CH equation, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 43, ISSN: 1751-8113

Journal article

Holm DD, Putkaradze V, Tronci C, 2010, Double-bracket dissipation in kinetic theory for particles with anisotropic interactions, PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 466, Pages: 2991-3012, ISSN: 1364-5021

Journal article

Ellis DCP, Gay-Balmaz F, Holm DD, Putkaradze V, Ratiu TSet al., 2010, Symmetry Reduced Dynamics of Charged Molecular Strands, ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, Vol: 197, Pages: 811-902, ISSN: 0003-9527

Journal article

Gibbon JD, Holm DD, 2010, The dynamics of the gradient of potential vorticity, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 43, ISSN: 1751-8113

Journal article

Risser L, Vialard F-X, Wolz R, Holm DD, Rueckert Det al., 2010, Simultaneous Fine and Coarse Diffeomorphic Registration: Application to Atrophy Measurement in Alzheimer's Disease, 13th International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI), Publisher: SPRINGER-VERLAG BERLIN, Pages: 610-+, ISSN: 0302-9743

Conference paper

Risser L, Vialard F-X, Murgasova M, Holm D, Rueckert Det al., 2010, Large Deformation Diffeomorphic Registration Using Fine and Coarse Strategies, 4th Workshop on Biomedical Image Registration, Publisher: SPRINGER-VERLAG BERLIN, Pages: 186-+, ISSN: 0302-9743

Conference paper

Cotter CJ, Holm DD, 2010, Geodesic boundary value problems with symmetry, J. Geom. Mech., Vol: 2, Pages: 51-68

Journal article

Holm DD, Trouve A, Younes L, 2009, THE EULER-POINCARE THEORY OF METAMORPHOSIS, QUARTERLY OF APPLIED MATHEMATICS, Vol: 67, Pages: 661-685, ISSN: 0033-569X

Journal article

Gay-Balmaz F, Holm DD, Ratiu TS, 2009, VARIATIONAL PRINCIPLES FOR SPIN SYSTEMS AND THE KIRCHHOFF ROD, JOURNAL OF GEOMETRIC MECHANICS, Vol: 1, Pages: 417-444, ISSN: 1941-4889

Journal article

Holm DD, 2009, Euler's fluid equations: Optimal control vs optimization, PHYSICS LETTERS A, Vol: 373, Pages: 4354-4359, ISSN: 0375-9601

Journal article

Holm DD, Putkaradze V, 2009, Nonlocal orientation-dependent dynamics of charged strands and ribbons, COMPTES RENDUS MATHEMATIQUE, Vol: 347, Pages: 1093-1098, ISSN: 1631-073X

Journal article

Holm DD, Tronci C, 2009, GEODESIC VLASOV EQUATIONS AND THEIR INTEGRABLE MOMENT CLOSURES, JOURNAL OF GEOMETRIC MECHANICS, Vol: 1, Pages: 181-208, ISSN: 1941-4889

Journal article

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