Problemas inversos em termodinâmica: tratamento quântico e semiclássico

Abstract

This dissertation shows the optimization of experimental phonon density of states for aluminum, to describe the behavior of heat capacity versus temperature as well as other experimentally obtained thermodynamic properties. The connection between heat capacity, CV , and phonon density of states, g( ), is given by a Fredholm rst order integral equation, which means that obtaining g( ) from CV will be an ill posed problem. We used the Tikhonov regularization to re ne the experimental phonons density of states. In chapter 3 the calculation of the quantum second virial coe cient is discussed for a recent potential of the He{He system. The quantum treatment allowed the comparison of the calculated data with the experimental results at temperatures around 10K ; temperatures where quantum e ects are important. The study was conducted to verify the quality of this potential. In chapter 4 the sensitivity of the second virial coe cient was studied in relation to the interatomic potential for temperatures below 100 K, the semiclassical method was used. The best data region of the second virial coe cient was sought, to re ne the interatomic potential within 2 and 5 angstroms. The originally nonlinear problem was linearized by the functional sensitivity analysis method and, represented in this way, could be investigated. In this case, the Tikhonov regularization was explored to give an appropriate solution to the interatomic potential.