  We derive expression for energy flux in terms of lattice normal mode
coordinates. Energy transmission across solid junctions from lattice dynamic
point of view is given and its relation with atomic masses, lattice constants,
and group velocities is clarified. A scattering boundary method (SBM) is
proposed for calculating the amplitude transmission across solid junctions. The
phonon transmission coefficients and thermal conductance are calculated for two
kinds of acoustically mismatched junctions: different chirality nanotubes
(11,0) to (8,0), and Si-Ge interface structure. Our calculation shows a
mode-dependent transmission in nanotube junction due to the high symmetry
vibrating motions for nanotube atoms, indicating its possible important role in
nanotube mixture thermal conductance. Energy transmission and Kapitza
conductance across the Si-Ge interface [001] are calculated for the Si-Ge
diamond-type structure. It is shown that the energy transmission across the
Si-Ge interface depends on the incident angle and on the interface mode
conversion. A critical incident angle about 42 degrees numerically found for
waves incident from Ge to Si. Our numerical result of the Kapitza conductance
at temperature T=200K is G_K=4.6x10^8 W/(Km^2) We find numerically scaling law
G_K proportional to T^{2.87} for [001] interface at low temperature.
