Miles H. Wheeler

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I am a Lecturer in the Department of Mathematical Sciences at the University of Bath. Before coming to Bath, I was a University Assistant at the Faculty of Mathematics at the University of Vienna, and before that I was a postdoc at the Courant Institute of Mathematical Sciences supported by an NSF fellowship. I am interested in partial differential equations coming from fluid mechanics, especially “large-amplitude” solutions that cannot be captured using perturbative techniques.

Email

mw2319@bath.ac.uk

Office

4W 1.12

Office hours

By appointment

News

PhD students

I am happy to be contacted by potential PhD students, who may also find these informal notes useful. They are from a 2019 lecture to a group of masters students in mathematics and physics, and provide a quick introduction to local and global bifurcation theory.

Papers and preprints

1

T Truong, E Wahlén, and MH Wheeler, Global bifurcation of solitary waves for the Whitham equation, submitted. arxiv (38 pages)

2

RM Chen, S Walsh, and MH Wheeler, Global bifurcation of anti-plane shear fronts, submitted. arxiv (21 pages)

3(1,2)

VS Krishnamurthy, MH Wheeler, DG Crowdy, and A Constantin, A transformation between stationary point vortex equilibria, Proc. R. Soc. A. 476:20200310, 2020. postprint, journal (21 pages)

4

A Constantin, DG Crowdy, VS Krishnamurthy, and MH Wheeler, Stuart-type polar vortices on a rotating sphere, to appear in Discrete Contin. Dyn. Syst. journal (15 pages)

5

VM Hur and MH Wheeler, Exact free surfaces in constant vorticity flows, J. Fluid Mech. (Rapids) 896:R1, 2020. postprint, journal (10 pages)

6

RM Chen, S Walsh, and MH Wheeler, Global bifurcation for monotone fronts of elliptic equations, submitted. arxiv (60 pages)

7

V Kozlov, E Lokharu, and MH Wheeler, Nonexistence of subcritical solitary waves, submitted. arxiv (13 pages)

8

RM Chen, S Walsh, and MH Wheeler, Center manifolds without a phase space for quasilinear problems in elasticity, biology, and hydrodynamics, submitted. arxiv (45 pages)

9

Z Hassainia, N Masmoudi, and MH Wheeler, Global bifurcation of rotating vortex patches, Comm. Pure Appl. Math. 73(9):1933, 2020. journal, arxiv (48 pages)

10

VS Krishnamurthy, MH Wheeler, DG Crowdy, and A Constantin, Steady point vortex pair in a field of Stuart-type vorticity, J. Fluid Mech. (Rapids) 874:R1, 2019. journal, preprint (11 pages)

11

MH Wheeler, On stratified water waves with critical layers and Coriolis forces, Discrete Contin. Dyn. Syst. 39(8):4747, 2019. journal, preprint (24 pages)

12

RM Chen, S Walsh, and MH Wheeler, Existence, nonexistence, and asymptotics of deep water solitary waves with localized vorticity, Arch. Rational Mech. Anal., 234(2):595, 2019 journal, arxiv (39 pages)

13

MH Wheeler, Simplified Models for Equatorial Waves with Vertical Structure, Oceanography 31(3):36, 2018. journal (open access) (6 pages)

14

MH Wheeler, Integral and asymptotic properties of solitary waves in deep water, Comm. Pure Appl. Math. 71: 1941–1956, 2018. preprint, arxiv, journal (16 pages)

15

RM Chen, S Walsh, and MH Wheeler, Existence and qualitative theory for stratified solitary water waves, Ann. Inst. H. Poincaré Anal. Non Linéaire 35(2):517, 2017. arxiv, journal (62 pages)

16

RM Chen, S Walsh, and MH Wheeler, On the existence and qualitative theory for stratified solitary water waves, C. R. Math. Acad. Sci. Paris 354(6):601, 2016. announcement (5 pages)

17

WA Strauss and MH Wheeler, Bound on the slope of steady water waves with favorable vorticity, Arch. Rational Mech. Anal. 222:1555, 2016. preprint, arxiv, journal (26 pages)

18

MH Wheeler, The Froude number for solitary water waves with vorticity, J. Fluid Mech. 768:91, 2015. arxiv, journal, (22 pages)

19

MH Wheeler, Solitary water waves of large amplitude generated by surface pressure, Arch. Rational Mech. Anal. 218(2):1131, 2015. preprint, journal, (57 pages)

20

MH Wheeler, Large-amplitude solitary water waves with vorticity. SIAM J. Math. Anal. 45(5):2937, 2013. preprint, journal, (58 pages)

21

S Constantin, RS Strichartz, and M Wheeler, Analysis of the Laplacian and spectral operators on the Vicsek set Commun. Pure Appl. Anal. 10(1):1, 2011. arxiv, journal, website (44 pages)

Teaching

  • Spring 2020, University of Bath: Theory of Partial Differential Equations

  • Summer 2019, University of Vienna: Tutorial on ordinary differential equations.

  • Winter 2018, University of Vienna: Topics in analysis: fluid mechanics

  • Summer 2018, University of Vienna: Tutorial on ordinary differential equations.

  • Winter 2017, University of Vienna: Tutorial on partial differential equations.

  • Fall 2016, NYU: Instructor for Math-UA 325, Analysis I (Section 3).

  • Spring 2015, NYU: Instructor for Math-UA 121, Calculus I (Section 6).

  • Fall 2014, NYU: Instructor for Math-UA 122, Calculus II (Section 3).

  • Fall 2012, Brown University: Instructor (TF) for Math 200, Intermediate (Multivariable, Physics/Engineering) Calculus.

  • Spring 2012, Brown University: Instructor (TF) for Math 200, Intermediate (Multivariable, Physics/Engineering) Calculus.

  • Spring 2012, Brown University: TA for Math 100 (Calculus II).

  • Fall 2010, Brown University: TA for Math 100 (Calculus II).

CV

Last updated May 2020

Some figures (mostly from talks)

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An extreme solitary wave solution of the Whitham equation in 1.

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An anti-plane shear front in 2, with a graph of its centerline.

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A family of point vortex equilibria which “collapses” in 3.

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Explicit overturning waves with constant vorticity in 5.

_images/nosubcrit.png

Speed of solitary waves compared to small periodic waves; see 7 and 18.

_images/bore.png

Bore with a critical layer in 8; see 6 for large-amplitude bores but without critical layers.

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Streamlines for a hybrid vortex equilibria in 10; also see 4.

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Vortex patch with streamlines from 9. See here for more plots.

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Waves with multiple fluid layers in 11 and 13.

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An integration by parts argument in 14 and 12

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The angle \(θ\) considered in 17

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A moving planes argument in 15 (also see 16)

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Constructing the global continuum in 20

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Waves with localized pressure forcing, see 19

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Eigenfunction of the Laplacian on the Vicsek set in 21.