Miles H. Wheeler

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I am a Lecturer (Assistant Professor) 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

Papers and preprints

Also see profiles on arXiv, MathSciNet, Google Scholar, ORCID.

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 (and Section 5 of [7]), 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.

Teaching

For a full list of past teaching see my CV. Recent teaching:

David Lowry-Duda and I wrote an expository paper aimed at undergraduates which appeared in the American Mathematical Monthly and won an award from the MAA.

PhD students

CV

Last updated May 2024

Some figures (mostly from talks)

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Hollow vortices in [3].

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Large-amplitude bores in [5] and [17].

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An overturning solitary wave in [6].

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A generalized solitary wave solution of the Whitham equation in [10].

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Simple mechanical analogy for solitary waves and bores in the survey [7].

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Speed of solitary waves compared to small periodic waves; see [16] and [29].

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Explicit overturning waves with constant vorticity in [19]; also see [8].

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An extreme solitary wave solution of the Whitham equation in [11].

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An anti-plane shear front in [14], with a graph of its centerline.

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Streamlines for a hybrid vortex equilibria in [21] and [13]; also see [15].

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A family of point vortex equilibria which “collapses” in [18]. Also see the August 2020 cover of Proceedings of the Royal Society A!

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Bore with a critical layer in [12].

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An integration by parts argument in [25] and [23]

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A moving planes argument in [26] (also see [27]).

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The angle \(θ\) considered in [28]

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Waves with localized pressure forcing, see [30].

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Vortex patch with streamlines from [20] (also see [9]). See here for more plots.

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Constructing the global continuum in [31].

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Waves with multiple fluid layers in [22], [24], and [4].

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Eigenfunction of the Laplacian on the Vicsek set in [32].