:orphan:

Examples
*************

Some examples for various models. The modeling details can be found in the article. 


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2D examples
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    <div class="sphx-glr-thumbcontainer" tooltip="We consider the motion of N active deformable spheres in a periodic box with different deformability properties. The particle are defined by their positions x_i and Brownian active directions of motion n_i, which follow the following set of stochastic differential equations:">

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  .. image:: /_auto_examples/2D/images/thumb/sphx_glr_ActiveBrownian_thumb.png
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  :doc:`/_auto_examples/2D/ActiveBrownian`

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      <div class="sphx-glr-thumbnail-title">Active Brownian Particles</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="We consider a chemo-attractant density u(x) and we assume that a particle located at x can sense the local gradient along the directions {x}-{x}_i (defined through a finite difference formula).  The only force is the incompresisbility force. We introduce the biased cost potential 
arphi = -\log c">

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  .. image:: /_auto_examples/2D/images/thumb/sphx_glr_ChemoDeformation_thumb.png
    :alt:

  :doc:`/_auto_examples/2D/ChemoDeformation`

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      <div class="sphx-glr-thumbnail-title">Chemotaxis induced by deformations</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="We consider a two-population system with surface interactions. The main force models surface tension-like effects by computing a pressure-like force acting on the centroid of each cell and computed as the sum of elementary forces orthognal to its boundary. The different relative magnitudes of the forces produced at the interfaces between different populations or between cells and the medium classicaly leads to various sorting effects. ">

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  .. image:: /_auto_examples/2D/images/thumb/sphx_glr_Engulfment_thumb.png
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  :doc:`/_auto_examples/2D/Engulfment`

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      <div class="sphx-glr-thumbnail-title">Engulfment due to surface tension effects</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="In this experiment, particles represent pedestrians in a crowd who all wish to escape a room via a single exit point located at the center of the right edge of the room.">

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  .. image:: /_auto_examples/2D/images/thumb/sphx_glr_Evacuation_thumb.png
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  :doc:`/_auto_examples/2D/Evacuation`

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      <div class="sphx-glr-thumbnail-title">Crowd evacuation</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="We consider falling soft spheres, associated to the power cost ">

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  .. image:: /_auto_examples/2D/images/thumb/sphx_glr_FallingSpheres_thumb.png
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  :doc:`/_auto_examples/2D/FallingSpheres`

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      <div class="sphx-glr-thumbnail-title">Falling soft spheres in 2D</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Viscoelastic properties of individual biological cells are often quantified using micropipette aspiration techniques: a single cell is first placed at the tip of a thin micropipette tube and a controlled pressure difference then creates an aspiration force which sucks the cell inside the micropipette.  The biomechanical properties are quantitatively evaluated by measuring the portion of the cell that effectively travels through the tube.  This aspiration length ranges from zero for solid-like cell to the full tube for liquid-like cells.  This experiment can be mimicked in silico by considering a micropipette-shaped domain and, for a given set of fixed parameters (cell size, micropipette width, force magnitude τi), increasing the value of the deformability parameter \alpha in the power cost">

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  .. image:: /_auto_examples/2D/images/thumb/sphx_glr_Micropipette_thumb.png
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  :doc:`/_auto_examples/2D/Micropipette`

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      <div class="sphx-glr-thumbnail-title">Micropipette experiment</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Random protrusions">

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  .. image:: /_auto_examples/2D/images/thumb/sphx_glr_Protrusions_thumb.png
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  :doc:`/_auto_examples/2D/Protrusions`

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      <div class="sphx-glr-thumbnail-title">Random protrusions</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="We consider a system of rod-shaped particles defined by their positions x_i and active directions of motion n_i.  Each n_i is defined at each time step as the maximal eigenvector associated to the PCA of the Laguerre cell (with the correct sign to avoid flipping). The collisions between particles thus lead to a local re-orientation process and eventually to the emergence of a globally aligned state. ">

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  .. image:: /_auto_examples/2D/images/thumb/sphx_glr_RodShape_thumb.png
    :alt:

  :doc:`/_auto_examples/2D/RodShape`

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      <div class="sphx-glr-thumbnail-title">Emergence of alignment in a system of active rod-shaped particles</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Run-and-tumble in 2D with soft spheres in a disk domain">

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  .. image:: /_auto_examples/2D/images/thumb/sphx_glr_RunTumbleDisk_thumb.png
    :alt:

  :doc:`/_auto_examples/2D/RunTumbleDisk`

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      <div class="sphx-glr-thumbnail-title">Run-and-tumble in 2D with soft spheres in a disk domain</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="We consider a two-population system with surface interactions. The main force models surface tension-like effects by computing a pressure-like force acting on the centroid of each cell and computed as the sum of elementary forces orthognal to its boundary. The different relative magnitudes of the forces produced at the interfaces between different populations or between cells and the medium classicaly leads to various sorting effects. ">

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  .. image:: /_auto_examples/2D/images/thumb/sphx_glr_SurfaceTension_thumb.png
    :alt:

  :doc:`/_auto_examples/2D/SurfaceTension`

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      <div class="sphx-glr-thumbnail-title">Sorting due to surface tension effects</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="We consider a 2D cell aggregate growing according to a basic somatic cell cycle. Starting from one cell, each cell grows at a linear speed until a target volume is reached, then it  divides after a random exponential time producing two daughter cells with identical half volumes.">

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  .. image:: /_auto_examples/2D/images/thumb/sphx_glr_TissueGrowth_thumb.png
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  :doc:`/_auto_examples/2D/TissueGrowth`

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      <div class="sphx-glr-thumbnail-title">Growth of a 2D cell aggregate</div>
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3D examples
---------------


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    <div class="sphx-glr-thumbcontainer" tooltip="As a benchmark, we consider a 3D system of self-propelled deformable ellipsoids in a strongly packed domain. Each particle moves in the direction of its principal axis which evolves according to a re-orientation process subject to the deformations caused by the surrounding particles.  We consider N particles in a 3D bounded box, discretized on a grid of size M^3.">

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  .. image:: /_auto_examples/3D/images/thumb/sphx_glr_Benchmark_3D_thumb.png
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  :doc:`/_auto_examples/3D/Benchmark_3D`

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      <div class="sphx-glr-thumbnail-title">Benchmark: 3D Run-and-Tumble with deformations.</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This is a non-scientific experiment with bubbles. ">

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  .. image:: /_auto_examples/3D/images/thumb/sphx_glr_Bubbles_thumb.png
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  :doc:`/_auto_examples/3D/Bubbles`

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      <div class="sphx-glr-thumbnail-title">Bubbles</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This script simulates 3D cell aggregates with the following weighted L^2 cost and force for the cell i">

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  .. image:: /_auto_examples/3D/images/thumb/sphx_glr_CellSorting3D_thumb.png
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  :doc:`/_auto_examples/3D/CellSorting3D`

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      <div class="sphx-glr-thumbnail-title">Cell sorting in 3D</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Our framework can handle arbitrary domains by considering appropriately distributed source points. ">

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  .. image:: /_auto_examples/3D/images/thumb/sphx_glr_FallingStuff_thumb.png
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  :doc:`/_auto_examples/3D/FallingStuff`

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      <div class="sphx-glr-thumbnail-title">Falling soft spheres in a 3D hourglass domain</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Run-and-tumble in 3D with soft spheres">

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  .. image:: /_auto_examples/3D/images/thumb/sphx_glr_RunTumble3D_thumb.png
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  :doc:`/_auto_examples/3D/RunTumble3D`

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      <div class="sphx-glr-thumbnail-title">Run-and-tumble in 3D with soft spheres</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="We consider a 3D cell aggregate growing according to a basic somatic cell cycle. Starting from one cell, each cell grows at a linear speed until a target volume is reached, then it  divides after a random exponential time producing two daughter cells with identical half volumes.">

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  .. image:: /_auto_examples/3D/images/thumb/sphx_glr_TissueGrowth_3D_thumb.png
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  :doc:`/_auto_examples/3D/TissueGrowth_3D`

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      <div class="sphx-glr-thumbnail-title">Growth of a 3D cell aggregate</div>
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    </div>


.. toctree::
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   :includehidden:


   /./_auto_examples/2D/index.rst
   /./_auto_examples/3D/index.rst


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    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download all examples in Python source code: _auto_examples_python.zip </_auto_examples/_auto_examples_python.zip>`

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download all examples in Jupyter notebooks: _auto_examples_jupyter.zip </_auto_examples/_auto_examples_jupyter.zip>`


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