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<html>
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  <title>Kartik Jain</title>
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    <img height=300 src="kartik_2024.png">
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      <source src="V.mp4" type="video/mp4">
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    <p>
    <b>
    Kartik Jain, Associate Professor of Biofluid Dynamics,<br>
    Department of Thermal and Fluid Engineering, <br>
    <a href="https://people.utwente.nl/k.jain?tab=about-me">University of Twente</a>, <br>
    The Netherlands <br>
    E-mail: k.jain@utwente.nl <br>
    <a href="https://www.linkedin.com/in/kartikjain5/">                               <img src="img/linkedin.svg" width=20> </a>              &nbsp
    <a href="https://scholar.google.co.uk/citations?user=bPoP9RIAAAAJ&hl=en">         <img src="img/google-scholar-square.svg" width=20> </a> &nbsp
    <a href="https://www.researchgate.net/profile/Kartik_Jain3">                      <img src="img/researchgate.svg" width=20> </a>          &nbsp
    <a href="https://orcid.org/0000-0002-6540-9304">                                  <img src="img/orcid.svg" width=20> </a>                 &nbsp
    <a href="https://publons.com/researcher/3073142/kartik-jain/">                    <img src="img/publons-square.svg" width=20> </a>        &nbsp
    <a href="https://www.ncbi.nlm.nih.gov/myncbi/1DuEBDU8mrlQv/bibliography/public/"> <img src="img/pubmed-square.svg" width=20> </a>

    </b>
    </p>

    <h2><button> <a href="index.html"   >About</a> </button>
        <button> <a href="projects.html">Research Projects</a></button>
        <button> <a href="cophi.html"   >Team members</a> </button>
        <button> <a href="lehre.html"   >Teaching     </a> </button>
        <button> <a href="apes.html"    >Research Code</a> </button>
        <button> <a href="pub.html"     >Publications</a> </button>
    </h2>


    <h2><span style="color:#006666">Teaching Activities</h2>

    <ol>
      <li>
        <b> <a
        href="https://utwente.osiris-student.nl/onderwijscatalogus/extern/cursus?cursuscode=202001436&collegejaar=2024&taal=en">
        Biofluid Dynamics - Theory and Analysis </a> </b>
        This course is an outcome of my experiences as an engineer who pursued the path of
        research on biofluid dynamics.
        Taught at the master level in Twente, I teach basics of the cardiovascular system,
        lymphatic system, the central nervous system and microcirculation.
        The engineering students adopt a mathematical perspective into the physiology of various
        biomedical flows.
        The second part of the course educates students on the analysis of physiologic flows using
        experiments like PIV flow measurements and computational modeling, with elements of medical imaging
        and high performance computing.
        A brief video introduction to my work and teaching can be seen on <a
        href="https://www.utwente.nl/en/et/tfe/education2/personalized-health-technology/">
        this page</a>.
        <!--  <video style="position:absolute;width:580px;top:400px;left:200px" autoplay loop controls>
            <source src="record.mp4" type="video/mp4">
          </video>
        -->

        \[
            \frac{\partial u_i}{\partial t}
           + u_j \frac{\partial u_i}{\partial x_j}
           -\frac{1}{\rho}\frac{\partial \sigma_{ij}}{\partial x_j}
           -g_i =0
        \]
      </li>
      <br><br>
      <li>
        <b> <a
        href="https://utwente.osiris-student.nl/onderwijscatalogus/extern/cursus?cursuscode=202100009&collegejaar=2025&taal=en">
        Fluid Mechanics, Vrije University Amsterdam</a> </b>
        The University of Twente and the Vrije University of Amsterdam have
        started a joint bachelor program in mechanical engineering.
        I am involved in the teaching of fluid mechanics at the bachelor level within this program.

        \[
            \frac{\partial \tilde{u}}{\partial \tilde{x}}
          + \frac{\partial \tilde{v}}{\partial \tilde{y}} = 0
        \]
        \[
            \tilde{u}\frac{\partial \tilde{u}}{\partial \tilde{x}}
          + \tilde{v}\frac{\partial \tilde{u}}{\partial \tilde{y}}
          = \frac{\partial^2\tilde{u}}{\partial\tilde{y}^2}
        \]
      </li>
      <br><br>
      <li>
        <b> <a
        href="https://www.utwente.nl/en/courses/1458442/capita-selecta-lattice-boltzmann-methods/">
        Lattice Boltzmann Methods</a> </b>
        The course on LBM is what is called as Capita Selecta in Twente.
        This is a self-learning with supervision type course in which
        participants at the doctoral and post-doctoral level learn theory of
        LBM, advanced concepts like collision operators, and elements of
        parallel computing.
        The apply their learnings to perform simulations of few canonical cases
        using <i>Musubi</i> which equips them with sufficient skills to embark
        further in the direction of LBM.
        Based on the background of the participant, the contents are quite
        dynamic and the elements of physics, mathematics and computer science
        are accordingly fine-tuned.

        \[
            f_i (\vec{r} + c_i\Delta t , t + \Delta t)
          = f_i(\vec{r}, t) + \Omega (f_{i}^{e}(\vec{r},t) - f_i(\vec{r}, t))

        \]
      </li>


    </ol>

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