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        <h1>Beskjeder
          
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              <div class="vrtx-result-1 vrtx-resource">
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            <a class="vrtx-title" href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/oral-exam-times-10-june-in-nha1120-.html">Oral exam times 10 June in NHA1120. </a>
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            <div class="published-date">
              <span class="published-date-prefix">
Publisert              </span>
7. juni 2022 00:18            </div>


            <div class="description introduction">
                <p>This is the schedule for the oral exam friday June 10th in NHA1120. Best of luck with the exam!&nbsp;</p>

<p>10.00 Vetle<br/>
10.40 Vebj?rn<br/>
11.20 Michal<br/>
12.30 Boxue&nbsp;<br/>
13.10 Vira<br/>
&nbsp;</p>

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              <div class="vrtx-result-2 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/this-weeks-lecture-is-moved-to-friday.html">This weeks lecture is moved to friday</a>
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            <div class="published-date">
              <span class="published-date-prefix">
Publisert              </span>
2. juni 2022 01:07            </div>


            <div class="description introduction">
                <p>This weeks lecture is moved to friday</p>

            </div>
        </div>



              <div class="vrtx-result-3 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/no-exercise-class-thursday-may-12th.html">No exercise class Thursday May 12th</a>
          </div>

            <div class="published-date">
              <span class="published-date-prefix">
Publisert              </span>
11. mai 2022 13:41            </div>


            <div class="description introduction">
                <p>Since the last part of the excursuses will be presented in class next week, there will be no exercise class Thursday May 12th.</p>

            </div>
        </div>



              <div class="vrtx-result-4 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/summary-lecture-may-13-and-seminars-by-v.html">Summary lecture May 13 and seminars by Vira and Boxue May 20.</a>
          </div>

            <div class="published-date">
              <span class="published-date-prefix">
Publisert              </span>
6. mai 2022 13:37            </div>


            <div class="description introduction">
                <p>The will be a summary lecture May 13 and May 20 Vira and Boxue will present two different ways to describe water entry through surfaces. For the lecture on May 20, everyone should have read the article by <a href="https://www.nature.com/articles/nphys545">Duez et al</a>. Please let us know if you have any difficulty with accessing the article.&nbsp;</p>

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              <div class="vrtx-result-5 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/no-thursday-lecture.html">No Thursday lecture</a>
          </div>

            <div class="published-date">
              <span class="published-date-prefix">
Publisert              </span>
3. mai 2022 15:25            </div>


            <div class="description introduction">
                <p>There will be no lecture this Thursday so that you can work on your mandatory assignment.</p>

<p>Also, after we finish the phase field module we will have two lectures on "water impact of solid spheres" by Vira and Boxue. Everyone should read&nbsp;<a href="/studier/emner/matnat/math/MEK4480/v22/oppgaver/nphys545.pdf">this article</a> before the lectures.</p>

            </div>
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              <div class="vrtx-result-6 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/mandatory-assignment-3--phase-field.html">Mandatory assignment 3 - Phase Field</a>
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            <div class="published-date">
              <span class="published-date-prefix">
Publisert              </span>
26. apr. 2022 16:51            </div>


            <div class="description introduction">
                <p>Here is <a href="/studier/emner/matnat/math/MEK4480/v22/oppgaver/oblig3_v2022.pdf">mandatory assignment 3</a>. A numerical solver that can be used for the final exercise is found <a href="/studier/emner/matnat/math/MEK4480/v22/oppgaver/cahn-hilliardfem.py">here</a>. The deadline is 12th of May.</p>

<p>For additional reading material: the original paper by Cahn and Hilliard (1958) is located <a href="/studier/emner/matnat/math/MEK4480/v22/oppgaver/1.1744102.pdf">here</a> and you can also check out this <a href="https://nvlpubs.nist.gov/nistpubs/Legacy/IR/nistir6018.pdf">review paper</a> on the phase-field method.</p>

            </div>
        </div>



              <div class="vrtx-result-7 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/todays-lecture-substituted-with-the-talk.html">Todays lecture substituted with the talk by Anne Juel at 12.15 in the same room</a>
          </div>

            <div class="published-date">
              <span class="published-date-prefix">
Publisert              </span>
22. apr. 2022 08:17            </div>


            <div class="description introduction">
                <p>Todays lecture substituted with the talk by Anne Juel at 12.15 in the same room</p>

            </div>
        </div>



              <div class="vrtx-result-8 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/capillary-instability.html">Capillary instability</a>
          </div>

            <div class="published-date">
              <span class="published-date-prefix">
Publisert              </span>
6. apr. 2022 10:08            </div>


            <div class="description introduction">
                <p>of a thin film coating a wire. Here is the original paper by <a href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/the-instability-of-an-annular-thread-of-fluid.pdf">Goren (1962)</a>.</p>

            </div>
        </div>



              <div class="vrtx-result-9 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/mandatory-assignment-2.html">Mandatory assignment 2</a>
          </div>

            <div class="published-date">
              <span class="published-date-prefix">
Publisert              </span>
23. mars 2022 13:54            </div>


            <div class="description introduction">
                <p>Here is <a href="/studier/emner/matnat/math/MEK4480/v22/oppgaver/oblig2_2022.pdf">mandatory assignment 2</a>. The delivery date is set to Wednesday 13th of April at 1430. In the assignment you are to compare two data sets with your theoretical predictions. The two sets are for droplets of two different viscosities and they are found here: <a href="https://www-adm.uio.no/studier/emner/matnat/math/MEK4480/v22/oppgaver/silconeoil_50cst.txt?vrtx=admin">mu=50cSt</a> and <a href="https://www-adm.uio.no/studier/emner/matnat/math/MEK4480/v22/oppgaver/siliconeoil_100cst.txt?vrtx=admin">mu=100cSt</a>.&nbsp;</p>

            </div>
        </div>



              <div class="vrtx-result-10 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/exercise-5.html">Exercise 5</a>
          </div>

            <div class="published-date">
              <span class="published-date-prefix">
Publisert              </span>
11. mars 2022 15:31            </div>


            <div class="description introduction">
                <p>Do Q2-3 <a href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/revisedexer3%286%29.pdf">here</a>. We will discuss them next Thursday.</p>

            </div>
        </div>



              <div class="vrtx-result-11 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/reading-material--similarity-solutions.html">Reading material - similarity solutions</a>
          </div>

            <div class="published-date">
              <span class="published-date-prefix">
Publisert              </span>
11. mars 2022 15:30            </div>


            <div class="description introduction">
                <p>See article about 2D similarity solutions for thin film rupture <a href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/1.870110.pdf">here</a>. What we discussed today can be found in Leal's book, section 6D.</p>

            </div>
        </div>



              <div class="vrtx-result-12 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/article-about-gravity-driven-thin-films.html">Article about gravity driven thin films</a>
          </div>

            <div class="published-date">
              <span class="published-date-prefix">
Publisert              </span>
10. mars 2022 12:30            </div>


            <div class="description introduction">
                <p>Read <a href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/300427a0.pdf">this</a> for more information about similarity solutions for the gravity driven thin film equation.</p>

            </div>
        </div>



              <div class="vrtx-result-13 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/reading-material--thin-films.html">Reading material - thin films</a>
          </div>

            <div class="published-date">
              <span class="published-date-prefix">
Publisert              </span>
9. mars 2022 08:39            </div>


            <div class="description introduction">
                <p>The relevant reading material from Leal's book is section 6A-D.</p>

            </div>
        </div>



              <div class="vrtx-result-14 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/exercise-4.html">Exercise 4</a>
          </div>

            <div class="published-date">
              <span class="published-date-prefix">
Publisert              </span>
2. mars 2022 10:42            </div>


            <div class="description introduction">
                <p>Please do Q2 <a href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/exer2%283%29.pdf">here</a> and Q1-2 <a href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/revisedexer3%286%29.pdf">here</a>. We will discuss them next Thursday (10th).</p>

            </div>
        </div>



              <div class="vrtx-result-15 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/hints-for-mandatory-assignment-1.html">Hints for mandatory assignment 1</a>
          </div>

            <div class="published-date">
              <span class="published-date-prefix">
Publisert              </span>
28. feb. 2022 16:28            </div>


            <div class="description introduction">
                <p>I have received some questions regarding the derivation of the Rayleigh-Plesset equation using the principle of energy conservation. <a href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/hints_oblig1.pdf">Here</a> are the definition of the relevant energies.&nbsp;</p>

            </div>
        </div>



              <div class="vrtx-result-16 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/minnaerts-original-article.html">Minnaerts original article</a>
          </div>

            <div class="published-date">
              <span class="published-date-prefix">
Publisert              </span>
25. feb. 2022 13:20            </div>


            <div class="description introduction">
                <p>Here is the <a href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/xvi-on-musical-air-bubbles-and-the-sounds-of-running-water.pdf">original article</a> by Minneart.</p>

            </div>
        </div>



              <div class="vrtx-result-17 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/viscous-dissipation.html">Viscous Dissipation</a>
          </div>

            <div class="published-date">
              <span class="published-date-prefix">
Publisert              </span>
25. feb. 2022 12:07            </div>


            <div class="description introduction">
                <p><a href="/studier/emner/matnat/math/MEK4480/v18/oppgaver/viscous-dissipation.pdf">This</a> can be helpful if you are not sure about the expression of viscous dissipation per unit volume.</p>
            </div>
        </div>



              <div class="vrtx-result-18 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/mandatory-assignment-1.html">Mandatory assignment 1</a>
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            <div class="published-date">
              <span class="published-date-prefix">
Publisert              </span>
16. feb. 2022 15:42            </div>


            <div class="description introduction">
                <p>Here is <a href="/studier/emner/matnat/math/MEK4480/v22/oppgaver/oblig1_2022.pdf">mandatory assignment 1</a>. The delivery date is Thursday 3rd of march. We will discuss how to organise&nbsp;the&nbsp;experimental part on Friday.</p>

            </div>
        </div>



              <div class="vrtx-result-19 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/no-execises--reading-material.html">No execises - reading material</a>
          </div>

            <div class="published-date">
              <span class="published-date-prefix">
Publisert              </span>
14. feb. 2022 10:32            </div>


            <div class="description introduction">
                <p>There are?no exercises for this week. Instead you should read section 4G 1-2 in Leal's book. For additional material you can check out this review paper on bubble dynamics.</p><p>We meet on Friday for our usual lecture.</p>
            </div>
        </div>



              <div class="vrtx-result-20 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/artikkel.html">Artikkel</a>
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            <div class="published-date">
              <span class="published-date-prefix">
Publisert              </span>
4. feb. 2022 14:05            </div>


            <div class="description introduction">
                <p>Her er artikkelen til <a href="/studier/emner/matnat/math/MEK4480/v22/oppgaver/proudman1956expansions.pdf">Proudman og Pearson</a> som vi pratet om i timen.</p>

            </div>
        </div>



              <div class="vrtx-result-21 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/exercise-3.html">Exercise 3</a>
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            <div class="published-date">
              <span class="published-date-prefix">
Publisert              </span>
3. feb. 2022 21:53            </div>


            <div class="description introduction">
                <p>Please finish Q5-Q7&nbsp;found&nbsp;<a href="/studier/emner/matnat/math/MEK4480/v22/oppgaver/pset1.pdf">here</a>. We will discuss it&nbsp;next Thursday&nbsp;(10th&nbsp;Feb).</p>

            </div>
        </div>



              <div class="vrtx-result-22 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/exercise-2.html">Exercise 2</a>
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            <div class="published-date">
              <span class="published-date-prefix">
Publisert              </span>
27. jan. 2022 14:33            </div>


            <div class="description introduction">
                <p>Please finish Q1-Q4 found <a href="/studier/emner/matnat/math/MEK4480/v22/oppgaver/pset1.pdf">here</a>. We will discuss it&nbsp;next Thursday&nbsp;(3rd&nbsp;Feb).</p>

            </div>
        </div>



              <div class="vrtx-result-23 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/creeping-flow.html">Creeping flow</a>
          </div>

            <div class="published-date">
              <span class="published-date-prefix">
Publisert              </span>
20. jan. 2022 15:04            </div>


            <div class="description introduction">
                <p>The first section of the course is discussed in&nbsp;chapter 7A-H in Leal's Advanced Transport Phenomena.</p>

            </div>
        </div>



              <div class="vrtx-result-24 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/exercise-1.html">Exercise 1</a>
          </div>

            <div class="published-date">
              <span class="published-date-prefix">
Publisert              </span>
20. jan. 2022 15:01            </div>


            <div class="description introduction">
                <p>Problems 2-2, 2-4 and 2-8 on pages 99-100 inn Leal's book. We will discuss them next Thursday.</p>

            </div>
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              <div class="vrtx-result-25 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MEK4480/v22/beskjeder/course-syllabus.html">Course syllabus</a>
          </div>

            <div class="published-date">
              <span class="published-date-prefix">
Publisert              </span>
20. jan. 2022 14:58            </div>


            <div class="description introduction">
                <p>The syllabus for the spring will be selected from these books:</p>

<p>Primarily follow the book by:</p>

<p>“Advanced Transport Phenomena”, Gary Leal, Cambridge U. P.</p>

<p>“Capillarity and wetting phenomena”, de Gennes et al., Springer.</p>

<p>As mentioned, you should be able to access&nbsp;the book from Leal using your uio account here:</p>

<p><a href="https://www.cambridge.org/core/books/advanced-transport-phenomena/9F2A633638780413DA73C6CB70A1D341" target="_blank">https://www.cambridge.org/core/books/advanced-transport-phenomena/9F2A633638780413DA73C6CB70A1D341</a>&nbsp;.</p>

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