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<li class="toctree-l1"><a class="reference internal" href="Section_intro.html">1. Introduction</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_start.html">2. Getting Started</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_commands.html">3. Commands</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_accelerate.html">5. Accelerating LAMMPS performance</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_howto.html">6. How-to discussions</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_python.html">11. Python interface to LAMMPS</a></li>
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<li>Manifolds (surfacse)</li>
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<div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
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<div class="section" id="manifolds-surfacse">
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<h1>Manifolds (surfacse)</h1>
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<p><strong>Overview:</strong></p>
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<p>This doc page is not about a LAMMPS input script command, but about
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manifolds, which are generalized surfaces, as defined and used by the
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USER-MANIFOLD package, to track particle motion on the manifolds. See
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the src/USER-MANIFOLD/README file for more details about the package
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and its commands.</p>
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<p>Below is a list of currently supported manifolds by the USER-MANIFOLD
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package, their parameters and a short description of them. The
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parameters listed here are in the same order as they should be passed
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to the relevant fixes.</p>
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<table border="1" class="docutils">
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<colgroup>
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<col width="5%" />
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<col width="6%" />
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<col width="43%" />
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<col width="46%" />
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<col width="1%" />
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</colgroup>
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<tbody valign="top">
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<tr class="row-odd"><td><em>manifold</em></td>
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<td><em>parameters</em></td>
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<td><em>equation</em></td>
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<td><em>description</em></td>
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<td> </td>
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</tr>
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<tr class="row-even"><td>cylinder</td>
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<td>R</td>
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<td>x^2 + y^2 - R^2 = 0</td>
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<td>Cylinder along z-axis, axis going through (0,0,0)</td>
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<td> </td>
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</tr>
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<tr class="row-odd"><td>cylinder_dent</td>
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<td>R l a</td>
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<td>x^2 + y^2 - r(z)^2 = 0, r(x) = R if <a href="#id7"><span class="problematic" id="id8">|z|</span></a> > l, r(z) = R - a*(1 + cos(z/l))/2 otherwise</td>
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<td>A cylinder with a dent around z = 0</td>
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<td> </td>
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</tr>
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<tr class="row-even"><td>dumbbell</td>
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<td>a A B c</td>
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<td>-( x^2 + y^2 ) * (a^2 - z^2/c^2) * ( 1 + (A*sin(B*z^2))^4) = 0</td>
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<td>A dumbbell</td>
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<td> </td>
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</tr>
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<tr class="row-odd"><td>ellipsoid</td>
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<td>a b c</td>
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<td>(x/a)^2 + (y/b)^2 + (z/c)^2 = 0</td>
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<td>An ellipsoid</td>
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<td> </td>
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</tr>
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<tr class="row-even"><td>plane</td>
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<td>a b c x0 y0 z0</td>
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<td>a*(x-x0) + b*(y-y0) + c*(z-z0) = 0</td>
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<td>A plane with normal (a,b,c) going through point (x0,y0,z0)</td>
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<td> </td>
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</tr>
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<tr class="row-odd"><td>plane_wiggle</td>
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<td>a w</td>
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<td>z - a*sin(w*x) = 0</td>
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<td>A plane with a sinusoidal modulation on z along x.</td>
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<td> </td>
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</tr>
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<tr class="row-even"><td>sphere</td>
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<td>R</td>
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<td>x^2 + y^2 + z^2 - R^2 = 0</td>
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<td>A sphere of radius R</td>
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<td> </td>
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</tr>
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<tr class="row-odd"><td>supersphere</td>
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<td>R q</td>
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<td><a href="#id1"><span class="problematic" id="id2">|</span></a>x|^q + <a href="#id3"><span class="problematic" id="id4">|</span></a>y|^q + <a href="#id5"><span class="problematic" id="id6">|</span></a>z|^q - R^q = 0</td>
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<td>A supersphere of hyperradius R</td>
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<td> </td>
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</tr>
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<tr class="row-even"><td>spine</td>
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<td>a, A, B, B2, c</td>
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<td>-(x^2 + y^2)*(a^2 - z^2/f(z)^2)*(1 + (A*sin(g(z)*z^2))^4), f(z) = c if z > 0, 1 otherwise; g(z) = B if z > 0, B2 otherwise</td>
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<td>An approximation to a dendtritic spine</td>
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<td> </td>
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</tr>
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<tr class="row-odd"><td>spine_two</td>
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<td>a, A, B, B2, c</td>
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<td>-(x^2 + y^2)*(a^2 - z^2/f(z)^2)*(1 + (A*sin(g(z)*z^2))^2), f(z) = c if z > 0, 1 otherwise; g(z) = B if z > 0, B2 otherwise</td>
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<td>Another approximation to a dendtritic spine</td>
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<td> </td>
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</tr>
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<tr class="row-even"><td>thylakoid</td>
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<td>wB LB lB</td>
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<td>Various, see <a class="reference internal" href="#paquay"><span class="std std-ref">(Paquay)</span></a></td>
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<td>A model grana thylakoid consisting of two block-like compartments connected by a bridge of width wB, length LB and taper length lB</td>
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<td> </td>
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</tr>
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<tr class="row-odd"><td>torus</td>
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<td>R r</td>
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<td>(R - sqrt( x^2 + y^2 ) )^2 + z^2 - r^2</td>
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<td>A torus with large radius R and small radius r, centered on (0,0,0)</td>
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<td> </td>
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</tr>
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</tbody>
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</table>
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<p id="paquay"><strong>(Paquay)</strong> Paquay and Kusters, Biophys. J., 110, ???, (2016), to be published,
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preprint available at <a class="reference external" href="http://arxiv.org/abs/1411.3019/">arXiv:1411.3019</a>.</p>
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