Professor James McCoy
Professor
School of Information and Physical Sciences (Mathematics)
- Email:james.mccoy@newcastle.edu.au
- Phone:(02) 4033 9633
Career Summary
Biography
James McCoy completed his PhD in mathematics in 2002 under the supervision of Klaus Ecker at Monash University. The title of his thesis was "The surface area preserving mean curvature flow". After completing post doctoral positions at the Australian National University with Ben Andrews and Neil Trudinger, in 2005 James took up an ARC Postdoctoral Fellowship as part of a joint ARC grant with Ben Andrews. In July that year he moved to the University of Wollongong, combining a lecturing position with his ARC research grant. In January 2018 he moved to the University of Newcastle; in July that year he became Head of Mathematics Discipline at Newcastle. He relinquished this role in early 2020 to take up a secondment to the Vice Chancellor's Academic Excellence team, where he contributed to several projects including the Foundations for Inspiring People. He has since joined the CESE College Board and Academic Senate, was the university's recent ERA Champion for applied mathematics and is a member of the team responsible for development of the university's Athena SWAN silver application. Since 2018 James has been the University of Newcastle Joint Venture Partner representative to the Australian Mathematical Sciences Institute (AMSI), whose mission is to champion the mathematical sciences for Australia's advancement. In 2023 and 2024 James is the Deputy Director of AMSI.
James is a 'geometric analyst' whose main research interests are questions related to curvature driven heat-type flows of hypersurfaces. Such questions include long time existence of globally constrained curvature flows, formation of singularities (where the curvature becomes unbounded) in curvature flows and extension of classical flow solutions beyond singularities using a 'surgery' procedure. Such analysis relies heavily on techniques from differential geometry, partial differential equations (second and higher even order elliptic and parabolic equations) and topology. Most of the relevant differential equations are nonlinear but recently James has worked in settings where the equations are linear, thus permitting different methods of analysis including Fourier series.
James has refereed articles for over 30 international journals, see his record at publons.com
James has reviewed over 140 articles for Math Reviews of the American Mathematical Society, see ams.org/mathscinet and search for "McCoy, James" under "Reviewer".
James has been an Associate Editor of the Journal of the Australian Mathematical Society since 2018 and in 2024 became Deputy Editor. He was also a guest editor of "Geometric Partial Differential Equations in Engineering" for the American Institute for Mathematical Sciences journal "Mathematics in Engineering".
Qualifications
- Doctor of Philosophy, Monash University
- Bachelor of Science (Honours), Monash University
Keywords
- calculus of variations
- curvature flow
- differential geometry
- geometric evolution problems
- mathematical analysis
- mathematical modelling
- partial differential equations
Languages
- English (Mother)
Fields of Research
| Code | Description | Percentage |
|---|---|---|
| 490402 | Algebraic and differential geometry | 30 |
| 490410 | Partial differential equations | 60 |
| 490103 | Calculus of variations, mathematical aspects of systems theory and control theory | 10 |
Professional Experience
UON Appointment
| Title | Organisation / Department |
|---|---|
| Professor | University of Newcastle School of Mathematical and Physical Sciences Australia |
Academic appointment
| Dates | Title | Organisation / Department |
|---|---|---|
| 1/12/2019 - 31/3/2020 | Visiting Professor and Excellence Chair in Pure Mathematics | Okinawa Institute of Science and Technology Japan |
| 15/1/2018 - 31/1/2025 | Honourary Principal Fellow | University of Wollongong School of Mathematics and Applied Statistics Australia |
| 15/1/2018 - 31/12/2021 | Associate Profesor | Faculty of Science | University of Newcastle School of Mathematics & Physical Sciences Australia |
Professional appointment
| Dates | Title | Organisation / Department |
|---|---|---|
| 1/2/2023 - 1/2/2025 | Deputy Director | AMSI Australian Mathematical Sciences Institute Australia |
| 1/7/2005 - 14/1/2018 | Lecturer-Associate Professor | University of Wollongong Australia |
| 1/1/2005 - 31/12/2008 | ARC Postdoctoral Fellow | University of Wollongong Australia |
| 1/4/2002 - 31/12/2004 | Research Associate | Australian National University Centre for Mathematics and its Applications (CMA) Australia |
Invitations
Distinguished Visitor
| Year | Title / Rationale |
|---|---|
| 2019 |
Visiting Professor During this time I held a position as part of the Visiting Mathematics Professors program. |
Thesis Examinations
| Year | Level | Discipline | Thesis |
|---|---|---|---|
| 2019 | PHD | Mathematics | Thesis |
| 2019 | PHD | Mathematics | Thesis |
| 2014 | PHD | Mathematics |
Thesis Examination details not publicly available. |
| 2011 | PHD | Mathematics |
Thesis Examination details not publicly available. |
| 2010 | PHD | Mathematics | Mean curvature flow of graphs with free boundaries |
Publications
For publications that are currently unpublished or in-press, details are shown in italics.
Chapter (4 outputs)
| Year | Citation | Altmetrics | Link | ||
|---|---|---|---|---|---|
| 2019 |
McCoy J, Wheeler G, Wu Y, 'A Sixth Order Curvature Flow of Plane Curves with Boundary
Conditions.', 2017 Matrix Annals, Springer, Switzerland 213-222 (2019) [B1]
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| 2018 |
McCoy JA, Wheeler G, Wu Y, 'A sixth order curvature flow of plane curves with boundary conditions', Elliptic Partial Differential Equations of Second Order: Celebrating 40 Years of Gilbarg and Trudinger s Book, Springer, Unknown (2018)
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| 2016 |
Edwards M, Gerhardt-Bourke A, McCoy J, Wheeler G, Wheeler VM, 'The mechanics of ribbons and möbius bands', The Mechanics of Ribbons and Möbius Bands 191-212 (2016) In this article we investigate the dynamics of special solutions to the surface diffusion flow of idealised ribbons. This reduces to studying the curve diffusion flow for the prof... [more] In this article we investigate the dynamics of special solutions to the surface diffusion flow of idealised ribbons. This reduces to studying the curve diffusion flow for the profile curve of the ribbon.We provide: (1) a complete classification of stationary solutions; (2) qualitative results on shrinkers, translators, and rotators; and (3) an explicit parametrisation of a shrinking figure eight curve.
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| 2011 |
Mccoy J, 'Mathematical modelling of helical protein structure', Protein Structure 105-122 (2011) We review recent work on modelling helical parts of protein structure mathematically. We use classical calculus of variations and consider mathematical energies dependent on the c... [more] We review recent work on modelling helical parts of protein structure mathematically. We use classical calculus of variations and consider mathematical energies dependent on the curvature and torsion of the protein backbone curve. We demonstrate classes of mathematical energies for which a given helix, or all helices, are extremisers. A future goal is to find within these energies some which permit less regular protein backbone curves, as also observed in nature. As a step in this direction we incorporate a new function into the model, dependent on position along the backbone curve, which permits some allowance for variability in structure due to different amino acid components, side chains, or obstacles. © 2011 by Nova Science Publishers, Inc. All rights reserved. |
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Journal article (39 outputs)
| Year | Citation | Altmetrics | Link | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 2024 |
McCoy JA, Otuf I, 'Representation formulae for linear hyperbolic curvature flows', Journal of Differential Equations, 397 166-198 (2024)
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| 2024 | Gazwani M, McCoy J, 'Curvature diffusion of planar curves with generalised Neumann boundary conditions inside cones', Communications on Pure and Applied Analysis, (2024) [C1] | Nova | |||||||||
| 2023 |
McCoy JA, Schrader P, Wheeler G, 'Representation formulae for higher order curvature flows', Journal of Differential Equations, 344 1-43 (2023) [C1] In [25], Smoczyk showed that expansion of convex curves and hypersurfaces by the reciprocal of the harmonic mean curvature gives rise to a linear second order equation for the evo... [more] In [25], Smoczyk showed that expansion of convex curves and hypersurfaces by the reciprocal of the harmonic mean curvature gives rise to a linear second order equation for the evolution of the support function, with corresponding representation formulae for solutions. In this article we consider L2(d¿)-gradient flows for a class of higher-order curvature functionals. These give rise to higher order linear parabolic equations for which we derive similar representation formulae for their solutions. Solutions exist for all time under natural conditions on the initial curve and converge exponentially fast in the smooth topology to multiply-covered circles. We consider both closed, embedded convex curves and closed, convex curves of higher rotation number. We give some corresponding remarks where relevant on open convex curves. We also consider corresponding ¿globally constrained¿ flows which preserve the length or enclosed area of the evolving curve and a higher order approach to the Yau problem of evolving one convex planar curve to another. In an Appendix, we give some related second order results, including a version of the Yau problem for star-shaped curves.
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| 2022 |
McCoy J, Wheeler G, Wu Y, 'High order curvature flows of plane curves with generalised Neumann boundary conditions', Advances in Calculus of Variations, 15 497-513 (2022) [C1] We consider the parabolic polyharmonic diffusion and the L 2-gradient flow for the square integral of the m-th arclength derivative of curvature for regular closed curves evolving... [more] We consider the parabolic polyharmonic diffusion and the L 2-gradient flow for the square integral of the m-th arclength derivative of curvature for regular closed curves evolving with generalised Neumann boundary conditions. In the polyharmonic case, we prove that if the curvature of the initial curve is small in L 2, then the evolving curve converges exponentially in the C 8 topology to a straight horizontal line segment. The same behaviour is shown for the L 2-gradient flow provided the energy of the initial curve is sufficiently small. In each case the smallness conditions depend only on m.
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| 2022 |
McCoy JA, Wheeler GE, Wu Y, 'A Length-Constrained Ideal Curve Flow', QUARTERLY JOURNAL OF MATHEMATICS, 73 685-699 (2022) [C1]
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| 2021 |
McCoy J, 'Contraction of convex hypersurfaces by nonhomogeneous functions of curvature', Journal of Evolution Equations, (2021) [C1]
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| 2020 |
McCoy J, Wheeler G, 'A rigidity theorem for ideal surfaces with flat boundary', Annals of Global Analysis and Geometry, 57 (2020) [C1]
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| 2020 |
Andrews B, McCoy J, Wheeler G, Wheeler V, 'Closed ideal planar curves', Geometry and Topology, 24 1019-1049 (2020) [C1]
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| 2020 |
McCoy J, Wheeler G, Wu Y, 'A sixth order curvature flow with boundary conditions', Tohuko Mathematical Journal, 72 379-393 (2020) [C1]
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| 2020 |
McCoy JA, 'Contracting Self-similar Solutions of Nonhomogeneous Curvature Flows', The Journal of Geometric Analysis, (2020) [C1]
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| 2019 |
McCoy J, Wheeler G, Wu Y, 'Evolution of closed curves by length-constrained curve diffusion', Proceedings of the American Mathematical Society, 147 3493-3506 (2019) [C1]
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| 2018 |
Sripaturad P, Alshamarri NA, Thamwattana N, McCoy JA, Baowan D, 'Willmore energy for joining of carbon nanostructures', PHILOSOPHICAL MAGAZINE, 98 1511-1524 (2018) [C1]
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| 2018 |
Alshammari NA, Thamwattana N, McCoy JA, Baowan D, Cox BJ, Hill JM, 'Modelling joining of various carbon nanostructures using calculus of variations', Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms, 25 307-339 (2018) [C1]
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| 2017 |
Andrews B, Holder A, McCoy J, Wheeler G, Wheeler VM, Williams G, 'Curvature contraction of convex hypersurfaces by nonsmooth speeds', Journal fur die Reine und Angewandte Mathematik, 2017 169-190 (2017) [C1]
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| 2016 |
Andrews B, McCoy J, 'Contraction of convex surfaces by nonsmooth functions of curvature', Communications in Partial Differential Equations, 41 1089-1107 (2016) [C1] ABSTRACT: We consider the motion of convex surfaces with normal speed given by arbitrary strictly monotone, homogeneous degree one functions of the principal curvatures (with no f... [more] ABSTRACT: We consider the motion of convex surfaces with normal speed given by arbitrary strictly monotone, homogeneous degree one functions of the principal curvatures (with no further smoothness assumptions). We prove that such processes deform arbitrary uniformly convex initial surfaces to points in finite time, with spherical limiting shape. This result was known previously only for smooth speeds. The crucial new ingredient in the argument, used to prove convergence of the rescaled surfaces to a sphere without requiring smoothness of the speed, is a surprising hidden divergence form structure in the evolution of certain curvature quantities.
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| 2016 |
Mccoy J, Wheeler G, 'Finite time singularities for the locally constrained willmore flow of surfaces', Communications in Analysis and Geometry, 24 843-886 (2016) [C1] In this paper we study the steepest descent L2-gradient flow of the functional W¿1,¿2 , which is the the sum of the Willmore energy, ¿1-weighted surface area, and ¿2-weighted encl... [more] In this paper we study the steepest descent L2-gradient flow of the functional W¿1,¿2 , which is the the sum of the Willmore energy, ¿1-weighted surface area, and ¿2-weighted enclosed volume, for surfaces immersed in R3. This coincides with the Helfrich functional with zero 'spontaneous curvature'. Our first results are a concentration-compactness alternative and interior estimates for the flow. For initial data with small energy, we prove preservation of embeddedness, and by directly estimating the Euler-Lagrange operator from below in L2 we obtain that the maximal time of existence is finite. Combining this result with the analysis of a suitable blowup allows us to show that for such initial data the flow contracts to a round point in finite time.
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| 2015 |
Ben A, Langford M, McCoy J, 'CONVEXITY ESTIMATES FOR SURFACES MOVING BY CURVATURE FUNCTIONS', JOURNAL OF DIFFERENTIAL GEOMETRY, 99 47-75 (2015)
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| 2015 |
Andrews B, Chen X, Fang H, McCoy J, 'Expansion of Co-Compact Convex Spacelike Hypersurfaces in Minkowski Space by their Curvature', INDIANA UNIVERSITY MATHEMATICS JOURNAL, 64 635-662 (2015)
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| 2015 |
Edwards M, Gerhardt-Bourke A, McCoy J, Wheeler G, Wheeler V-M, 'The Shrinking Figure Eight and Other Solitons for the Curve Diffusion Flow', JOURNAL OF ELASTICITY, 119 191-211 (2015)
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| 2015 |
McCoy JA, Mofarreh FYY, Wheeler V-M, 'Fully nonlinear curvature flow of axially symmetric hypersurfaces', NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 22 325-343 (2015)
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| 2014 |
McCoy JA, Mofarreh FYY, Williams GH, 'Fully nonlinear curvature flow of axially symmetric hypersurfaces with boundary conditions', Annali di Matematica Pura ed Applicata, 193 1443-1455 (2014) Inspired by earlier results on the quasilinear mean curvature flow, and recent investigations of fully nonlinear curvature flow of closed hypersurfaces which are not convex, we co... [more] Inspired by earlier results on the quasilinear mean curvature flow, and recent investigations of fully nonlinear curvature flow of closed hypersurfaces which are not convex, we consider contraction of axially symmetric hypersurfaces by convex, degree-one homogeneous fully nonlinear functions of curvature. With a natural class of Neumann boundary conditions, we show that evolving hypersurfaces exist for a finite maximal time. The maximal time is characterised by a curvature singularity at either boundary. Some results continue to hold in the cases of mixed Neumann¿Dirichlet boundary conditions and more general curvature-dependent speeds.
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| 2014 |
Andrews B, Langford M, McCoy J, 'CONVEXITY ESTIMATES FOR HYPERSURFACES MOVING BY CONVEX CURVATURE FUNCTIONS', ANALYSIS & PDE, 7 407-433 (2014)
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| 2013 |
McCoy J, Wheeler G, 'A classification theorem for Helfrich surfaces', Mathematische Annalen, 357 1485-1508 (2013) In this paper we study the functional W¿1,¿2,, which is the sum of the Willmore energy, ¿1-weighted surface area, and ¿2-weighted volume, for surfaces immersed in R3. This coincid... [more] In this paper we study the functional W¿1,¿2,, which is the sum of the Willmore energy, ¿1-weighted surface area, and ¿2-weighted volume, for surfaces immersed in R3. This coincides with the Helfrich functional with zero 'spontaneous curvature'. Our main result is a complete classification of all smooth immersed critical points of the functional with ¿1=0 and small L2 norm of tracefree curvature, with no assumption on the growth of the curvature in L2 at infinity. This not only improves the gap lemma due to Kuwert and Schätzle for Willmore surfaces immersed in R3 but also implies the non-existence of critical points of the functional satisfying the energy condition for which the surface area and enclosed volume are positively weighted. © 2013 Springer-Verlag Berlin Heidelberg.
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| 2013 |
Andrews B, Langford M, McCoy J, 'Non-collapsing in fully non-linear curvature flows', ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 30 23-32 (2013)
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| 2013 |
Andrews B, McCoy J, Zheng Y, 'Contracting convex hypersurfaces by curvature', CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 47 611-665 (2013)
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| 2012 |
Andrews B, McCoy J, 'CONVEX HYPERSURFACES WITH PINCHED PRINCIPAL CURVATURES AND FLOW OF CONVEX HYPERSURFACES BY HIGH POWERS OF CURVATURE', TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 364 3427-3447 (2012)
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| 2011 |
McCoy J, Wheeler G, Williams G, 'Lifespan theorem for constrained surface diffusion flows', MATHEMATISCHE ZEITSCHRIFT, 269 147-178 (2011)
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| 2011 |
McCoy JA, 'Self-similar solutions of fully nonlinear curvature flows', ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 10 317-333 (2011)
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| 2008 |
Mccoy J, 'Helices for mathematical modelling of proteins, nucleic acids and polymers', JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 347 255-265 (2008)
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| 2008 |
Thamwattana N, McCoy JA, Hill JM, 'Energy density functions for protein structures', QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, 61 431-451 (2008)
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| 2007 |
McCoy JA, 'A Bernstein property of solutions to a class of prescribed affine mean curvature equations', ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 32 147-165 (2007)
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| 2007 |
McCoy JA, 'BERNSTEIN PROPERTIES OF SOLUTIONS TO SOME HIGHER-ORDER EQUATIONS', DIFFERENTIAL AND INTEGRAL EQUATIONS, 20 1153-1166 (2007)
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| 2005 |
McCoy JA, 'Mixed volume preserving curvature flows', CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 24 131-154 (2005)
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| 2004 |
McCoy JA, 'The mixed volume preserving mean curvature flow', MATHEMATISCHE ZEITSCHRIFT, 246 155-166 (2004)
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Conference (6 outputs)
| Year | Citation | Altmetrics | Link | ||
|---|---|---|---|---|---|
| 2020 |
McCoy J, Wheeler G, 'A Rigidity Theorem for Ideal Surfaces with Flat Boundary', 2018 MATRIX Annals, Creswick, Victoria (2020) [E1]
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| 2017 |
Dyer T, Thamwattana N, Cox B, McCoy J, 'ICTAM 2016', Intercalation of carbon nanotubes into a graphene sheet, Montreal, Canada (2017)
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| 2015 | Wheeler V-M, Wheeler G, McCoy JA, Sharples JJ, 'Modelling bushfires using curvature flow', Gold Coast (2015) | ||||
| 2015 |
Wheeler V-M, Wheeler GE, McCoy JA, Sharples JJ, 'Modelling dynamic bushfire spread: perspectives from the theory of curvature flow', 21ST INTERNATIONAL CONGRESS ON MODELLING AND SIMULATION (MODSIM2015), Gold Coast, AUSTRALIA (2015)
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| 2013 |
Wheeler V-M, McCoy JA, Wheeler GE, Sharples JJ, 'Curvature flows and barriers in fire front modelling', 20TH INTERNATIONAL CONGRESS ON MODELLING AND SIMULATION (MODSIM2013), Adelaide, AUSTRALIA (2013)
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| 2013 |
Sharples JJ, Towers IN, Wheeler G, Wheeler V-M, McCoy JA, 'Modelling fire line merging using plane curvature flow', 20TH INTERNATIONAL CONGRESS ON MODELLING AND SIMULATION (MODSIM2013), Adelaide, AUSTRALIA (2013)
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Grants and Funding
Summary
| Number of grants | 22 |
|---|---|
| Total funding | $1,857,518 |
Click on a grant title below to expand the full details for that specific grant.
20242 grants / $31,000
President's International Fellowship Initiative Visiting Fellow$24,000
Funding body: Chinese Academy of Sciences
| Funding body | Chinese Academy of Sciences |
|---|---|
| Project Team | James McCoy, Prof Yong Wei |
| Scheme | President's International Fellowship Initiative |
| Role | Lead |
| Funding Start | 2024 |
| Funding Finish | 2024 |
| GNo | |
| Type Of Funding | International - Competitive |
| Category | 3IFA |
| UON | N |
Deputy Director's Allowance$7,000
Funding body: Australian Mathematical Sciences Institute
| Funding body | Australian Mathematical Sciences Institute |
|---|---|
| Scheme | Deputy Director's allowance |
| Role | Lead |
| Funding Start | 2024 |
| Funding Finish | 2024 |
| GNo | |
| Type Of Funding | External |
| Category | EXTE |
| UON | N |
20232 grants / $10,000
Deputy Director's Allowance$7,000
Funding body: Australian Mathematical Sciences Institute
| Funding body | Australian Mathematical Sciences Institute |
|---|---|
| Scheme | Deputy Director's allowance |
| Role | Lead |
| Funding Start | 2023 |
| Funding Finish | 2023 |
| GNo | |
| Type Of Funding | External |
| Category | EXTE |
| UON | N |
School of Information and Physical Sciences$3,000
Funding body: School of Information and Physical Sciences (SIPS) Course Development Funding
| Funding body | School of Information and Physical Sciences (SIPS) Course Development Funding |
|---|---|
| Project Team | James McCoy, Hamed Ghaffari, Jahne Meyer |
| Scheme | School of Information and Physical Sciences (SIPS) Course Development Funding |
| Role | Lead |
| Funding Start | 2023 |
| Funding Finish | 2023 |
| GNo | |
| Type Of Funding | Internal |
| Category | INTE |
| UON | N |
20211 grants / $3,000
College of Engineering, Science and Environment Lockdown support scheme$3,000
Funding body: College of Engineering, Science and Environment, University of Newcastle
| Funding body | College of Engineering, Science and Environment, University of Newcastle |
|---|---|
| Project Team | James McCoy, Glen Wheeler (University of Wollongong), TBA |
| Scheme | Lockdown support scheme |
| Role | Lead |
| Funding Start | 2021 |
| Funding Finish | 2021 |
| GNo | |
| Type Of Funding | Internal |
| Category | INTE |
| UON | N |
20201 grants / $1,436
Faculty of Science Course Develoment Funds Grant$1,436
Funding body: Faculty of Science | University of Newcastle
| Funding body | Faculty of Science | University of Newcastle |
|---|---|
| Project Team | James McCoy, Hamed Baghal Ghaffari |
| Scheme | Course Development Fund |
| Role | Lead |
| Funding Start | 2020 |
| Funding Finish | 2020 |
| GNo | |
| Type Of Funding | Internal |
| Category | INTE |
| UON | N |
20191 grants / $76,050
Visiting Professor in Mathematics$76,050
Under this scheme I conducted research in second and higher order nonlinear parabolic partial differential equations in geometry and also organised a specialist mini-symposium with over 30 guests from Australia, China, Japan, Korea, Taiwan, the US and UK, see
https://groups.oist.jp/mathprog/yyy-symposium
Funding body: Okinawa Institute of Science and Technology
| Funding body | Okinawa Institute of Science and Technology |
|---|---|
| Project Team | James McCoy |
| Scheme | Visiting Mathematics Professor Program |
| Role | Lead |
| Funding Start | 2019 |
| Funding Finish | 2020 |
| GNo | |
| Type Of Funding | External |
| Category | EXTE |
| UON | N |
20182 grants / $506,332
Parabolic methods for elliptic boundary value problems$311,642
Funding body: ARC (Australian Research Council)
| Funding body | ARC (Australian Research Council) |
|---|---|
| Project Team | Professor James McCoy |
| Scheme | Discovery Projects |
| Role | Lead |
| Funding Start | 2018 |
| Funding Finish | 2020 |
| GNo | G1800524 |
| Type Of Funding | C1200 - Aust Competitive - ARC |
| Category | 1200 |
| UON | Y |
Higher order curvature flow of curves and hypersurfaces$194,690
Funding body: ARC (Australian Research Council)
| Funding body | ARC (Australian Research Council) |
|---|---|
| Project Team | Professor James McCoy, Dr Glen Wheeler, Professor Ben Andrews |
| Scheme | Discovery Projects |
| Role | Lead |
| Funding Start | 2018 |
| Funding Finish | 2018 |
| GNo | G1800523 |
| Type Of Funding | C1200 - Aust Competitive - ARC |
| Category | 1200 |
| UON | Y |
20153 grants / $463,300
Higher order curvature flow of curves and hypersurfaces$450,800
Funding body: ARC (Australian Research Council)
| Funding body | ARC (Australian Research Council) |
|---|---|
| Project Team | James McCoy, Glen Wheeler, Ben Andrews |
| Scheme | Discovery Projects |
| Role | Lead |
| Funding Start | 2015 |
| Funding Finish | 2018 |
| GNo | |
| Type Of Funding | Aust Competitive - Commonwealth |
| Category | 1CS |
| UON | N |
Geometric analysis and curvature flow$10,000
Funding body: University of Wollongong
| Funding body | University of Wollongong |
|---|---|
| Project Team | James McCoy, Glen Wheeler, Valentina-Mira Wheeler |
| Scheme | International Links Grant Scheme |
| Role | Lead |
| Funding Start | 2015 |
| Funding Finish | 2015 |
| GNo | |
| Type Of Funding | Internal |
| Category | INTE |
| UON | N |
Study Leave Assistance Grant$2,500
Funding body: University of Wollongong
| Funding body | University of Wollongong |
|---|---|
| Scheme | Study Leave Assistance Grant |
| Role | Lead |
| Funding Start | 2015 |
| Funding Finish | 2015 |
| GNo | |
| Type Of Funding | Internal |
| Category | INTE |
| UON | N |
20131 grants / $10,000
Curvature flow of surfaces with constraints and boundaries$10,000
Funding body: University of Wollongong
| Funding body | University of Wollongong |
|---|---|
| Scheme | Near miss grant |
| Role | Lead |
| Funding Start | 2013 |
| Funding Finish | 2013 |
| GNo | |
| Type Of Funding | Internal |
| Category | INTE |
| UON | N |
20122 grants / $347,562
New directions in geometric evolution equations$343,562
Funding body: ARC (Australian Research Council)
| Funding body | ARC (Australian Research Council) |
|---|---|
| Project Team | James McCoy, Ben Andrews |
| Scheme | Discovery Projects |
| Role | Lead |
| Funding Start | 2012 |
| Funding Finish | 2014 |
| GNo | |
| Type Of Funding | Aust Competitive - Commonwealth |
| Category | 1CS |
| UON | N |
Study leave assistance grant$4,000
Funding body: University of Wollongong
| Funding body | University of Wollongong |
|---|---|
| Scheme | Study Leave Assistance Grant |
| Role | Lead |
| Funding Start | 2012 |
| Funding Finish | 2012 |
| GNo | |
| Type Of Funding | Internal |
| Category | INTE |
| UON | N |
20111 grants / $2,500
Singularities in fully nonlinear curvature flow$2,500
Funding body: University of Wollongong
| Funding body | University of Wollongong |
|---|---|
| Scheme | Faculty of Informatics Research Development Scheme |
| Role | Lead |
| Funding Start | 2011 |
| Funding Finish | 2011 |
| GNo | |
| Type Of Funding | Internal |
| Category | INTE |
| UON | N |
20101 grants / $6,000
Flow of convex hypersurfaces to spheres by high powers of curvature$6,000
Funding body: University of Wollongong
| Funding body | University of Wollongong |
|---|---|
| Scheme | University Research Council Small Grant Scheme |
| Role | Lead |
| Funding Start | 2010 |
| Funding Finish | 2010 |
| GNo | |
| Type Of Funding | Internal |
| Category | INTE |
| UON | N |
20091 grants / $4,000
Study Leave Assistance Grant$4,000
Funding body: University of Wollongong
| Funding body | University of Wollongong |
|---|---|
| Scheme | Study Leave Assistance Grant |
| Role | Lead |
| Funding Start | 2009 |
| Funding Finish | 2009 |
| GNo | |
| Type Of Funding | Internal |
| Category | INTE |
| UON | N |
20071 grants / $2,500
Helfrich flow of small initial energy surfaces into spheres$2,500
Funding body: University of Wollongong
| Funding body | University of Wollongong |
|---|---|
| Scheme | Faculty of Informatics Research Development Scheme |
| Role | Lead |
| Funding Start | 2007 |
| Funding Finish | 2007 |
| GNo | |
| Type Of Funding | Internal |
| Category | INTE |
| UON | N |
20061 grants / $8,000
Curvature contraction of nonsmooth, weakly convex hypersurfaces into spheres$8,000
Funding body: University of Wollongong
| Funding body | University of Wollongong |
|---|---|
| Scheme | University Research Council Small Grant Scheme |
| Role | Lead |
| Funding Start | 2006 |
| Funding Finish | 2006 |
| GNo | |
| Type Of Funding | Internal |
| Category | INTE |
| UON | N |
20051 grants / $379,838
Singularities and surgery in curvature flows$379,838
Funding body: ARC (Australian Research Council)
| Funding body | ARC (Australian Research Council) |
|---|---|
| Project Team | Ben Andrews, James McCoy |
| Scheme | Discovery Projects |
| Role | Investigator |
| Funding Start | 2005 |
| Funding Finish | 2008 |
| GNo | |
| Type Of Funding | Aust Competitive - Commonwealth |
| Category | 1CS |
| UON | N |
20021 grants / $6,000
The surface area preserving mean curvature flow$6,000
Funding body: Monash University
| Funding body | Monash University |
|---|---|
| Scheme | Postgraduate Publications Award |
| Role | Lead |
| Funding Start | 2002 |
| Funding Finish | 2002 |
| GNo | |
| Type Of Funding | Internal |
| Category | INTE |
| UON | N |
Research Supervision
Number of supervisions
Current Supervision
| Commenced | Level of Study | Research Title | Program | Supervisor Type |
|---|---|---|---|---|
| 2024 | PhD | Study Of CR-Submanifold Of T-Manifold With Focus On Integrability Conditions Of Distributions, Sectional Curvature, Ricci Tensor And Scalar Curvature | PhD (Mathematics), College of Engineering, Science and Environment, The University of Newcastle | Principal Supervisor |
| 2024 | PhD | Cross Curvature Flow: Existence, Uniqueness, and Negative Sectional Curvature | PhD (Mathematics), College of Engineering, Science and Environment, The University of Newcastle | Principal Supervisor |
| 2023 | PhD | Higher Order Semi-discrete Curvature Flows | PhD (Mathematics), College of Engineering, Science and Environment, The University of Newcastle | Principal Supervisor |
| 2022 | PhD | Examining the Efficacy of a Tier 3 Number Sense Intervention for K-2 Students at risk of Mathematical Failure: Implications for Practice & Policy | PhD (Education), College of Human and Social Futures, The University of Newcastle | Co-Supervisor |
| 2022 | PhD | Numerical Solutions Of Higher Order Flow Of Curves | PhD (Mathematics), College of Engineering, Science and Environment, The University of Newcastle | Principal Supervisor |
| 2022 | PhD | Higher Order Curvature Flow of Axially Symmetric Surfaces with Generalised Neumann Boundary Conditions | PhD (Mathematics), College of Engineering, Science and Environment, The University of Newcastle | Principal Supervisor |
Past Supervision
| Year | Level of Study | Research Title | Program | Supervisor Type |
|---|---|---|---|---|
| 2021 | PhD | Higher order curvature flow of planar curves | Mathematics, University of Wollongong | Consultant Supervisor |
| 2017 | PhD | A selection of higher-order parabolic curvature flows | Mathematics, University of Wollongong | Principal Supervisor |
| 2015 | PhD | Fully nonlinear curvature flow of axially symmetric hypersurfaces | Mathematics, University of Wollongong | Principal Supervisor |
| 2015 | PhD | Mathematical modelling in nanotechnology | Mathematical Sciences, University of Wollongong | Principal Supervisor |
| 2009 | PhD | Fourth order geometric evolution equations | Mathematics, University of Wollongong | Principal Supervisor |
Research Projects
Modelling carbon nanostructures 2015 - 2018
In this project we used calculus of variations to model the joining of various carbon nanostructures.
Publications
Sripaturad P, Alshamarri NA, Thamwattana N, McCoy JA, Baowan D, 'Willmore energy for joining of carbon nanostructures', PHILOSOPHICAL MAGAZINE, 98 1511-1524 (2018) [C1]
Alshammari NA, Thamwattana N, McCoy JA, Baowan D, Cox BJ, Hill JM, 'Modelling joining of various carbon nanostructures using calculus of variations', Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms, 25 307-339 (2018) [C1]
Students
| Program | Research Title |
|---|---|
| PhD University of Wollongong |
Mathematical modelling in nanotechnology |
Fire front modelling using curvature flow 2013 - 2015
In this project we modelled fire line merging using flow of planar curves by their curvature, a suitable model for uniform fuel over flat terrain (eg grass fires). We also introduced an evolving surface model that could take into account height dependence from varying topography and fuel properties.
Publications
Wheeler V-M, McCoy JA, Wheeler GE, Sharples JJ, 'Curvature flows and barriers in fire front modelling', 20TH INTERNATIONAL CONGRESS ON MODELLING AND SIMULATION (MODSIM2013), Adelaide, AUSTRALIA (2013)
Sharples JJ, Towers IN, Wheeler G, Wheeler V-M, McCoy JA, 'Modelling fire line merging using plane curvature flow', 20TH INTERNATIONAL CONGRESS ON MODELLING AND SIMULATION (MODSIM2013), Adelaide, AUSTRALIA (2013)
Wheeler V-M, Wheeler GE, McCoy JA, Sharples JJ, 'Modelling dynamic bushfire spread: perspectives from the theory of curvature flow', 21ST INTERNATIONAL CONGRESS ON MODELLING AND SIMULATION (MODSIM2015), Gold Coast, AUSTRALIA (2015)
Modelling protein structure 2007 - 2008
In this project we used calculus of variations to find mathematical energies that would support the regular helical structures commonly seen in proteins.
Publications
Thamwattana N, McCoy JA, Hill JM, 'Energy density functions for protein structures', QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, 61 431-451 (2008)
Mccoy J, 'Helices for mathematical modelling of proteins, nucleic acids and polymers', JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 347 255-265 (2008)
Mccoy J, 'Mathematical modelling of helical protein structure', Protein Structure 105-122 (2011)
Higher order elliptic and parabolic geometric partial differential equations 2007 -
This is a long-term ongoing project covering one of my main research areas: geometrically-inspired higher even order elliptic and parabolic partial differential equations, many eminating from geometric problems in the calculus of variations. I have supervised PhD students in this field and postdoctoral fellows who have gone on to be successful academic mathematicians in their own rights or found lucrative positions working in industry.
We have considered various scenarios of static (elliptic) and evolving (parabolic) curves, surfaces and hypersurfaces, with or without boundaries. Much ongoing work and collaborations continue.
Applications of this work include improving understanding of the Helfrich model for biomembranes such as the red blood cell.
Grants
Higher order curvature flow of curves and hypersurfaces
Funding body: ARC (Australian Research Council)
| Funding body | ARC (Australian Research Council) |
|---|---|
| Scheme | Discovery Projects |
Publications
McCoy JA, 'A Bernstein property of solutions to a class of prescribed affine mean curvature equations', ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 32 147-165 (2007)
McCoy JA, 'BERNSTEIN PROPERTIES OF SOLUTIONS TO SOME HIGHER-ORDER EQUATIONS', DIFFERENTIAL AND INTEGRAL EQUATIONS, 20 1153-1166 (2007)
McCoy J, Wheeler G, Williams G, 'Lifespan theorem for constrained surface diffusion flows', MATHEMATISCHE ZEITSCHRIFT, 269 147-178 (2011)
McCoy J, Wheeler G, 'A classification theorem for Helfrich surfaces', Mathematische Annalen, 357 1485-1508 (2013)
Edwards M, Gerhardt-Bourke A, McCoy J, Wheeler G, Wheeler V-M, 'The Shrinking Figure Eight and Other Solitons for the Curve Diffusion Flow', JOURNAL OF ELASTICITY, 119 191-211 (2015)
Mccoy J, Wheeler G, 'Finite time singularities for the locally constrained willmore flow of surfaces', Communications in Analysis and Geometry, 24 843-886 (2016) [C1]
McCoy JA, Wheeler G, Wu Y, 'A sixth order curvature flow of plane curves with boundary conditions', Elliptic Partial Differential Equations of Second Order: Celebrating 40 Years of Gilbarg and Trudinger s Book, Springer, Unknown (2018)
McCoy J, Wheeler G, Wu Y, 'A sixth order curvature flow with boundary conditions', Tohuko Mathematical Journal, 72 379-393 (2020) [C1]
McCoy J, Wheeler G, 'A rigidity theorem for ideal surfaces with flat boundary', Annals of Global Analysis and Geometry, 57 (2020) [C1]
Students
| Program | Research Title |
|---|---|
| PhD University of Wollongong |
A selection of higher-order parabolic curvature flows |
| PhD University of Wollongong |
Fourth order geometric evolution equations |
Second order fully nonlinear elliptic and parabolic partial differential equations related to curvature flow of hypersurfaces 1999 -
I have worked on second order fully nonlinear curvature flow and associated elliptic problems since I was a PhD student. I continue to work in this area. I have supervised PhD students in this field.
I have worked in particular on globally constrained curvature flows and unconstrained contraction flows. I have considered with collaborators nonsmooth speeds and characterised singular behaviour.
Grants
Singularities and surgery in curvature flows
Funding body: ARC (Australian Research Council)
| Funding body | ARC (Australian Research Council) |
|---|---|
| Scheme | Discovery Projects |
New directions in geometric evolution equations
Funding body: ARC (Australian Research Council)
| Funding body | ARC (Australian Research Council) |
|---|---|
| Scheme | Discovery Projects |
Curvature flow of surfaces with constraints and boundaries
Funding body: University of Wollongong
| Funding body | University of Wollongong |
|---|---|
| Scheme | Near miss grant |
Parabolic methods for elliptic boundary value problems
Funding body: ARC (Australian Research Council)
| Funding body | ARC (Australian Research Council) |
|---|---|
| Project Team | Professor James McCoy |
| Scheme | Discovery Projects |
Flow of convex hypersurfaces to spheres by high powers of curvature
Funding body: University of Wollongong
| Funding body | University of Wollongong |
|---|---|
| Scheme | University Research Council Small Grant Scheme |
Publications
McCoy J, 'The surface area preserving mean curvature flow', Asian Journal of Mathematics, 7 7-30 (2003)
McCoy JA, 'The mixed volume preserving mean curvature flow', MATHEMATISCHE ZEITSCHRIFT, 246 155-166 (2004)
McCoy JA, 'Mixed volume preserving curvature flows', CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 24 131-154 (2005)
McCoy JA, 'A new class of fully nonlinear curvature flows', East Journal on Approximations, 15 349-373 (2009)
McCoy JA, 'Self-similar solutions of fully nonlinear curvature flows', ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 10 317-333 (2011)
Andrews B, McCoy J, 'CONVEX HYPERSURFACES WITH PINCHED PRINCIPAL CURVATURES AND FLOW OF CONVEX HYPERSURFACES BY HIGH POWERS OF CURVATURE', TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 364 3427-3447 (2012)
Andrews B, Langford M, McCoy J, 'Non-collapsing in fully non-linear curvature flows', ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 30 23-32 (2013)
McCoy JA, Mofarreh FYY, Williams GH, 'Fully nonlinear curvature flow of axially symmetric hypersurfaces with boundary conditions', Annali di Matematica Pura ed Applicata, 193 1443-1455 (2014)
Andrews B, Langford M, McCoy J, 'CONVEXITY ESTIMATES FOR HYPERSURFACES MOVING BY CONVEX CURVATURE FUNCTIONS', ANALYSIS & PDE, 7 407-433 (2014)
McCoy JA, Mofarreh FYY, Wheeler V-M, 'Fully nonlinear curvature flow of axially symmetric hypersurfaces', NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 22 325-343 (2015)
Ben A, Langford M, McCoy J, 'CONVEXITY ESTIMATES FOR SURFACES MOVING BY CURVATURE FUNCTIONS', JOURNAL OF DIFFERENTIAL GEOMETRY, 99 47-75 (2015)
Andrews B, Chen X, Fang H, McCoy J, 'Expansion of Co-Compact Convex Spacelike Hypersurfaces in Minkowski Space by their Curvature', INDIANA UNIVERSITY MATHEMATICS JOURNAL, 64 635-662 (2015)
Andrews B, McCoy J, 'Contraction of convex surfaces by nonsmooth functions of curvature', Communications in Partial Differential Equations, 41 1089-1107 (2016) [C1]
Andrews B, Holder A, McCoy J, Wheeler G, Wheeler VM, Williams G, 'Curvature contraction of convex hypersurfaces by nonsmooth speeds', Journal fur die Reine und Angewandte Mathematik, 2017 169-190 (2017) [C1]
Students
| Program | Research Title |
|---|---|
| PhD University of Wollongong |
Fully nonlinear curvature flow of axially symmetric hypersurfaces |
Shape of the red blood cell 2013 -
The shape of the red blood cell is a minimiser of the curvature-dependent Helfrich energy functional which includes several parameters that can permit different minimising shapes. In particular, certain parameter combinations can lead to spherical blood cells instead of the normal biconcave shape; such cells lead to the blood condition named spherocytocis.
Minimisers of the Helfrich functional satisfy a fourth-order Euler Lagrange elliptic partial differential equation that in view of its high order is relatively difficult to analyse. In the early stage of this project, collaborators and I uncovered combinations of the parameters that could lead to spherical minimisers. In the next multidisciplinary stage I will work with colleges in the college of Health, Medicine and Wellbeing to establish relationships between drugs, diet and other environmental features and the parameters in the model. This should lead to greater understanding of the model and the associated blood condition. Knowledge uncovered could be relevant to other conditions including diabetes.
Edit
Professor James McCoy
Position
Professor
School of Information and Physical Sciences
College of Engineering, Science and Environment
Focus area
Mathematics
Contact Details
| james.mccoy@newcastle.edu.au | |
| Phone | (02) 4033 9633 |
Office
| Room | SR-266 |
|---|---|
| Building | SR Building |
| Location | Callaghan University Drive Callaghan, NSW 2308 Australia |