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    <div class="moz-cite-prefix">Hi Alok,</div>
    <div class="moz-cite-prefix"><br>
    </div>
    <div class="moz-cite-prefix">First of all I think you should
      increase the number of steps per Arnoldi iteration (p109) even
      more, for example multiplying it by 4. The columns 2 and 3 (
      re(RITZ) and im(RITZ)) show that the operator seen by ARPACK is
      close to identity, all the Ritz values are close to 1.</div>
    <div class="moz-cite-prefix"><br>
    </div>
    <div class="moz-cite-prefix">I forgot to mention this earlier, but
      it might also converge faster if you increase the Krylov space
      size p111 to 120 (four times the number of eigenvalues that you
      request).</div>
    <div class="moz-cite-prefix"><br>
    </div>
    <div class="moz-cite-prefix">Regarding the 0 frequency modes, I
      often see them related to boundaries. I am not exactly sure where
      they come from. It is difficult to say anything without seeing
      what the eigenvectors look like.<br>
    </div>
    <div class="moz-cite-prefix"><br>
    </div>
    <div class="moz-cite-prefix">Regards,</div>
    <div class="moz-cite-prefix">Guillaume</div>
    <div class="moz-cite-prefix"><br>
    </div>
    <div class="moz-cite-prefix">On 30/10/2018 06:40, nek5000-users---
      via Nek5000-users wrote:<br>
    </div>
    <blockquote type="cite"
cite="mid:mailman.13585.1540878088.86639.nek5000-users@lists.mcs.anl.gov">
      <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
      <div dir="ltr">
        <div dir="ltr">Hi Guillaume,
          <div><br>
          </div>
          <div>I tried with the help of your valuable suggestions. I am
            getting dominant Eigenvalue with time period 8.34 which is
            very much close to the literature. However, I require 30
            Eigen values by setting P112=30 and P111=90. Below is the
            eigenvalues I am getting after many restarts.</div>
          <div><br>
          </div>
          <div>
            <div>                                            re(RITZ);  
                                  im(RITZ)<span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">                </span> 
                          ln|RITZ|;                                
              arg(RITZ)</div>
            <div>           1  <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">                         </span>0.991128702238537
                    0.150881402754817     <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">             </span>1.272083634754888E-002
                  0.755360071443281     </div>
            <div>           2  <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">                         </span>0.991128702238537
                   -0.150881402754817     <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">             </span>1.272083634754888E-002
                 -0.755360071443281     </div>
            <div>           3  <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">                         </span>0.991728721496092
                    1.806383192432841E-002<span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">       </span>-4.069909517841635E-002
                  9.106237555496137E-002</div>
            <div>           4  <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">                         </span>0.991728721496092
                   -1.806383192432841E-002<span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">       </span>-4.069909517841635E-002
                 -9.106237555496137E-002</div>
            <div>           5  <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">                         </span>0.989791831070271
                    3.446186469202143E-002<span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">       </span>-4.827437507304033E-002
                  0.174016133198715     </div>
            <div>           6  <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">                         </span>0.989791831070271
                   -3.446186469202143E-002<span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">       </span>-4.827437507304033E-002
                 -0.174016133198715     </div>
            <div>           7  <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">                         </span>0.987601103156919
                    5.049392478862426E-000<span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">       </span>-5.585540570484418E-002
                  0.255416865677410     </div>
            <div>           8  <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">                         </span>0.987601103156919
                   -5.049392478862426E-002<span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">       </span>-5.585540570484418E-002
                 -0.255416865677410     </div>
            <div>           9  <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">                         </span>0.995627135254111
                    0.000000000000000E+000<span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">       </span>-2.191226841613384E-002
                  0.000000000000000E+000</div>
            <div>          10  <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">         </span>0.995700191328997
                    0.000000000000000E+000<span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">       </span>-2.154539716426180E-002
                  0.000000000000000E+000</div>
            <div>          11  <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">         </span>0.995229254767405
                    0.000000000000000E+000<span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">       </span>-2.391080780851450E-002
                  0.000000000000000E+000</div>
            <div>          12  <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">         </span>0.995434205850176
                    0.000000000000000E+00<span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">        </span>-2.288124611941097E-002
                  0.000000000000000E+000</div>
            <div>          13  <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">         </span>0.994877066906734
                    0.000000000000000E+000<span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">       </span>-2.568050152041379E-002
                  0.000000000000000E+000</div>
            <div>          14  <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">         </span>0.994526533813701
                    0.000000000000000E+000<span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">       </span>-2.744250243633435E-002.
                 0.000000000000000E+000</div>
            <div>          15  <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">         </span>0.994024234181460
                    0.000000000000000E+000<span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">       </span>-2.996846079257938E-002.
                 0.000000000000000E+000</div>
            <div>          16  <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">         </span>0.992886352948494
                    0.000000000000000E+000<span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">       </span>-3.569534837742794E-002
                  0.000000000000000E+000</div>
            <div>          17  <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">         </span>0.993531725861019
                    0.000000000000000E+000<span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">       </span>-3.244642035911912E-002
                  0.000000000000000E+000</div>
            <div>          18  <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">         </span>0.992269436061858
                    0.000000000000000E+000<span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">       </span>-3.880299821483946E-002
                  0.000000000000000E+000</div>
            <div>          19  <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">         </span>0.991568951835935
                    0.000000000000000E+000<span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">       </span>-4.233395244633451E-002
                  0.000000000000000E+000</div>
            <div>          20  <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">         </span>0.991491977086931
                    0.000000000000000E+000<span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">       </span>-4.272211373739676E-002
                  0.000000000000000E+000</div>
            <div>          21  <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">         </span>0.991513431383682
                    0.000000000000000E+000<span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">       </span>-4.261392292430112E-002
                  0.000000000000000E+000</div>
            <div>          22  <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">         </span>0.991180149347166
                    0.000000000000000E+00<span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">        </span>-4.429487878603097E-002
                  0.000000000000000E+000</div>
            <div>          23  <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">         </span>0.991284115416627
                    0.000000000000000E+000<span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">       </span>-4.377045031887505E-002
                  0.000000000000000E+000</div>
            <div>          24  <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">         </span>0.990874009258556
                    0.000000000000000E+000<span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">       </span>-4.583943845265666E-002
                  0.000000000000000E+000</div>
            <div>          25  <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">         </span>0.990632850108536
                    0.000000000000000E+000<span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">       </span>-4.705648774052894E-002
                  0.000000000000000E+000</div>
            <div>          26  <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">         </span>0.990852910254318
                    0.000000000000000E+000<span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">       </span>-4.594590622089855E-002.
                 0.000000000000000E+000</div>
            <div>          27  <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">         </span>0.990206173286647
                    0.000000000000000E+000<span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">       </span>-4.921050845320660E-002
                  0.000000000000000E+000</div>
            <div>          28  <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">         </span>0.990051445648789
                    0.000000000000000E+000<span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">       </span>-4.999185950921724E-002
                  0.000000000000000E+000</div>
            <div>          29  <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">         </span>0.989332783273003
                    0.000000000000000E+000<span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">       </span>-5.362259677015029E-002
                  0.000000000000000E+000</div>
            <div>          30  <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">         </span>0.989848247701740
                    0.000000000000000E+000<span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">       </span>-5.101816376314156E-002
                  0.000000000000000E+000</div>
            <div>          31  <span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">         </span>0.989278105749528
                    0.000000000000000E+000<span class="m_-1585782076635606836gmail-m_-3742669899213310607gmail-Apple-tab-span" style="white-space:pre-wrap">       </span>-5.389893975295782E-002
                  0.000000000000000E+000</div>
          </div>
          <div><br>
          </div>
          <div>   I am unable to understand the reason behind getting so
            many Eigenvalues with zero imaginary part/rotation. Please
            help.</div>
          <div><br>
          </div>
          <div>Regards,</div>
        </div>
        <br>
        <div class="gmail_quote">
          <div dir="ltr">On Wed, Oct 3, 2018 at 2:54 PM <<a
              href="mailto:nek5000-users@lists.mcs.anl.gov"
              target="_blank" moz-do-not-send="true">nek5000-users@lists.mcs.anl.gov</a>>
            wrote:<br>
          </div>
          <blockquote class="gmail_quote" style="margin:0 0 0
            .8ex;border-left:1px #ccc solid;padding-left:1ex">
            <div text="#000000" bgcolor="#FFFFFF">
              <div
                class="m_-1585782076635606836m_9031516644251136374moz-cite-prefix">Hi,</div>
              <div
                class="m_-1585782076635606836m_9031516644251136374moz-cite-prefix"><br>
              </div>
              <div
                class="m_-1585782076635606836m_9031516644251136374moz-cite-prefix">What
                is your time step? I calculated the spectrum of the
                cylinder flow a while ago at Re=44 and I got an angular
                frequency of 0.7278, which corresponds to a period of
                8.63.<br>
              </div>
              <div
                class="m_-1585782076635606836m_9031516644251136374moz-cite-prefix">It
                is possible that 40 time steps per Arnoldi iteration is
                too small; a good start is to integrate for 1/10th of
                the period, so dt*p109 = 0.8 approximately. I used 120
                time steps at dt=4.2e-3 but it may be faster with more
                steps.<br>
              </div>
              <div
                class="m_-1585782076635606836m_9031516644251136374moz-cite-prefix">It
                depends on which frequencies you want to resolve; if you
                integrate for a short time your operator is close to
                identity and all eigenvalues are close to 1, but if you
                integrate for too long then the frequencies of the
                eigenvalues you are interested in will be aliased.</div>
              <div
                class="m_-1585782076635606836m_9031516644251136374moz-cite-prefix"><br>
              </div>
              <div
                class="m_-1585782076635606836m_9031516644251136374moz-cite-prefix">I
                think you could try decreasing p021 and p022 to maybe
                1e-10 or 1e-12 and see if helps, too.<br>
              </div>
              <div
                class="m_-1585782076635606836m_9031516644251136374moz-cite-prefix"><br>
              </div>
              <div
                class="m_-1585782076635606836m_9031516644251136374moz-cite-prefix">Best,</div>
              <div
                class="m_-1585782076635606836m_9031516644251136374moz-cite-prefix">Guillaume<br>
              </div>
              <div
                class="m_-1585782076635606836m_9031516644251136374moz-cite-prefix"><br>
              </div>
              <div
                class="m_-1585782076635606836m_9031516644251136374moz-cite-prefix">On
                03/10/2018 07:24, <a
class="m_-1585782076635606836m_9031516644251136374moz-txt-link-abbreviated"
                  href="mailto:nek5000-users@lists.mcs.anl.gov"
                  target="_blank" moz-do-not-send="true">nek5000-users@lists.mcs.anl.gov</a>
                wrote:<br>
              </div>
              <blockquote type="cite">
                <div dir="ltr">
                  <div dir="ltr">
                    <div dir="ltr">
                      <div dir="ltr">
                        <div dir="ltr">
                          <div dir="ltr">
                            <div dir="ltr"><span
                                class="m_-1585782076635606836m_9031516644251136374gmail-im"
                                style="color:rgb(80,0,80)">Hi Guillaume,
                                <div><br>
                                </div>
                                <div>Thanks for your reply. My reply to
                                  your queries is as below:-</div>
                                <div><br>
                                </div>
                              </span>
                              <div>1) I am getting unstable pair of
                                Eigen values with growth rate around
                                0.02.</div>
                              <span
                                class="m_-1585782076635606836m_9031516644251136374gmail-im"
                                style="color:rgb(80,0,80)">
                                <div>2) Solver tolerance that I used are
                                  ;</div>
                                <div>
                                  <div>  7.00000              p020
                                    NORDER</div>
                                  <div>  0.100000E-09    p021 DIVERGENCE</div>
                                  <div>  0.100000E-09.   p022 HELMHOLTZ</div>
                                  <div>   0.00000             p023
                                    NPSCAL</div>
                                  <div>  0.100000E-09    p024 TOLREL</div>
                                  <div>  0.100000E-04    p025 TOLABS</div>
                                </div>
                              </span>
                              <div>1.00000E-05.       p113 : ARNOLDI:
                                arpack tolerance</div>
                              <div><br>
                              </div>
                              <div><br>
                              </div>
                              <div>3) Boundary conditions are :</div>
                              <div><br>
                              </div>
                              <div>I am using sponge strength at inlet
                                and outlet with following details in
                                .rea file</div>
                              <div>
                                <div>   1.00000     p119 : SPONGE
                                  STRENGTH</div>
                                <div>   25.0000     p120 : SPONGE TOTAL
                                  WIDTH</div>
                                <div>   3.00000     p121 : SPONGE DROP
                                  WIDTH (INFLOW)</div>
                                <div>   5.00000     p122 : SPONGE RISE
                                  WIDTH (OUTFLOW) </div>
                              </div>
                              <div>the sponge function and its cal is
                                detailed in userf subroutine of .usr
                                file</div>
                              <div><br>
                              </div>
                              <div>Also following is defined in .usr
                                file</div>
                              <div>
                                <div>c-----------------------------------------------------------------------</div>
                                <div>      subroutine userbc
                                  (ix,iy,iz,iside,eg)</div>
                                <div><br>
                                </div>
                                <div>      include 'SIZE'</div>
                                <div>      include 'NEKUSE'          !
                                  UX, UY, UZ, TEMP, X, Y</div>
                                <div>      include 'PARALLEL'        !
                                  GLLEL</div>
                                <div><br>
                                </div>
                                <div><br>
                                </div>
                                <div>      integer e,eg</div>
                                <div><br>
                                </div>
                                <div>c     velocity</div>
                                <div>c      e  =  GLLEL(eg)</div>
                                <div>      UX = 0.0</div>
                                <div>      UY = 0.0</div>
                                <div>      UZ = 0.0</div>
                                <div><br>
                                </div>
                                <div>c     t</div>
                                <div>      TEMP=0.0</div>
                                <div><br>
                                </div>
                                <div>      return</div>
                                <div>      end</div>
                                <div>c-----------------------------------------------------------------------</div>
                                <div>      subroutine useric
                                  (ix,iy,iz,ieg)</div>
                                <div><br>
                                </div>
                                <div>      include 'SIZE'</div>
                                <div>      include 'NEKUSE'          !
                                  UX, UY, UZ, TEMP, Z</div>
                                <div>      </div>
                                <div>      integer idum</div>
                                <div>      save    idum </div>
                                <div>      data    idum / 0 /</div>
                                <div><br>
                                </div>
                                <div>      real eps</div>
                                <div><br>
                                </div>
                                <div>      if (idum.eq.0) idum = 99 +
                                  nid</div>
                                <div>      eps = 0.1</div>
                                <div><br>
                                </div>
                                <div>c     velocity</div>
                                <div>c     random distribution</div>
                                <div>      UX = eps*(ran1(idum)-0.50)</div>
                                <div>      UY = eps*(ran1(idum)-0.50)</div>
                                <div>      UZ = eps*(ran1(idum)-0.50)</div>
                                <div><br>
                                </div>
                                <div>c     t</div>
                                <div>      TEMP=0</div>
                                <div><br>
                                </div>
                                <div>      return</div>
                                <div>      end</div>
                              </div>
                              <div><br>
                              </div>
                              <div><br>
                              </div>
                              <div>
                                <div>40.0000     p109 : ARNOLDI:
                                  frequency of calling arn_solve</div>
                                <div>   4.00000     p110 : ARNOLDI:
                                  maximal number of arnoldi cycles</div>
                                <div>  90.0000     p111 : ARNOLDI: size
                                  of Krylov space</div>
                                <div>   30.0000     p112 : ARNOLDI:
                                  number of eigenvectors</div>
                              </div>
                              <div><br>
                              </div>
                              <div><br>
                              </div>
                              <div>If I am increasing the Krylov
                                subspace then will I get Eigen values at
                                lesser restart ?</div>
                              <div><br>
                              </div>
                              <div>Kindly help please as I am new to
                                this. Thanks in advance.</div>
                              <div><br>
                              </div>
                            </div>
                          </div>
                        </div>
                      </div>
                    </div>
                  </div>
                  <div dir="ltr"
                    class="m_-1585782076635606836m_9031516644251136374gmail_signature"
                    data-smartmail="gmail_signature">
                    <div dir="ltr">
                      <div>
                        <div dir="ltr">Alok Mishra
                          <div>Research Scholar </div>
                          <div>Computational Propulsion Lab </div>
                          <div>Aerospace Department IIT Kanpur</div>
                          <div>+91-8795844555</div>
                        </div>
                      </div>
                    </div>
                  </div>
                </div>
                <br>
                <fieldset
                  class="m_-1585782076635606836m_9031516644251136374mimeAttachmentHeader"></fieldset>
                <pre class="m_-1585782076635606836m_9031516644251136374moz-quote-pre">_______________________________________________
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        <div><br>
        </div>
        -- <br>
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      <div dir="ltr" class="m_-1585782076635606836gmail_signature"
        data-smartmail="gmail_signature">
        <div dir="ltr">
          <div>
            <div dir="ltr">Alok Mishra
              <div>Research Scholar </div>
              <div>Computational Propulsion Lab </div>
              <div>Aerospace Department IIT Kanpur</div>
              <div>+91-8795844555</div>
            </div>
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      <pre class="moz-quote-pre" wrap="">_______________________________________________
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