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| − | Michael Meylan is a senior lecturer at the University of Auckland. He completed his Ph.D. under [[Vernon Squire]] | + | Michael Meylan is a Professor at the [http://www.newcastle.edu.au The University of Newcastle]. The wikiwaves site is largely his work. His home page can be found at [https://www.newcastle.edu.au/profile/mike-meylan] |
| − | in 1993 which was concerned with modelling ice floes using linear wave theory.
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| − | He has worked on various problem connected with linear water wave theory in the subsequent time.
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| − | [[Image:Mikem.jpg|thumb|right|Photo taken in 1999]]
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| − | = Research =
| + | [[Category:People|Meylan, Michael]] |
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| − | == PhD Otago 1991 - 1993==
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| − | Mike's PhD thesis concerned a two-dimensional floating elastic plate which was solved
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| − | using a Green function method. The motivation for the solution was to model ice floe
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| − | and at the time he was ignorant of the engineering applications (e.g. [[VLFS]]).
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| − | Mike independently derived the Green function which
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| − | was well known in water waves and goes back to [[John_1950a| John 1950]].
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| − | The derivation method was copied by [[Squire_Dixon_2000a| Squire and Dixon 2000]]
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| − | (based on a close reading of his Phd thesis) for the case, not of a free surface,
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| − | but for a free surface covered by a plate
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| − | The results
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| − | of this research were publised in the ''Journal of Geophysical Research'' were largely
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| − | ignored by later researchers. His Phd thesis probably had a much greater influence, through
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| − | the researchers who followed at Otago and it is continuing to appear in journal citations.
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| − | The solution method using a Green function coupled with a Green function for the plate
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| − | (the later Green function does not extend to three dimensions because of the much
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| − | more complicated boundary conditions which exist). The solution method has been
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| − | superseeded by more efficient methods, most notably the [[Wiener-Hopf]] method developed
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| − | by [[Tim Williams]] and the [[Eigenfunction Matching Method]] (which applied to
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| − | multiple plates) developed by
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| − | [[Kohout_Meylan_Sakai_Hanai_Leman_Brossard_2006a | Kohout et. al. 2006]].
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| − | == Post-Doc in Otago 1994 - 1996 ==
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| − | Mike then extended the two-dimensional solution to a three-dimensional circular elastic plate
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| − | ([[Meylan_Squire_1996a|Meylan and Squire 1996]]).
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| − | This solution again used a Green function method coupled with the eigenfunctions for a circular
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| − | plate (which can be computed in exact form, at least up to solving an equation involving
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| − | Bessel functions. The solution method has been superseeded by [[Peter_Meylan_Chung_2004a | Peter, Meylan and Chung 2004]].
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| − | Mike also developed a method to solve for plates of arbitrary geometry, initially using
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| − | a variational method ([[Meylan_2001a|Meylan 2001]]) and later using the [[Finite Element Method]]
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| − | ([[Meylan_2002a|Meylan 2002]]).
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| − | == Post Doc Auckland 1996 - 1998 ==
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| − | Mike then worked on using the solution for a circular elastic plate to try and construct a model
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| − | for wave scattering in the Marginal Ice Zone ([[Meylan_Squire_Fox_1997a| Meylan, Squire and Fox 1997]]).
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| − | This model was developed independently of the model of [[Masson_LeBlond_1989a | Masson and LeBlond 1989]]
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| − | but shares many similarities with it.
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| − | Mike then began to work on a very abstract (and difficult problems) of an eigenfunction
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| − | expansion method for the non-selfadjoint operator which arises in the scattering model
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| − | of [[Meylan_Squire_Fox_1997a| Meylan, Squire and Fox 1997]]. This work is still
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| − | unpublished although a paper has been submitted. It is not a problem in water wave theory.
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| − | ==Massey University 1999 - 2003 ==
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| − | Mike began working on the [[Time-Dependent Linear Water Wave]] problem.
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| − | He solved for the time-dependent motion of a [[Floating Elastic Plate]]
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| − | on [[Shallow Water]]. The solution was found using a [[Generalised Eigenfunction Expansion]]
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| − | and as a sum over [[Scattering Frequencies]] ([[Meylan_2002b|Meylan 2002]]. This lead to a collaboration with
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| − | [[Christophe Hazard]] and to a solution of the problem of a [[Floating Elastic Plate]]
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| − | on [[Finite Depth Water]].
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| − | [[Cynthia Wang]] worked with Mike as a masters (2000) and Phd student (2001-2003). Her master thesis concerned
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| − | wave scattering by a [[Floating Elastic Plate]] on water of [[Variable Bottom Topography]]
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| − | ([[Wang_Meylan_2002a| Wang and Meylan 2002]]). Cynthia's PhD concerned a higher-order
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| − | coupled [[Boundary Element Method]] [[Finite Element Method]] for the three-dimensional
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| − | [[Floating Elastic Plate]] ([[Wang_Meylan_2004b|Wang and Meylan 2004]]) and applied this
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| − | method to the problem of an [[Infinite Array]] of [[Floating Elastic Plate|Floating Elastic Plates]]
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| − | ([[Wang_Meylan_Porter_2006a|Wang, Meylan and Porter 2006]]).
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| − | Mike developed a method to solve for multiple floes using an extension of the method
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| − | of [[Meylan_2002a|Meylan 2002]]. This was not published but was used to test the
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| − | multiple floe scattering method which was developed with [[Malte Peter]] using [[Kagemoto and Yue Interaction Theory]]
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| − | which was developed during his masters in 2002.
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| − | Specifically, in [[Peter_Meylan_2004a | Peter and Meylan 2004]] the [[Kagemoto and Yue Interaction Theory]] was extended
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| − | to infinite depth and a coherent account of the theory for bodies of arbitrary geometry was given.
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| − | This work required the development of very sophisticated wave scattering code for bodies of
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| − | arbitrary geometry. As a direct result of this work a new expression for the [[Free-Surface Green Function]] was
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| − | developed and this was published separately ([[Peter_Meylan_2004b | Peter and Meylan 2004]]).
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| − | Mike also revisited the problem of a floating circular plate and developed a method
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| − | based on the [[Eigenfunction Matching Method]] ([[Peter_Meylan_Chung_2004a|Peter, Meylan, and Chung 2004]]).
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| − | == Auckland 2003 - present ==
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| − | [[Malte Peter]] and Mike have continued to work together and have developed an alternative method
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| − | for the [[Infinite Array]] based on [[Kagemoto and Yue Interaction Theory]]
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| − | ([[Peter_Meylan_Linton_2006a|Peter, Meylan and Linton 2006]]). This method has been recently
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| − | extended to a [[Semi-Infinite Array]].
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