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Manifolds (surfaces) :h3

[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 "(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) :tb(s=@)

:link(Paquay1)
[(Paquay)] Paquay and Kusters, Biophys. J., 110, 6, (2016).
preprint available at "arXiv:1411.3019"_http://arxiv.org/abs/1411.3019/.
