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<!DOCTYPE html>
<html>
<title>Tyler Meadows</title>
<meta charset="UTF-8">
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<h2 style="text-align:left;"> Tyler Meadows</h2>
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<img src="Images/Tyler.jpg" style="width:100%" alt="Avatar">
</div>
<div class="w3-container">
<p><i class="fa fa-briefcase fa-fw w3-margin-right w3-large w3-text-green"></i>Postdoctoral Fellow</p>
<p><i class="fa fa-briefcase fa-fw w3-margin-right w3-large w3-text-green"></i>University of Idaho</p>
<p><i class="fa fa-home fa-fw w3-margin-right w3-large w3-text-green"></i>Moscow, Idaho</p>
<p><i class="fa fa-envelope fa-fw w3-margin-right w3-large w3-text-green"></i>tmeadows@uidaho.edu</p>
<hr>
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<p class="w3-large"><b><i class="fa fa-asterisk fa-fw w3-margin-right w3-text-green"></i>Recent Projects</b></p>
<p>Partial Nitritation and Anammox</p>
<div class="w3-light-grey w3-round-xlarge w3-small">
<div class="w3-container w3-center w3-round-xlarge w3-green" style="width:25%">
<div class="w3-center w3-text-white">25%</div>
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<p>Radially Symmetric Vortex Solutions to A Ginzburg-Landau Model with Ferromagnetic Interactions</p>
<div class="w3-light-grey w3-round-xlarge w3-small">
<div class="w3=container w3-center w3-round-xlarge w3-green" style="width:80%">80%</div>
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<br>
<p class="w3-large w3-text-theme"><b><i class="fa fa-asterisk fa-fw w3-margin-right w3-text-green"></i>Education</b></p>
<p style="text-align:left;">PhD. Applied Mathematics <span style="float:right;"> McMaster University</span></p>
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<p style = "text-align:left;">MSc. Applied Mathematics <span style="float:right;"> McMaster University</span></p>
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<div class="w3-round-xlarge w3-green" style="height:24px;width:100%"></div>
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<p style = "text-align:left;">BSc. Physics <span style = "float:right;"> Brock University</span></p>
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<div class="w3-round-xlarge w3-green" style="height:24px;width:100%"></div>
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<br>
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<h2 class="w3-text-grey w3-padding-16"><i class="fa fa-certificate fa-fw w3-margin-right w3-xxlarge w3-text-green"></i> Research Interests</h2>
<div class="w3-container">
<h5 class="w3-opacity"><b> Mathematics </b></h5>
<p> My interests lie in the qualitative study of dynamical systems.
A dynamical system, loosely speaking, is a mathematical object
that describes how something will change with time. The dynamical systems
that interest me the most are hybrid dynamical systems that are described by
systems of impulsive differential equations. </p>
<h5 class="w3-opacity"><b> Biology </b> </h5>
<p> I'm interested in ecology and evolution, particularly involving
microbes. </p>
<h5 class="w3-opacity"><b> Physics </b> </h5>
<p>I have done some work studying the conservation laws of motion under a
central force. A conservation law is a statement that some quantity (called a conserved quantity) will not
change over time as the rest of a system changes. A famous example would be
that matter cannot be created or destroyed, this is the law of conservation of matter.
For central force dynamics, there are four conserved quantities; energy, angular momentum,
the Laplace-Runge-Lenz vector, which describes the shape and orientation of the orbit, and
the time between when the particle reaches the maximum distance from the center of motion.
Each conserved quantity can be associated with a Lagrangian symmetry through
<a href="https://en.wikipedia.org/wiki/Noether%27s_theorem">Noether's theorem</a>.</p>
<p>I have also done some work studying the Ginzburg-Landau theory of superconductivity. The GL
theory of superconductivity is an extremely succesful mean-field theory describing the properties of
superconductors. In particular, the theory predicted the formation of a lattice structure of vortices
in superconductors when a strong magnetic field is applied. The
topic of my master's thesis was investigating the vortex structure in a modified Ginzburg-Landau system
that also accounts for ferromagnetic interactions near the superconducting transition temperature. These
interactions are observed in some so-called high-temperature superconductors.</p>
</div>
</div>
<!-- Publications -->
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<h2 class="w3-text-grey w3-padding-16"><i class="fa fa-certificate fa-fw w3-margin-right w3-xxlarge w3-text-green"></i>Publications</h2>
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<h5 class="w3-opacity"><b>In Physics</b></h5>
<h6 class="w3-text-green">
<p> <a href ="https://arxiv.org/pdf/1508.07258"> <i class="fa fa-file-text-o fa-fw w3-margin-left w3-text-green"></i></a> S. Anco, <b>T. Meadows</b>, V. Pascuzzi <i>Some new aspects of first integrals and symmetries for central force dynamics</i> J. Math. Phys. 57 (2016) pp 1-35</p>
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<div class="w3-container">
<h5 class="w3-opacity"><b>In Mathematical Biology</b></h5>
<h6 class="w3-text-green">
<p><a href="http://www.aimspress.com/fileOther/PDF/MBE/mbe-16-01-004.pdf"><i class="fa fa-file-text-o fa-fw w3-margin-left w3-text-green"></i></a> T.H. Hsu, <b>T. Meadows</b>, L. Wang, and G.S.K. Wolkowicz <i>Growth on two limiting essential resources in a self-cycling fermentor</i> Math. Biosci. Eng. 16 (2018) pp 78-100 </p>
<p><a href="https://arxiv.org/abs/1903.01257"><i class="fa fa-file-text-o fa-fw w3-margin-left w3-text-green"></i></a> <b>T. Meadows</b>, M. Weedermann, and G.S.K. Wolkowicz <i>Global analysis of a simplified model of anaerobic digestion and a new result for the chemostat</i> SIAM J. Appl. Math. 79 (2019) pp 668-689 </p>
<p><a href="https://arxiv.org/abs/2004.12242"><i class="fa fa-file-text-o fa-fw w3-margin-left w3-text-green"></i></a> <b>T. Meadows</b>, G.S.K. Wolkowicz, <i>Growth on multiple interactive-essential nutrients in a self-cycling fermentor: an impulsive differential equations approach</i> Nonlinear Anal. Real 56 (2020) 103157 </p>
</p>
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<h2 class="w3-text-grey w3-padding-16"><i class="fa fa-certificate fa-fw w3-margin-right w3-xxlarge w3-text-green"></i> Teaching</h2>
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<h5 class="w3-opacity">2018/2019</h5>
<h6 class="w3-text-green"> Winter 2019</h6>
<p style="text-align:left;"> Math 2C03: Introduction to Differential Equations <span style="float:right;"> Teaching Assistant</span></p>
<h6 class="w3-text-green"> Fall 2018</h6>
<p style="text-align:left;">Math 3F03: Advanced Differential Equations <span style="float:right;"> Teaching Assistant</span></p>
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<h5 class="w3-opacity"> <a href="Teaching.html">More</a></h5>
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