<div dir="ltr"><br clear="all"><div><div dir="ltr" class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div dir="ltr"><br></div><div dir="ltr"><br></div></div></div></div></div></div><div class="gmail_quote"><br><br><div dir="ltr"><div><div style="overflow:auto"><div style="max-height:10000px"><div dir="ltr"><div><div style="overflow:auto"><div style="max-height:10000px"><div dir="ltr"><p style="text-align:center;clear:both"><a href="https://lh3.googleusercontent.com/-ZPFNPh16sR0/Wt39FrXUP-I/AAAAAAAAAaw/3wQunGe20lUopmV_ggfPaDwE9cVAgVzxgCLcBGAs/s1600/image001.jpg" style="margin-left:1em;margin-right:1em" target="_blank"><img src="https://lh3.googleusercontent.com/-ZPFNPh16sR0/Wt39FrXUP-I/AAAAAAAAAaw/3wQunGe20lUopmV_ggfPaDwE9cVAgVzxgCLcBGAs/s1600/image001.jpg" border="0"></a></p><br>
<p class="MsoNormal" style="text-align:center" align="center"><span style="font-family:"Verdana",sans-serif;color:black">DATE:</span><span style="font-size:10.0pt;font-family:"Verdana",sans-serif;color:black"> </span><span style="font-size:13.5pt;font-family:"Verdana",sans-serif;color:black"> </span><b><span style="font-size:18.0pt;font-family:"Verdana",sans-serif">Friday, October 5, 2018</span></b></p>
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<p class="MsoNormal" style="text-align:center" align="center"><span style="font-family:"Verdana",sans-serif;color:black">TITLE:</span><span style="font-size:10.0pt;font-family:"Verdana",sans-serif;color:black"> <br></span></p><p class="MsoNormal" style="text-align:center" align="center"><span style="font-size:10.0pt;font-family:"Verdana",sans-serif;color:black"> <br></span></p><p class="MsoNormal" style="text-align:center" align="center"><font size="6"><span style="font-family:verdana,sans-serif"></span></font></p><p class="MsoNormal" style="text-align:center" align="center"><font size="6"><span style="font-family:verdana,sans-serif"><b><span style="background:white none repeat scroll 0% 0%"></span></b></span></font></p><div style="text-align:center"><span style="font-family:verdana,sans-serif"><font size="6"><b><span></span></b></font></span><span style="font-family:verdana,sans-serif"><font size="6"><b><span>Proper Orthogonal Decomposition (POD) of the flow dynamics for a
viscoelastic fluid in a four-roll mill geometry at the Stokes Limit</span></b></font><br></span><span style="font-family:verdana,sans-serif"><font size="6"><b><span style="font-size:11pt"></span></b> </font></span></div><p class="MsoNormal" style="text-align:center" align="center"><span style="font-family:"Verdana",sans-serif;color:black"> </span></p>
<p class="MsoNormal" style="text-align:center" align="center"><span style="font-family:"Verdana",sans-serif;color:black"><br></span></p><p class="MsoNormal" style="text-align:center" align="center"><span style="font-family:"Verdana",sans-serif;color:black">TIME:</span><span style="font-size:10.0pt;font-family:"Verdana",sans-serif;color:black"> </span><span style="font-size:13.5pt;font-family:"Verdana",sans-serif;color:black"> </span><b><span style="font-size:18.0pt;font-family:"Verdana",sans-serif">3<span style="color:black">:30PM</span></span></b></p>
<p class="MsoNormal" style="text-align:center" align="center"><span style="font-size:10.0pt;font-family:"Verdana",sans-serif;color:black"> </span></p>
<p class="MsoNormal" style="text-align:center" align="center"><span style="font-family:"Verdana",sans-serif;color:black">LOCATION:</span><span style="font-size:10.0pt;font-family:"Verdana",sans-serif;color:black"> <b> </b></span><b><span style="font-size:18.0pt;font-family:"Verdana",sans-serif">GMCS 314</span></b></p>
<p class="MsoNormal" style="text-align:center" align="center"><span style="font-size:10.0pt;font-family:"Verdana",sans-serif;color:black"> </span></p>
<p class="MsoNormal" style="text-align:center" align="center"><span style="font-family:"Verdana",sans-serif;color:black">SPEAKER/BIO:</span><span style="font-size:13.5pt;font-family:"Verdana",sans-serif;color:black"> </span><b><span style="font-size:18.0pt;font-family:"Verdana",sans-serif"></span></b></p><p class="MsoNormal" style="text-align:center" align="center"><font size="4"><span style="font-family:verdana,sans-serif"><b><span><b><span style="font-size:18.0pt;font-family:"Verdana",sans-serif"><span style="color:black"></span></span></b></span></b></span></font><b><span style="font-size:18.0pt;font-family:"Verdana",sans-serif"></span></b><b><span style="font-size:18.0pt;font-family:"Verdana",sans-serif">Paloma Gutierrez, </span></b><b><span style="font-size:18.0pt;font-family:"Verdana",sans-serif">Krener Assistant Professor, <br></span></b></p><p class="MsoNormal" style="text-align:center" align="center"><b><span style="font-size:18.0pt;font-family:"Verdana",sans-serif">Department of Mathmetics, UC Davis <br></span></b><font size="4"><span style="font-family:verdana,sans-serif"><b><span><b><span style="font-size:18.0pt;font-family:"Verdana",sans-serif"><span style="color:black"></span></span></b></span><span></span></b></span></font></p><p class="MsoNormal" style="text-align:center" align="center"><b><span style="font-size:18.0pt;font-family:"Verdana",sans-serif"><br></span></b></p>
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<p class="MsoNormal"><span style="font-family:"Verdana",sans-serif;color:black"><br></span></p><p class="MsoNormal"><span style="font-family:"Verdana",sans-serif;color:black">ABSTRACT:</span></p>
<p><font size="4"><span style="font-family:verdana,sans-serif">Numerical simulations of viscoelastic fluids in the Stokes limit with a
four-roll mill background force were performed at a range of Weissenberg
number (non-dimensional relaxation time).
For small Weissenberg number the flow is steady and symmetric but upon
increasing the Weissenberg number (corresponding to increased
elasticity or flow memory time), the flow becomes unstable leading to a
variety of temporal evolutions to different periodic and aperiodic
solutions. These dynamics were analyzed using a Proper Orthogonal
Decomposition (POD) that extracted elastic modes in terms of their
contribution to the energy of the system. The temporal behavior of the
system, captured by the decomposition, indicates that the motion of the
stagnation points drives the different flow transitions. In particular, a
transition to an asymmetric state occurs when the extensional
stagnation points lose their pinning to the background forcing. A
further transition to higher frequency modal dynamics occurs when the
stagnation points that were initially tied by the forcing to the centers
of the rolls, begin to move. The relative frequencies of the motion of
these stagnation points is a critical factor in determining the
complexity of the flow, measured by the number of modes needed to
capture most of the energy in the system. Even when the flows are more
complex a small number of modes is sufficient to capture the time
evolution of these flows, demonstrating the usefulness of the POD
applied to viscoelastic fluids at the Stokes limit.</span></font></p>
<h2><span></span><span style="font-size:11.0pt;font-family:"Verdana",sans-serif;font-weight:normal"><span></span></span><span><span style="font-size:11.0pt;font-family:"Verdana",sans-serif;font-weight:normal"></span></span></h2>
<h2><span> </span></h2>
<h2><span style="font-size:11.0pt;font-family:"Verdana",sans-serif;color:black;font-weight:normal">HOST:</span><span style="font-family:"Verdana",sans-serif;color:#1f497d"> </span>Gustaaf Jacobs</h2></div></div></div></div></div></div></div></div></div>
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