Chapter 5: Monte Carlo resolution of the Boltzmann Transport Equation
Résumé
Heat transport in solid materials can be understood in the framework of lattice dynamic. Collective motion of atoms generates acoustic waves that carry heat. The motion and the interactions of phonons rule heat transport at the microscale and these mechanisms can be described by the Boltzmann transport equation (BTE) for structures length in range of tens of nanometer till tens of micron, according to the wave-corpuscle duality the latter ones can be considered as pseudo-particles. The BTE is used in physics to describe the behavior of a system which is not in thermodynamic equilibrium from a statistical standpoint. Typically BTE can be used to model the transport and interactions of moving particles. The Monte Carlo (MC) method is a numerical technique based on the use of random numbers sampling according to probability laws to model and solve physical or mathematical problems. Using the MC method for BTE solution can help to determine the thermal properties of nanostructures.