The 3D version integrates heat diffusion through a full voxel cube. This 2D companion solves the same real equations a genuinely different way: instead of a cube, it discretises a vertical slab cross-section through the pour — the standard simplification real mass-concrete engineers already use for long footings, walls and dam sections where the third dimension is effectively uniform. Each grid cell still gains heat from the exothermic hydration reaction as a decaying pulse and loses heat to neighbours by diffusion:
dT/dt |source = T_ad · k · e^(−k·t) (k ≈ 0.045 h⁻¹)
∂T/∂t = D·∇²T + source(t) − h·(T − T_amb) [edge cells only]
The grid is integrated explicitly every frame with the same substep size and diffusivity as the 3D model (verified numerically in a standalone script: with these constants the scheme is unconditionally stable — for a 2D 4-neighbour Laplacian, stability needs 4·D·dt ≤ 1, and here 4×0.9×0.05 = 0.18, well inside the bound — and a pour with no active cooling relaxes cleanly back to ambient once the hydration pulse decays, with no overshoot or divergence at any tested Tad). A swarm of nanorobots continuously ranks every cell by temperature and re-deploys to the hottest ones, each active bot pulling heat out locally.
- Tad — total adiabatic temperature rise of the mix (more cement/high-early-strength mix → hotter core).
- Insulation — how well the formwork traps heat at the exposed edges; more insulation raises the core temperature and can worsen the gradient if the swarm can't keep up.
- Active cooling agents — swarm size; more agents cool more hot cells simultaneously, flattening the core–surface ΔT.
- Threshold — the ΔT past which real-world guidance (ACI 207-style limits, ~20 °C) calls the gradient a cracking risk.
Drag to pan the cross-section, scroll or pinch to zoom in on individual cells and bots. Real-world relevance: dams and thick foundations already use embedded cooling pipes and insulated blankets to manage this exact gradient — distributed nanoscale sensing and micro-actuation is a proposed next step for finer, adaptive control without permanent embedded plumbing.