This is a genuine coupled mass-spring lattice — the same microscopic model that gives rise to phonons in a real crystal — not a ray-traced particle picture. Chain A (atoms of mass m₁, springs of stiffness k₁) is joined at one point to chain B (mass m₂, springs k₂) by an interface spring kint = √(k₁k₂). Every atom's motion is integrated directly from Newton's second law with velocity-Verlet, the same numerical scheme used in real molecular dynamics:
a_n = [k_L(u_{n-1}-u_n) + k_R(u_{n+1}-u_n)] / m_n
u(t+dt) = u(t) + v·dt + ½a·dt² (then re-evaluate a, average to update v)
A localized, long-wavelength Gaussian wavepacket is launched in chain A toward the junction. Long wavelength means the chain behaves like a continuous elastic string, so each side has a well-defined mechanical impedance Z = √(k·m) — exactly analogous to acoustic impedance Z = ρc. Wave theory then predicts the packet splits into a transmitted and a reflected part with no randomness at all:
T = 4·Z1·Z2 / (Z1+Z2)² R = [(Z1-Z2)/(Z1+Z2)]² T + R = 1
- Sound speed sliders — set c1 = √(k1/m1), c2 = √(k2/m2) in each chain (mass of chain A fixed at 1).
- Impedance ratio Z2/Z1 — together with c1, c2 this fixes m2 and k2, so all three sliders act independently just like the acoustic-mismatch continuum model.
- Launch wavepacket — fires one packet; it auto-relaunches once the transmitted and reflected pieces have cleanly separated from the junction and their energies have been tallied.
- The live "measured ⟨T⟩" readout is the running average of Σ(kinetic+potential energy right of the junction) ⁄ (total packet energy) across launches — a deterministic classical-wave measurement, in contrast to the probabilistic per-phonon transmit/reflect coin-flip used by Monte-Carlo phonon-scattering models of the same interface.
- A well-matched interface (Z1≈Z2) transmits almost all the wave energy — low Kapitza (thermal boundary) resistance; a strongly mismatched one reflects most of it back — high R_K, the dominant heat-flow bottleneck at real nanoscale material interfaces.