Lattice Phonon Scattering: Mass-Spring Chain Kapitza Model

Heat carried by phonons rarely flows across a material interface unimpeded — some fraction is reflected back, producing the thermal boundary (Kapitza) resistance that dominates heat flow at nanoscale contacts. This simulation builds the phenomenon from the ground up as a real one-dimensional lattice: two coupled mass-spring chains with different mass and stiffness, joined at a single interface spring, integrated directly with a velocity-Verlet molecular-dynamics scheme. A long-wavelength Gaussian wavepacket launched in the "hot" chain travels to the junction and splits deterministically into a transmitted and a reflected wave, exactly as continuum wave theory predicts through each chain's mechanical impedance. Live readouts compare the analytic impedance-mismatch transmission coefficient against the energy fraction actually measured in the running lattice simulation.