4. Geometry and Boundaries

4.1. Box geometry

For a rectangular domain:

[geometry]
model = "box"
sizes = [1000, 100, 100]

The three sizes are positive lengths in nm. The box is triangulated internally and coplanar triangles are merged into six facets by default.

4.2. Mesh geometry

model may point to an ASCII/binary STL or OBJ file. STL coordinates are interpreted as nm and converted internally to angstroms. The loaded mesh is shifted so its bounding-box minimum is at the origin.

A production mesh should be:

  • closed and manifold

  • free of zero-area triangles

  • consistently scaled in nm

  • simple enough that facet merging and ray intersection remain robust

merge_coplanar_facets = true groups connected coplanar triangles. Boundary selectors operate on the resulting facet centroids, not on every triangle vertex.

4.3. Relative boundary selectors

Each boundary region is a six-value relative box:

[xmin, ymin, zmin, xmax, ymax, zmax]

0 and 1 correspond to the geometry bounding-box minimum and maximum. Small extensions such as -0.01 and 1.01 make boundary-plane selectors robust to floating-point tolerances.

Every declared selector must match at least one facet. The three arrays boundary_position, boundary_conditions, and boundary_values must have identical lengths. When selectors overlap, the later selector determines the final condition.

4.4. Thermal reservoirs

T values are non-negative temperatures in K. A particle that reaches a thermal facet is marked absorbed, and the facet’s leaving count contributes to the next reservoir-refill step.

Use at least two reservoirs with different temperatures for a conductivity calculation. Linear initialization chooses the coldest and hottest valid reservoirs and interpolates along their centroid-to-centroid direction.

4.5. Periodic boundaries

P values must be 0. Every periodic selector must appear exactly once in periodic_pair and the total number of regions must be even.

For each pair, PhonoMC validates:

  • both selected facets are marked periodic

  • the two regions match the same number of facets

  • normals point in opposite directions

  • areas agree within tolerance

  • boundary-edge length spectra agree

  • no facet is assigned to two different partners

The centroid difference defines the translation from one periodic facet to the other.

4.6. Rough boundaries

R values are non-negative RMS roughness values in nm. Unselected facets default to R with zero roughness. Explicitly list important surfaces rather than relying on this default in production inputs.

4.7. Grid construction

grid_xyz divides the bounding box into regular candidate cells. For a box, all centers are retained and position-to-grid indexing is direct. For a mesh, only centers inside the surface are retained. Initialization fills a complete voxel-to-active-grid table from those cells, so particle positions use an O(1) lookup for both boxes and arbitrary closed meshes.

Every 100 time steps, mesh particles are checked against the actual closed surface rather than only its axis-aligned bounding box. A failed boundary trace is retried from a nearby interior point without changing velocity; a persistent failure stops the run with the particle position and an STL validation hint. Likewise, more than 64 boundary collisions within one time step is reported as an input/time-step error instead of silently dropping the remaining travel time.

Current limitation: retained mesh cells receive the same volume domain volume / retained cell count. Cells cut by a curved or oblique surface are not assigned exact intersection volumes. Perform a grid-sensitivity study for strongly non-rectangular devices.

The domain volume itself is evaluated from the oriented surface using the signed tetrahedral-volume identity. For topologically closed meshes, inconsistent triangle winding is repaired once during loading. Cached volume tetrahedra are accepted only when their summed volume agrees with the surface volume; otherwise sampling falls back to the robust surface test.

4.8. Geometry validation workflow

Before a long mesh run:

  1. use a coarse grid and small particle count

  2. verify the reported face and facet counts

  3. inspect grid_centers.csv

  4. check thermal-reservoir, rough-facet, and periodic-pair counts in summary.txt

  5. render the mesh and temperature slices with plot_temperature_3d.py