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lammps/doc/src/Howto_manifold.rst
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Manifolds (surfaces)
====================
**Overview:**
This doc page is not about a LAMMPS input script command, but about
manifolds, which are generalized surfaces, as defined and used by the
USER-MANIFOLD package, to track particle motion on the manifolds. See
the src/USER-MANIFOLD/README file for more details about the package
and its commands.
Below is a list of currently supported manifolds by the USER-MANIFOLD
package, their parameters and a short description of them. The
parameters listed here are in the same order as they should be passed
to the relevant fixes.
+----------------+----------------+----------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------+
| *manifold* | *parameters* | *equation* | *description* |
+----------------+----------------+----------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------+
| cylinder | R | x\^2 + y\^2 - R\^2 = 0 | Cylinder along z-axis, axis going through (0,0,0) |
+----------------+----------------+----------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------+
| cylinder\_dent | R l a | x\^2 + y\^2 - r(z)\^2 = 0, r(x) = R if \| z \| > l, r(z) = R - a\*(1 + cos(z/l))/2 otherwise | A cylinder with a dent around z = 0 |
+----------------+----------------+----------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------+
| dumbbell | a A B c | -( x\^2 + y\^2 ) + (a\^2 - z\^2/c\^2) \* ( 1 + (A\*sin(B\*z\^2))\^4) = 0 | A dumbbell |
+----------------+----------------+----------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------+
| ellipsoid | a b c | (x/a)\^2 + (y/b)\^2 + (z/c)\^2 = 0 | An ellipsoid |
+----------------+----------------+----------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------+
| gaussian\_bump | A l rc1 rc2 | if( x < rc1) -z + A \* exp( -x\^2 / (2 l\^2) ); else if( x < rc2 ) -z + a + b\*x + c\*x\^2 + d\*x\^3; else z | A Gaussian bump at x = y = 0, smoothly tapered to a flat plane z = 0. |
+----------------+----------------+----------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------+
| plane | a b c x0 y0 z0 | a\*(x-x0) + b\*(y-y0) + c\*(z-z0) = 0 | A plane with normal (a,b,c) going through point (x0,y0,z0) |
+----------------+----------------+----------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------+
| plane\_wiggle | a w | z - a\*sin(w\*x) = 0 | A plane with a sinusoidal modulation on z along x. |
+----------------+----------------+----------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------+
| sphere | R | x\^2 + y\^2 + z\^2 - R\^2 = 0 | A sphere of radius R |
+----------------+----------------+----------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------+
| supersphere | R q | \| x \|\^q + \| y \|\^q + \| z \|\^q - R\^q = 0 | A supersphere of hyperradius R |
+----------------+----------------+----------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------+
| spine | a, A, B, B2, c | -(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 | An approximation to a dendritic spine |
+----------------+----------------+----------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------+
| spine\_two | a, A, B, B2, c | -(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 | Another approximation to a dendritic spine |
+----------------+----------------+----------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------+
| thylakoid | wB LB lB | Various, see :ref:`(Paquay) <Paquay1>` | A model grana thylakoid consisting of two block-like compartments connected by a bridge of width wB, length LB and taper length lB |
+----------------+----------------+----------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------+
| torus | R r | (R - sqrt( x\^2 + y\^2 ) )\^2 + z\^2 - r\^2 | A torus with large radius R and small radius r, centered on (0,0,0) |
+----------------+----------------+----------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------+
.. _Paquay1:
**(Paquay)** Paquay and Kusters, Biophys. J., 110, 6, (2016).
preprint available at `arXiv:1411.3019 <http://arxiv.org/abs/1411.3019/>`_.