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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
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 dendtritic 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 dendtritic spine
thylakoid | wB LB lB | Various, see (Paquay) | 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)

(Paquay) Paquay and Kusters, Biophys. J., 110, 6, (2016). preprint available at arXiv:1411.3019.