[petlenz]

Closes #105. Part of the uvwmaterial port (#94); stacked on #135.

Of uvwmaterial's three kinetics (polymer_curing_functions), autocatalytic_reaction already exists as a rate law (curing_rate, k z^m (1 − z)^n) and as a backward-Euler material; the nth-order law is curing_rate with m = 0 (its derivative is exact there), so no new material for it. What was missing is the Kamal–Sourour combination.

materials/kamal_sourour_rate.h (kamal_sourour_rate): dz/dt = (k₁ + k₂ zᵐ)(1 − z)ⁿ with k_i = A_i exp(−E_i/(R T)), temperature from a scalar source in °C like curing_rate, the state from an integrator; outputs rate and rate_derivative. z is clamped to [0, 1] and the rate vanishes at full cure; the nth-order term starts the reaction from z = 0 without a seed.

Tests (test_kamal_sourour_rate, 8): rate against the formula and the derivative against central differences; A₂ = 0 reproduces curing_rate with m = 0 exactly for z > 0 (curing_rate returns zero at z = 0, its lower clamp, so the nth-order law there cannot start without a seed — worth its own small fix); the rate vanishes at z = 1 and is positive at z = 0; integration with rk_integrator (rk4) at 120 °C is monotone and reaches z > 0.99; creation from JSON.

No report: the report runner has no time-only path yet (#126).

Review follow-up: z^m is std::pow(z, m) as is (z⁰ = 1, so the nth-order case keeps k₂ at z = 0 from the first RK stage); only the slope is guarded, and only where it diverges (m < 1 at z = 0) — m = 1 gives k₂ − n k₁ at z = 0. A₁, E₁, A₂, E₂, m, n are rejected when negative. The clamp of z says that it absorbs an integrator stage's overshoot. New tests: the m = 0 and m = 1 identities at z = 0, the rejections.

924/924 tests pass (GCC 14, reports on).

JSON input

New material types: kamal_sourour_rate. A json_model document that loads (the FromJson test of the PR):

{"materials": [
  {"type": "scalar_stepper", "name": "temperature", "increment": 0.0},
  {"type": "scalar_stepper", "name": "z", "increment": 0.0},
  {"type": "kamal_sourour_rate", "name": "rate", "integrator_source": "z", "temperature_name": "temperature",
   "A1": 2e5, "E1": 60000.0, "A2": 1e6, "E2": 50000.0, "m": 0.7, "n": 1.3}
]}

dz/dt = (k₁ + k₂ zᵐ)(1 − z)ⁿ with kᵢ = Aᵢ exp(−Eᵢ / (R T)); integrator_source the state producer (the Runge–Kutta integrator of the repo in practice), temperature_name the temperature history (state); outputs rate, rate_derivative.

[petlenz]

Review findings (design, tmech expressions instead of component loops, modern C++, comments, tests, correctness). Severity: must = wrong result, hang, build break or unreachable feature; should = design, duplication, accuracy; nit = style.

kamal_sourour_rate — needs changes

• [must] kamal_sourour_rate.h:171 zm = z > 0 ? pow(z,m) : 0 → 0 at z = 0 for m = 0 (z⁰ = 1); the advertised nth-order case loses k₂ on the first RK stage from z = 0. std::pow(0,m) is already 0 for m > 0; guard only the derivative.
• [should] :172 dzm = 0 at z = 0 for m = 1 (should be 1); guard only for m < 1.
• [should] no validation of m, n, A₁, A₂, E ≥ 0.
• [nit] clamp hides integrator overshoot (say so); 6-line header; test the m = 0 identity at z = 0.