feat(cad): Sneed-Folk maximum-projection sphericity#406
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Add measure::solid_bounding_box_max_projection_sphericity[_tol], the Sneed-Folk maximum-projection sphericity: psi_p = cbrt(c^2 / (a*b)) (dimensionless, in (0, 1]) where a >= b >= c are the sorted AABB extents -- a classic sedimentology particle-shape descriptor (the ratio of the particle's maximum projection area to that of an equal-volume sphere): 1 for an equant cube/sphere, small for a blade, rod, or disc. It is the cube root of the corey_shape_factor squared, psi_p = CSF^(2/3) (#387). Mirrors corey but with cbrt(c^2/(ab)); degenerate (zero intermediate/longest extent) -> CadError::Tessellation. Analytic test solid_bounding_box_max_projection_sphericity_is_cbrt_c2_over_ab: (a) worked box(2,4,6) -> cbrt(1/6) ~= 0.55032; (b) threads solid_bounding_box_extents (#363): cbrt(s0^2/(s1*s2)); (c) cross-check threading corey_shape_factor (#387) (non-tautological): psi_p = CSF^(2/3); (d) range 0 < psi_p <= 1; cube and sphere -> 1 (equant); (e) _tol wrapper agrees with the default. Both fns re-exported from lib.rs alphabetically. valenx-cad 68 lib tests (was 67), cargo clippy --all-targets -D warnings clean.
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Add FlowSolution::vorticity_std_dev(), the standard deviation of the interior vorticity: sigma_omega = sqrt( <(omega - <omega>)^2> ) (1/s) the spatial fluctuation of the central-difference vorticity about its area-average, completing the mean / rms / std vorticity-statistics triad (mean_vorticity #400, rms_vorticity #406). By the variance identity it satisfies sigma^2 = omega_rms^2 - <omega>^2. Mirrors pressure_std_dev's deviation-sum form (mean via mean_vorticity, then sum (omega-mean)^2); returns 0 for a grid too small (nx < 3 or ny < 3). Analytic test vorticity_std_dev_completes_the_variance_identity: (a) uniform shear u(y)=gamma*y has constant omega = -gamma -> sigma = 0; (b) quadratic shear u(y)=a*y^2 has omega = -2a*y varying in space -> sigma > 0, and the variance identity sigma = sqrt(omega_rms^2 - <omega>^2) threads mean_vorticity + rms_vorticity (three separate loops, non-tautological); (c) grid too small for an interior difference -> 0. Pure method on FlowSolution, no lib.rs change. cfd-native 124 lib tests (was 123), cargo clippy --all-targets -D warnings clean.
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Add FlowSolution::rms_divergence(), the root-mean-square divergence over all nx*ny cells: rms = sqrt( <(div u)^2> ) (1/s) the L2 continuity residual. Unlike the signed mean_divergence (whose +/- cells cancel), the RMS sums squares so it never cancels -- the standard convergence metric for how well the discrete continuity constraint div u = 0 is satisfied. The square-summing companion to the signed mean (#417) and the peak max_divergence, mirroring rms_vorticity (#406). Analytic test rms_divergence_is_the_l2_continuity_residual: (a) solenoidal shear -> rms = 0; (b) uniform expansion (div u = c everywhere) -> rms = c, and for the constant field rms == mean == max (threads both, non-tautological); (c) sign-varying "tent" (div u = [c,c,c,-c,-c] per row) -> rms = c while the signed mean cancels to c/5, so rms > |mean| (the RMS catches the local violations the mean misses); (d) zero-flow -> 0. Pure method on FlowSolution, no lib.rs change. cfd-native 126 lib tests (was 125), cargo clippy --all-targets -D warnings clean.
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Add FlowSolution::rms_strain_rate(), the root-mean-square rate-of-strain magnitude over the interior cells: rms = sqrt( <|S|^2> ) (1/s) the L2 deformation rate. Since |S|^2 = 2 S_ij S_ij, this is the quantity that sets the viscous dissipation eps = 2*nu*<S_ij S_ij> = nu*<|S|^2>, so it measures how strongly the flow is being strained (and thus dissipating energy). Completes the strain-rate family (at_cell / max / mean / rms), mirroring rms_vorticity (#406). Analytic test rms_strain_rate_is_the_l2_deformation_rate: (a) pure shear u(y)=gamma*y -> |S|=gamma uniformly -> rms=gamma, and since |S|=|omega|=gamma for a pure shear, rms_strain_rate == rms_vorticity (threads rms_vorticity via the grad-u decomposition); (b) solid-body rotation -> rms strain = 0 while rms vorticity = 2*Omega (strain != rotation); (c) non-uniform quadratic shear -> rms >= mean > 0 (Jensen); (d) grid too small for an interior difference -> 0. Pure method on FlowSolution, no lib.rs change. cfd-native 128 lib tests (was 127), cargo clippy --all-targets -D warnings clean.
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Add FlowSolution::mean_dissipation_rate(kinematic_viscosity), the rate at which the flow irreversibly converts kinetic energy to heat by viscosity: eps = nu * <|S|^2> = nu * (rms_strain_rate)^2 (m^2/s^3, per unit mass) the quantity that closes the turbulent energy budget (the Kolmogorov cascade rate). Since |S|^2 = 2 S_ij S_ij, eps = 2*nu*<S_ij S_ij>. It is the strain-squared companion to rms_strain_rate (#428), threading it directly. A pure rotation strains nothing and dissipates nothing; only deformation dissipates. Analytic test mean_dissipation_rate_is_viscosity_times_strain_squared: (a) worked: pure shear u(y)=gamma*y, |S|=gamma, nu=0.1 -> eps=nu*gamma^2=0.4; (b) threads rms_vorticity (#406) (non-tautological): for a pure shear |S|=|omega|, so eps = nu*rms_vorticity^2; (c) solid-body rotation -> no strain -> no dissipation (even though it spins); (d) proportional to nu, and zero at nu=0. Pure method on FlowSolution, no lib.rs change. cfd-native 129 lib tests (was 128), cargo clippy --all-targets -D warnings clean.
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What
Adds
measure::solid_bounding_box_max_projection_sphericityand_tol— the Sneed-Folk maximum-projection sphericity:// psi_p = cbrt(c^2 / (a*b)) (dimensionless, in (0, 1]), a >= b >= c sorted AABB extentsWhy
The AABB shape family has the Zingg pair (elongation #375, flatness #381) and the Corey shape factor (#387), but not the maximum-projection sphericity — the ratio of a particle's maximum projection area to that of an equal-volume sphere, a classic sedimentology descriptor.
psi_p = 1for an equant cube/sphere and drops toward0for a blade/rod/disc. It iscorey_shape_factor^(2/3)— a clean non-tautological cross-check. A degenerate solid (zero intermediate/longest extent) returnsCadError::Tessellation.Test
solid_bounding_box_max_projection_sphericity_is_cbrt_c2_over_ab:box(2,4,6) -> cbrt(1/6) ~= 0.55032;solid_bounding_box_extents(feat(cad): add solid_bounding_box_extents (raw AABB dimensions) #363) —cbrt(s0^2/(s1*s2));corey_shape_factor(feat(fem): elastic bending-moment capacity #387) (non-tautological) —psi_p = CSF^(2/3);0 < psi_p <= 1; cube and sphere ->1;_tolwrapper agrees with the default.Both fns re-exported from
lib.rsalphabetically.valenx-cad68 lib tests (was 67);cargo clippy -p valenx-cad --all-targets -- -D warningsclean. Research-grade particle-shape descriptor.