<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><div dir="ltr"><div><br></div></div></div></div></div></div></div></div><div class="gmail_quote"><br><br><div><div><div style="overflow:auto"><div style="max-height:10000px"><div dir="ltr"><p style="text-align:center;clear:both"><img src="cid:70e1252e-469c-4258-aed9-e7c61d0ddb05" alt="SDSU_CSRC Logo.jpg" style="margin-left:1em;margin-right:1em"></p><p class="MsoNormal" align="center" style="color:rgba(0,0,0,0.87);font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;font-size:14px;text-align:center"><span style="color:black"><font face="verdana, sans-serif"><br></font></span></p><p class="MsoNormal" align="center" style="color:rgba(0,0,0,0.87);font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;font-size:14px;text-align:center"><span style="color:black"><font face="verdana, sans-serif"><br>DATE:</font></span><font face="verdana, sans-serif"><span style="font-size:10pt;color:black"> </span><span style="font-size:13.5pt;color:black"> <br></span><b><font size="4">Friday, October 30, 2020</font></b></font></p><p class="MsoNormal" align="center" style="color:rgba(0,0,0,0.87);font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;font-size:14px;text-align:center"><b><span style="font-size:18pt"><font face="verdana, sans-serif"><br></font></span></b></p><p class="MsoNormal" align="center" style="color:rgba(0,0,0,0.87);font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;font-size:14px;text-align:center"><font face="verdana, sans-serif"><span style="font-size:10pt;color:black"></span></font></p><p class="MsoNormal" align="center" style="color:rgba(0,0,0,0.87);font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;font-size:14px;text-align:center"><span style="color:black"><font face="verdana, sans-serif"><br></font></span></p><div dir="ltr" style="color:rgba(0,0,0,0.87)"><p class="MsoNormal" align="center" style="font-size:14px;font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;text-align:center"><font face="verdana, sans-serif"><span style="font-size:10pt;color:black"></span></font></p><p class="MsoNormal" align="center" style="font-size:14px;font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;text-align:center"><font face="verdana, sans-serif"><span style="color:black"></span></font></p><p class="MsoNormal" align="center" style="font-size:14px;font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;text-align:center"><font face="verdana, sans-serif"><span style="color:black">TITLE:</span><span style="font-size:10pt;color:black"><br></span></font></p><p class="MsoNormal" align="center" style="font-size:14px;font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;text-align:center"><font face="verdana, sans-serif"><span style="font-size:10pt;color:black"></span></font></p><p class="MsoNormal" align="center" style="font-size:14px;font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;text-align:center"><font size="6" face="verdana, sans-serif"></font></p><p class="MsoNormal" align="center" style="font-size:14px;font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;text-align:center"><font size="6" face="verdana, sans-serif"><b><span style="background-image:none;background-position:0% 0%;background-repeat:repeat"></span></b></font></p><div style="text-align:center"><p class="MsoNormal" align="center"><font face="verdana, sans-serif" size="4"><b>Alternatives to the Beta Distribution in Assumed PDF Methods for Turbulent Reactive Flow</b></font><font face="verdana, sans-serif" size="4"><b> </b></font></p></div><div style="font-size:14px;font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;text-align:center"><font face="verdana, sans-serif"><font size="6"><b><br></b></font><font size="6"><b></b></font></font><p class="MsoNormal"><b><font face="verdana, sans-serif"><span style="font-size:11pt;color:black"></span></font></b></p><font face="verdana, sans-serif"><font size="6"><b></b></font><font size="6"><b><span style="font-size:12pt"></span></b></font><font size="6"><b></b></font><font size="6"><b><span style="font-size:11pt"></span></b></font></font></div><p class="MsoNormal" align="center" style="font-size:14px;font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;text-align:center"><font face="verdana, sans-serif"><span style="color:black"></span></font></p><p class="MsoNormal" align="center" style="font-size:14px;font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;text-align:center"><font face="verdana, sans-serif"><span style="color:black"></span></font></p><p class="MsoNormal" align="center" style="font-size:14px;font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;text-align:center"><span style="color:black"><font face="verdana, sans-serif"><br></font></span></p><p class="MsoNormal" align="center" style="font-size:14px;font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;text-align:center"><font face="verdana, sans-serif"><span style="color:black">TIME:</span><span style="font-size:10pt;color:black"> </span><span style="font-size:13.5pt;color:black"> <br></span><b><font size="4">3:30-4:30PM</font></b></font></p><p class="MsoNormal" align="center" style="font-size:14px;font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;text-align:center"><font face="verdana, sans-serif"><br><b><span style="font-size:18pt"><span style="color:black"></span></span></b></font></p><p class="MsoNormal" align="center" style="font-size:14px;font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;text-align:center"><span style="font-size:10pt;color:black"><font face="verdana, sans-serif"> </font></span></p><p class="MsoNormal" align="center" style="text-align:center"><font style="font-size:14px;font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif"><span style="color:black">LOCATION:<br></span><font size="4" style="font-weight:bold"><span style="color:black">Join Zoom Meeting -  </span></font></font><a href="https://sdsu.zoom.us/j/91071174391" title="https://SDSU.zoom.us/j/91071174391" target="_blank"><font face="verdana, sans-serif" size="4"><b>https://SDSU.zoom.us/j/91071174391</b></font></a><font style="font-size:14px;font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif"><font size="4"><font color="#000000"><br></font></font><span style="font-weight:bold"><font size="4"><br></font></span></font></p><p class="MsoNormal" align="center" style="font-size:14px;font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;text-align:center"><span style="font-size:10pt;color:black"><font face="verdana, sans-serif"> </font></span></p><p class="MsoNormal" align="center" style="font-size:14px;font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;text-align:center"><font face="verdana, sans-serif"><span style="color:black"></span></font></p><p class="MsoNormal" align="center" style="font-size:14px;font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;text-align:center"><font face="verdana, sans-serif"><span style="color:black">SPEAKER/BIO:</span><span style="font-size:13.5pt;color:black"> </span></font></p><p class="MsoNormal" align="center" style="text-align:center"><font face="verdana, sans-serif" size="4"><b>Dr. Pavel Popov, Aerospace Engineering, San Diego State University </b></font>             <font face="verdana, sans-serif"><br></font></p><p class="MsoNormal" align="center" style="font-size:14px;font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;text-align:center"><font size="4" face="verdana, sans-serif"><b><b><span style="font-size:18pt"><span style="color:black"></span></span></b></b></font></p><p class="MsoNormal" align="center" style="font-size:14px;font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;text-align:center"><b><font face="verdana, sans-serif"><span style="font-size:18pt"></span></font></b></p><p class="MsoNormal" align="center" style="font-size:14px;font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;text-align:center"><span style="color:black"><font face="verdana, sans-serif"> </font></span></p><p class="MsoNormal" style="font-size:14px;font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif"><font size="2" face="verdana, sans-serif"><span style="color:black"><br></span></font></p><p class="MsoNormal" style="font-size:14px;font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif"><font size="2" face="verdana, sans-serif"><span style="color:black"><br></span></font></p><p class="MsoNormal" style="font-size:14px;font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;text-align:center"><span style="color:black"><font size="2" face="verdana, sans-serif">ABSTRACT:</font></span></p></div><div dir="ltr" style="color:rgba(0,0,0,0.87);font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;font-size:14px"><font face="verdana, sans-serif"><br></font></div><div><div></div></div><div dir="ltr" style="color:rgba(0,0,0,0.87)"><font face="verdana, sans-serif" size="4"><span style="color:rgb(34,34,34)"><br></span></font></div><div><div>
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          <div dir="ltr" style="color:rgba(0,0,0,0.87)"><span style="color:rgb(34,34,34)"><font face="verdana, sans-serif" size="4">Due to their low computational cost, assumed probability density 
function (PDF) methods, such as the flamelet-progress variable (FPV) 
method, are widely used for combustion simulations. To model the subgrid
 variation of mixture fraction, assumed PDF methods generally use the 
beta distribution or one of its multivariate extensions. This work 
addresses a shortcoming of the beta distribution when applied to this 
setting. Regardless of parameter values, the beta distribution contains 
the entire sample space of a conserved scalar, which can be shown to 
violate the maximum principle of elliptic partial differential 
equations. To remedy this, a new class of PDF is introduced and tested 
on a conserved scalar mixing problem. The new PDF do not violate the 
maximum principle, and are in better quantitative agreement than the 
beta distribution with a transported PDF solution, which is inherently 
more accurate than assumed PDF solutions. The effects of residence time 
are examined, and extensions to multiple mixture fractions are outlined.</font></span><font face="verdana, sans-serif" size="4"><span style="color:rgb(34,34,34)"> </span><span style="color:rgb(34,34,34)">  </span></font><span style="font-family:"Times New Roman",serif;color:rgb(34,34,34)"> </span><font face="verdana, sans-serif" size="4"> </font><font face="verdana, sans-serif" size="4"><br></font><font face="verdana, sans-serif"><br></font></div><div dir="ltr" style="color:rgba(0,0,0,0.87);font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;font-size:14px"><font size="4" face="verdana, sans-serif"> <br></font></div><div dir="ltr" style="color:rgba(0,0,0,0.87);font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;font-size:14px"><font size="4" face="verdana, sans-serif"><br></font><p class="MsoNormal" style="margin:0in 5.2pt 0.0001pt 0in;line-height:13.91px"><font face="verdana, sans-serif"><br></font></p><font size="4" face="verdana, sans-serif"></font></div><font face="verdana, sans-serif" style="font-size:14px"><font size="4"><font color="#000000">Host:</font><font color="rgba(0, 0, 0, 0.870588235294118)"> </font><font color="#000000">Jose Castillo</font></font><br></font><div style="color:rgba(0,0,0,0.87);font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;font-size:14px"><font size="4" face="verdana, sans-serif"><br></font></div><div style="color:rgba(0,0,0,0.87);font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;font-size:14px"><p class="MsoNormal"><font face="verdana, sans-serif" size="4"><span style="font-weight:bold">Note:</span><span style="font-weight:bold"> </span>Videos of previous colloquium talks<span style="text-align:center"> can be seen on the CSRC website in the colloquium archive section or on the </span><a href="https://www.youtube.com/channel/UCN0ZEztlmyDqG2pm-Rle_Eg/feed" rel="nofollow" style="color:rgb(26,115,232);text-align:center" target="_blank">CSRC YouTube page here</a><span style="text-align:center">.</span></font></p><p class="MsoNormal"><font face="verdana, sans-serif" size="4"><span style="text-align:center"><br><br></span></font></p><p class="MsoNormal"><font face="verdana, sans-serif" size="4"><span style="text-align:center"><br></span></font></p></div></div></div></div></div><div></div><div></div></div><div><div></div></div><div><div><div style="display:inline-block"></div><div></div></div></div>

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