- Surface tension
- Gravitational potential energy
- Constraint energy integrals
- Named quantity energies
- Convex constraint gap energy
- Prescribed pressure energy
- Compressibility energy
- Crystalline energy

`set facet tension ...`

command.
The contribution to the total energy is the sum
of all the facet areas times their respective surface
tensions. The surface tension of a facet may also be specified
as depending on the phases
of the bodies it separates.
In the string model, the
tension resides on edges instead of facets.
Example datafile: cube.fe

E = \int\int\int_{body} G \rho z dVbut is calculated using the Divergence Theorem as

E = \int\int_{body surface} G\rho {z^2\over 2} \vec k \cdot \vec{dS}.This integral is done over each facet that bounds a body. If a facet bounds two bodies of different density, then the appropriate difference in density is used. Facets lying in the z = 0 plane make no contribution, and may be omitted if they are otherwise unneeded. Facets lying in constraints may be omitted if their contributions to the gravitational energy are contained in constraint energy integrals. In the string model, all this happens in one lower dimension.

Example datafile: mound.fe

E = \int_{edge}The integrand is defined in the constraint declaration in the datafile. The integral uses the innate orientation of the edge, but if the orientation attribute of the edge is negative, the value is negated. This is useful for prescribed contact angles on walls (in place of wall facets with equivalent tension) and for gravitational potential energy that would otherwise require facets in the constraint. The mound example illustrates this.F . dl.

Example datafile: ringblob.fe

E =where \vec S is the edge vector and \vec Q is the projection of the edge on the tangent plane of the constraint at the tail vertex of the edge. The constantk\left\Vert \vec S \times \vec Q \right\Vert / 6

The gap energy falls off quadratically as the surface is refined. That is, refining once reduces the gap energy by a factor of four. You can see if this energy has a significant effect on the surface by changing the gap constant.

Note: gap energy is effective only in the linear model.

Example datafile: tankex.fe

E = P*V_0*ln(V/V_0)where P is the ambient pressure, V_0 is the target volume of the body, and V is the actual volume. To account for work done against the ambeint pressure, each body also makes a negative contribution of

E = -P*V.The ambient pressure can be set in the datafile or with the p command. This energy is calculated only for bodies given a target volume.

Example datafile: crystal.fe

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