James MCCOY, PostDoc Position of University of British Columbia - Vancouver, Vancouver (UBC) | Read 19 publications | Contact James MCCOY 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. I have worked in particular on globally constrained curvature flows and unconstrained contraction flows. 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. A future goal is to find within these energies some which permit less regular protein backbone curves, as also observed in nature. I have worked on second order fully nonlinear curvature flow and associated elliptic problems since I was a PhD student. Erfahren Sie mehr über die Kontakte von James McCoy und über Jobs bei ähnlichen Unternehmen. We prove that such processes deform arbitrary uniformly convex initial surfaces to points in finite time, with spherical limiting shape. We have considered various scenarios of static (elliptic) and evolving (parabolic) curves, surfaces and hypersurfaces, with or without boundaries. Such analysis relies heavily on techniques from differential geometry, partial differential equations (second and higher even order elliptic and parabolic equations) and topology. 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), McCoy JA, 'More Mixed Volume Preserving Curvature Flows', JOURNAL OF GEOMETRIC ANALYSIS, 27 3140-3165 (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), McCoy JA, 'CURVATURE CONTRACTION FLOWS IN THE SPHERE', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 146 1243-1256 (2018), Associate ProfessorSchool of Mathematical and Physical SciencesFaculty of Science, Copyright 2020 CRICOS Provider Number 00109J The University of Newcastle, Australia, Parabolic methods for elliptic boundary value problems, Higher order curvature flow of curves and hypersurfaces, Curvature flow of surfaces with constraints and boundaries, New directions in geometric evolution equations, Singularities in fully nonlinear curvature flow, Flow of convex hypersurfaces to spheres by high powers of curvature, Helfrich flow of small initial energy surfaces into spheres, Curvature contraction of nonsmooth, weakly convex hypersurfaces into spheres, Singularities and surgery in curvature flows, The surface area preserving mean curvature flow, Calculus of Variations, Systems Theory and Control Theory, Okinawa Institute of Science and Technology, Faculty of Informatics Research Development Scheme, University Research Council Small Grant Scheme, Mathematical Sciences, University of Wollongong, Bachelor of Science (Honours), Monash University. This coincides with the Helfrich functional with zero 'spontaneous curvature'. This coincides with the Helfrich functional with zero 'spontaneous curvature'. LinkedIn is the world's largest business network, helping professionals like James Mc Coy discover inside connections to recommended job candidates, industry experts, and business partners. 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]. © Springer Science+Business Media Dordrecht 2015. © 2013 Springer-Verlag Berlin Heidelberg. We review recent work on modelling helical parts of protein structure mathematically. There are 900+ professionals named "James Mccoy", who use LinkedIn to exchange information, ideas, and opportunities. Click on a grant title below to expand the full details for that specific grant. Erfahren Sie mehr über die Kontakte von James McCoy und über Jobs bei ähnlichen Unternehmen. For publications that are currently unpublished or in-press, details are shown in italics. View James Mc Coy’s professional profile on LinkedIn. 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. James McCoy completed his PhD in pure mathematics in 2002 under the supervision of Klaus Ecker at Monash University. We review recent work on modelling helical parts of protein structure mathematically. 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. 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 this article we investigate the dynamics of special solutions to the surface diffusion flow of idealised ribbons. 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". 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]. 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. Sehen Sie sich auf LinkedIn das vollständige Profil an. James has 4 jobs listed on their profile. ABSTRACT: We consider the motion of convex surfaces with normal speed given by arbitrary strictly monotone, homogeneous degr... [more]. Sehen Sie sich das Profil von James McCoy auf LinkedIn an, dem weltweit größten beruflichen Netzwerk. Applications of this work include improving understanding of the Helfrich model for biomembranes such as the red blood cell. Sehen Sie sich das Profil von James McCoy auf LinkedIn an, dem weltweit größten beruflichen Netzwerk. Some results continue to hold in the cases of mixed Neumann¿Dirichlet boundary conditions and more general curvature-dependent speeds. 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. 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).