Collision strength, the measure of strength for a binary collision, hasn't been defined clearly. In practice, many physical arguments have been employed for the purpose and taken for granted. A scattering angle has been widely and intensively used as a measure of collision strength in plasma physics for years. The result of this is complication and unnecessary approximation in deriving some of the basic kinetic equations and in calculating some of the basic physical terms. The Boltzmann equation has a five-fold integral collision term that is complicated. Chandrasekhar and Spitzer's approaches to the linear Fokker-Planck coefficients have several approximations. An effective variable-change technique has been developed in this dissertation as an alternative to scattering angle as the measure of collision strength. By introducing the square of the reduced impulse or its equivalencies as a collision strength variable, many plasma calculations have been simplified. The five-fold linear Boltzmann collision integral and linearized Boltzmann collision integral are simplified to three-fold integrals. The arbitrary order linear Fokker-Planck coefficients are calculated and expressed in a uniform expression. The new theory provides a simple and exact method for describing the equilibrium plasma collision rate, and a precise calculation of the equilibrium relaxation time. It generalizes bimolecular collision reaction rate theory to a reaction rate theory for plasmas. A simple formula of high precision with wide temperature range has been developed for electron impact ionization rates for carbon atoms and ions. The universality of the concept of collision strength is emphasized. This dissertation will show how Arrhenius' chemical reaction rate theory and Thomson's ionization theory can be unified as one single theory under the concept of collision strength, and how many important physical terms in different disciplines, such as activation energy in chemical reaction theory, ionization energy in Thomson's ionization theory, and the Coulomb logarithm in plasma physics, can be unified into a single one -- the threshold value of collision strength. The collision strength, which is a measure of a transfer of momentum in units of energy, can be used to reconcile the differences between Descartes' opinion and Leibnitz's opinion about the "true'' measure of a force. Like Newton's second law, which provides an instantaneous measure of a force, collision strength, as a cumulative measure of a force, can be regarded as part of a law of force in general.

Orientador: Hans Ingo Weber / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica / Made available in DSpace on 2018-07-24T05:43:03Z (GMT). No. of bitstreams: 1 Mattos_MarcioCoelhode_D.pdf: 10130294 bytes, checksum: 5b9cef82256f8fd05f78a1341b08ac10 (MD5) Previous issue date: 1998 / Resumo: Apresentamos neste trabalho uma investigação sobre as mudanças na dinâmica de sistemas com vibroimpacto. Particularmente estamos interessados no estudo da migração das freqüências características destes sistemas. Podemos considerar que um dado sistema com vibroimpacto tende a um sistema com impacto degenerado quando a folga deste sistema tende a zero ou a um valor maior que a amplitude de vibração do sistema na coordenada de impacto. Podemos também denominar estes sistemas como sistemas lineares associados ao sistema com impacto, se o impacto' for a única não linearidade presente no sistema. Mostramos que existe uma relação intrínseca entre a resposta do sistema com impacto e os sistemas lineares associados, ou sistemas degenerados. Para investigar esta relação, analisamos a resposta de sistemas com dois e três graus de liberdade com impacto em uma de suas coordenadas. Além disto, investigamos experimentalmente a resposta de uma viga engastada-livre excitada randomicamente e com impactos em sua extremidade livre. Observamos boa correlação entre os resultados numéricos e, experimentais. Propomos uma função para a migração da primeira freqüência característica da resposta de sistemas com vibroimpacto. O caminho da migração depende da distribuição da energia total fornecida ao sistema entre os diversos modos de vibração dos sistemas lineares associados / Abstract: This works presents an investigation on the changes in the dynamics of vibroimpact systems as their clearance is varied. Particularly we are interested in the migration of the characteristic frequencies of impact systems. We can consider that a given vibroimpact system reaches to a degenerated impact system when the clearance reaches to zero or to a value which is greater than the amplitude of the response of the system at the impact coordinate. We also can call these systems as associated linear systems of a given impact system, if the impact is the only nonlinearity which takes place. We show that there is an intrinsic relation between impact systems and their associated linear systems, or degenerated systems. To investigate this relation we consider the free response of 2-DOF and 3-DOF impact systems with impact in one of their coordinates. On the other hand, we have performed an experimental investigation in a randomly excited cantilever beam with impacts on its free end. We have found good agreement between numerical and experimental results. We have proposed a function for the migration of the first characteristic frequency of impact systems. The migration way depends on distribution of the total energy supplied to system among the vibration modes of the associated linear systems / Doutorado / Mecanica dos Sólidos e Projeto Mecanico / Doutor em Engenharia Mecânica

In this thesis we numerically compute the scattering lengths and bound states for sodium-rubidium collisions at low energy. This work was motivated by experiments which aim to produce Bose-Einstein condensates (BEC) mixtures of sodium-rubidium. Elastic collision properties are important for the rethermalization of the atoms during the evaporative cooling process. Inelastic processes, which we also discuss to some extent, cause trap losses in those experiments. In order to reach the required temperature and density the elastic collision rates should be sufficiently large compared to the inelastic rates. The scattering lengths, which completely specify the elastic collision parameters at low energy, determine the miscibility and phase diagram of the sodium-rubidium condensate mixture. We calculate the scattering lengths approximately and find agreement with previous calculations indicating that miscible phases of sodium and rubidium condensates do not appear to be feasible in the absence of external fields.