Miles H. Wheeler

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I am a Lecturer in Analysis 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

Expository notes and talks

For a more accessible introduction to the sort of work I do, see this expository talk on solitary waves and fronts, or this short introduction to local and global bifurcation theory. The talk is from a series on steady water waves in the ONEPAS seminar, and the notes are from a 2019 lecture to a group of masters students in mathematics and physics.

Papers and preprints

1

RM Chen, S Walsh, and MH Wheeler, Large-amplitude internal fronts in two-fluid systems C. R. Math. Acad. Sci. Paris 358(9-10):1073, 2020. journal (11 pages)

2

VS Krishnamurthy, MH Wheeler, DG Crowdy, and A Constantin, Liouville chains: new hybrid vortex equilibria of the 2D Euler equation, submitted. arxiv (34 pages)

3

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

4

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

5(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)

6

A Constantin, DG Crowdy, VS Krishnamurthy, and MH Wheeler, Stuart-type polar vortices on a rotating sphere, Discrete Contin. Dyn. Syst. 41(1): 201, 2021. journal (15 pages)

7

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

8

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

9

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

10

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)

11

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)

12

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)

13

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

14

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)

15

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

16

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)

17

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)

18

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. journal (5 pages)

19

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)

20

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

21

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

22

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

23

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 2021, University of Bath: Theory of Partial Differential Equations

  • Fall 2020, University of Bath: Advanced Real Analysis

  • 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).

David Lowry-Duda and I also wrote an expository paper aimed an undergraduates which has appeared in the American Mathematical Monthly.

CV

Last updated December 2020

Some figures (mostly from talks)

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An extreme solitary wave solution of the Whitham equation in 3.

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An anti-plane shear front in 4, with a graph of its centerline.

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A family of point vortex equilibria which “collapses” in 5.

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Explicit overturning waves with constant vorticity in 7.

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Speed of solitary waves compared to small periodic waves; see 9 and 20.

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Bore with a critical layer in 10; see 8 (and 1) for large-amplitude bores but without critical layers.

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Streamlines for a hybrid vortex equilibria in 12 and 2; also see 6.

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Vortex patch with streamlines from 11. See here for more plots.

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Waves with multiple fluid layers in 13 and 15.

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An integration by parts argument in 16 and 14

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The angle \(θ\) considered in 19

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A moving planes argument in 17 (also see 18)

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Constructing the global continuum in 22

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Waves with localized pressure forcing, see 21

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Eigenfunction of the Laplacian on the Vicsek set in 23.