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 - Created functional contact page and privacy policy.
 - Linked contact page to existing page network.
 - Minor corrections
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@LewisN3142
LewisN3142 committed Nov 27, 2023
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<meta http-equiv="X-UA-Compatible" content="IE=edge">
<meta name="author" content="Lewis Napper">
<meta name="description"
content="Welcome to the personal portfolio of Lewis Napper! This page of his personal portfolio showcases his research applying abstract geometry to problems in mathematical physics, including fluid dynamics and general relativity. Explore the site to find out more!">
content="Welcome to the personal portfolio of Lewis Napper! This page showcases his research applying abstract geometry to problems in mathematical physics, including fluid dynamics and general relativity. Explore the site to find out more!">
<meta name=" robots" content="max-snippet:320, noodp, noydir">
<meta name="viewport" content="width=device-width, initial-scale=1.0, minimum-scale=1.0">

Expand Down Expand Up @@ -54,17 +54,17 @@ <h2> Terms and Conditions </h2>
resulting from use of this information.
</p>
<p>
Please <a href="mailto:ln00216@surrey.ac.uk" rel="noopener noreferrer"
class="external-link under-overlay">contact us</a> if you believe any information herein
Please <a href="../contact_page/contact.html" class="under-overlay internal-link">contact us</a> if you
believe
any information herein
to be
erronious or have issues with links to external material.
</p>
<p>
The material contained within this website is distributed under a
CC-BY-NC-SA license. Should you wish to license material under any other terms, or claim copyright to material
presented
herein, <a href="mailto:ln00216@surrey.ac.uk" rel="noopener noreferrer"
class="external-link under-overlay">contact us</a>.
herein, <a href="../contact_page/contact.html" class="under-overlay internal-link">contact us</a>.
</p>
</div>
</div>
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</ul>
</li>

<li> <!-- Contact Nav -->
<a href="../contact_page/contact.html"> Contact Me </a>
</li>

<li class="buffer-item"> </li> <!-- Blank Element So Scrolling Shows All Links -->
</ul>
</nav>
Expand All @@ -173,8 +177,9 @@ <h2> Research Interests </h2>
<p class="centered-text"> My research interests are many-fold, though predominantly revolve around geometry,
topology, and
PDE
theory, as well as their application to problems in mathematical physics. Feel free to contact
me if
theory, as well as their application to problems in mathematical physics. Feel free to <a
href="../contact_page/contact.html" class="under-overlay under-modal-overlay internal-link">contact me</a>
if
you have any questions or would like to propose a project or collaboration. What follows is a
summary of some of my research, past and present:
</p>
Expand Down Expand Up @@ -772,7 +777,7 @@ <h3> External Contributed Talks </h3>
<b> Monge&ndash;Ampère Geometry of the Navier&ndash;Stokes Equations </b> (23rd
November 2023)
<p class="small-para">
<em> GDR&mdash;GDM Meeting on Differential Geometry and Mechanics <br> International Conference Centre,
<em> GDR-GDM Meeting on Differential Geometry and Mechanics <br> International Conference Centre,
University of Sorbonne, Paris, France
</em>
</p>
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equation for the pressure arising from the Navier&ndash;Stokes equations under the assumptions of
incompressibility and inhomogeneity of density. In particular, we show that the associated
Lychagin&ndash;Rubtsov metric on the phase space of the
flow encodes the Laplacian of pressure, while the pull&mdash;back of this metric to a Lagrangian
flow encodes the Laplacian of pressure, while the pull-back of this metric to a Lagrangian
submanifold (which represents a solution of the origina parital differential equation) has
eigenvalues
and signature determined by the dominance of vorticity and strain. We conclude with comments on how
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<em>
While reviewing the geometry of Monge&ndash;Ampère equations presented by Rubtsov, D'Onofrio, and
Roulstone in earlier seminars of this series, we demonstrate how an associated metric on the phase
space of a two&mdash;dimensional fluid flow encodes the dominance of vorticity and strain. We then
discuss how multi&mdash;symplectic geometry may be used to generalise to fluid flows on Riemannian
manifolds in higher dimensions, culminating in a Weiss&ndash;Okubo&mdashtype criterion in these
space of a two-dimensional fluid flow encodes the dominance of vorticity and strain. We then
discuss how multi-symplectic geometry may be used to generalise to fluid flows on Riemannian
manifolds in higher dimensions, culminating in a Weiss&ndash;Okubo-type criterion in these
cases. Throughout, we make comments on how the signatures and curvatures of our structures may be
interpreted in terms of the geometric and topological properties of vortices.
</em>
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<p class="medium-para">
<em>
In particular, we show that the associated Lychagin&ndash;Rubtsov metric on the phase space of the
flow encodes the Laplacian of pressure, while the pull&mdash;back of this metric to a Lagrangian
flow encodes the Laplacian of pressure, while the pull-back of this metric to a Lagrangian
submanifold (which represents a solution of the origina parital differential equation) has
eigenvalues
and signature determined by the dominance of vorticity and strain. We highlight how this framework
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