CAMARÃO, Diego de Lucena. Propriedades difusivas de sistemas clássicos confinados. 2011. 79 f. Dissertação (Mestrado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2011. / Submitted by Edvander Pires (edvanderpires@gmail.com) on 2015-04-28T21:29:36Z No. of bitstreams: 1 2011_dis_dlcamarao.pdf: 2441556 bytes, checksum: ff4cb229929b646cece7ef667144d79d (MD5) / Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2015-04-29T17:54:40Z (GMT) No. of bitstreams: 1 2011_dis_dlcamarao.pdf: 2441556 bytes, checksum: ff4cb229929b646cece7ef667144d79d (MD5) / Made available in DSpace on 2015-04-29T17:54:41Z (GMT). No. of bitstreams: 1 2011_dis_dlcamarao.pdf: 2441556 bytes, checksum: ff4cb229929b646cece7ef667144d79d (MD5) Previous issue date: 2011 / Nesta dissertação, fizemos um estudo das propriedades difusivas de um sistema de partículas clássicas carregadas em canais quasi-unidimensionais. Mais especificamente, no Capítulo 2, apresentamos uma revisão do problema da difusão e do movimento browniano. Mostramos que as abordagens de Einstein e de Langevin para o movimento browniano são equivalentes no limite de tempos longos. Isto foi feito através do cálculo analítico do deslocamento quadrático médio (MSD) de um sistema unidimensional de N partículas não--interagentes através da solução da equação de difusão. No Capítulo 3, introduzimos o método de Dinâmica Molecular (DM), amplamente utilizado em simulações computacionais de sistemas de N partículas clássicas. Apresentamos dois métodos de integração numérica das equações de movimento: o algoritmo de Verlet e o algoritmo leapfrog. Abordamos brevemente o método de Dinâmica Molecular de Langevin (DML), que inclui um termo de flutuações térmicas (força estocástica), devido às colisões das moléculas do fluido com as partículas do sistema. Finalmente, apresentamos uma aproximação do método de DML chamada Dinâmica Browniana (DB). No Capítulo 4, estudamos as propriedades difusivas, através da análise do deslocamento quadrático médio, de um sistema de partículas clássicas carregadas sujeitas à ação de um potencial de confinamento unidimensional, analisando a transição do regime de difusão em linha (SFD) para o regime de difusão bidimensional (2D). Vimos como ocorre essa transição em função dos parâmetros que regulam o potencial de confinamento. Discutimos a validade dos resultados numéricos obtidos em relação a resultados analíticos teóricos encontrados na literatura. Finalmente, no Capítulo 5, apresentamos um resumo dos resultados obtidos, bem como discutimos perspectivas e sugestões para futuros trabalhos.

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / Nesta dissertaÃÃo, fizemos um estudo das propriedades difusivas de um sistema de partÃculas clÃssicas carregadas em canais quasi-unidimensionais. Mais especificamente, no CapÃtulo 2, apresentamos uma revisÃo do problema da difusÃo e do movimento browniano. Mostramos que as abordagens de Einstein e de Langevin para o movimento browniano sÃo equivalentes no limite de tempos longos. Isto foi feito atravÃs do cÃlculo analÃtico do deslocamento quadrÃtico mÃdio (MSD) de um sistema unidimensional de N partÃculas nÃo--interagentes atravÃs da soluÃÃo da equaÃÃo de difusÃo. No CapÃtulo 3, introduzimos o mÃtodo de DinÃmica Molecular (DM), amplamente utilizado em simulaÃÃes computacionais de sistemas de N partÃculas clÃssicas. Apresentamos dois mÃtodos de integraÃÃo numÃrica das equaÃÃes de movimento: o algoritmo de Verlet e o algoritmo leapfrog. Abordamos brevemente o mÃtodo de DinÃmica Molecular de Langevin (DML), que inclui um termo de flutuaÃÃes tÃrmicas (forÃa estocÃstica), devido Ãs colisÃes das molÃculas do fluido com as partÃculas do sistema. Finalmente, apresentamos uma aproximaÃÃo do mÃtodo de DML chamada DinÃmica Browniana (DB). No CapÃtulo 4, estudamos as propriedades difusivas, atravÃs da anÃlise do deslocamento quadrÃtico mÃdio, de um sistema de partÃculas clÃssicas carregadas sujeitas à aÃÃo de um potencial de confinamento unidimensional, analisando a transiÃÃo do regime de difusÃo em linha (SFD) para o regime de difusÃo bidimensional (2D). Vimos como ocorre essa transiÃÃo em funÃÃo dos parÃmetros que regulam o potencial de confinamento. Discutimos a validade dos resultados numÃricos obtidos em relaÃÃo a resultados analÃticos teÃricos encontrados na literatura. Finalmente, no CapÃtulo 5, apresentamos um resumo dos resultados obtidos, bem como discutimos perspectivas e sugestÃes para futuros trabalhos.

Until recently, numerical modulation models for the solar modulation of cosmic rays have been based primarily on finite difference approaches; however, models based on the solution of an appropriate set of stochastic differential equations have become increasingly popular. This study utilises such a spatially three-dimensional and time-stationary model, based on that of Strauss et al. (2011b). The remarkable numerical stability and powerful illustrative capabilities of this model are utilised extensively and in a distinctly comparative fashion to enable new insights into the processes of modulation. The model is refined to provide for both the Smith-Bieber (Smith and Bieber, 1991) and Jokipii-Kota (Jokipii and Kota, 1989) modifcations to the Parker heliospheric magnetic field (Parker, 1958) and the implications for modulation are investigated. During this investigation it is conclusively illustrated that the Parker field is most conducive to drift dominated modulation, while the Jokipii-Kota and Smith-Bieber modifcations are seen to induce successively larger contributions from diffusive processes. A further refinement to the model is the incorporation of a different profile for the heliospheric current sheet. This profile is defined by its latitudinal extent given by Kota and Jokipii (1983), as opposed to the profile given by Jokipii and Thomas (1981). An extensive investigation into current sheet related matters is launched, illustrating the difference between these current sheet geometries, the associated drift velocity fields and the effect on modulation. At high levels of solar activity, such that the current sheet enters deep enough into the polar regions, the profile of Kota and Jokipii (1983) is found to significantly reduce the effective inward (outward) drifts of positively (negatively) charged particles during A > 0 polarity cycles. The analogous effect is true for A < 0 polarity cycles and the overall effect is of such an extent that the A > 0 and A < 0 solutions are found to coincide at the highest levels of solar activity to form a closed loop. This is a result that has never before been achieved without having to scale down the drift coefficient to zero at solar maximum, as was done by e.g. Ndiitwani et al. (2005). Furthermore, it is found that the drift velocity fields associated with these two current sheet profiles lead to significant differences in modulation even at such low levels of solar activity where no difference in the geometries of these profiles are yet in evidence. The model is finally applied to reproduce four observed galactic proton spectra, selected from PAMELA measurements (Adriani et al., 2013) during the atypical solar minimum of 2006 to 2009; a new proton local interstellar spectrum was employed. The results are found to be in accordance with that found by other authors and in particular Vos (2011), i.e. the diffusion was required to consistently increase from 2006 to 2009 and, in addition, the rigidity dependence below ~ 3 GV was required to change over this time so that the spectra became increasingly softer. / MSc (Space Physics), North-West University, Potchefstroom Campus, 2015

Until recently, numerical modulation models for the solar modulation of cosmic rays have been based primarily on finite difference approaches; however, models based on the solution of an appropriate set of stochastic differential equations have become increasingly popular. This study utilises such a spatially three-dimensional and time-stationary model, based on that of Strauss et al. (2011b). The remarkable numerical stability and powerful illustrative capabilities of this model are utilised extensively and in a distinctly comparative fashion to enable new insights into the processes of modulation. The model is refined to provide for both the Smith-Bieber (Smith and Bieber, 1991) and Jokipii-Kota (Jokipii and Kota, 1989) modifcations to the Parker heliospheric magnetic field (Parker, 1958) and the implications for modulation are investigated. During this investigation it is conclusively illustrated that the Parker field is most conducive to drift dominated modulation, while the Jokipii-Kota and Smith-Bieber modifcations are seen to induce successively larger contributions from diffusive processes. A further refinement to the model is the incorporation of a different profile for the heliospheric current sheet. This profile is defined by its latitudinal extent given by Kota and Jokipii (1983), as opposed to the profile given by Jokipii and Thomas (1981). An extensive investigation into current sheet related matters is launched, illustrating the difference between these current sheet geometries, the associated drift velocity fields and the effect on modulation. At high levels of solar activity, such that the current sheet enters deep enough into the polar regions, the profile of Kota and Jokipii (1983) is found to significantly reduce the effective inward (outward) drifts of positively (negatively) charged particles during A > 0 polarity cycles. The analogous effect is true for A < 0 polarity cycles and the overall effect is of such an extent that the A > 0 and A < 0 solutions are found to coincide at the highest levels of solar activity to form a closed loop. This is a result that has never before been achieved without having to scale down the drift coefficient to zero at solar maximum, as was done by e.g. Ndiitwani et al. (2005). Furthermore, it is found that the drift velocity fields associated with these two current sheet profiles lead to significant differences in modulation even at such low levels of solar activity where no difference in the geometries of these profiles are yet in evidence. The model is finally applied to reproduce four observed galactic proton spectra, selected from PAMELA measurements (Adriani et al., 2013) during the atypical solar minimum of 2006 to 2009; a new proton local interstellar spectrum was employed. The results are found to be in accordance with that found by other authors and in particular Vos (2011), i.e. the diffusion was required to consistently increase from 2006 to 2009 and, in addition, the rigidity dependence below ~ 3 GV was required to change over this time so that the spectra became increasingly softer. / MSc (Space Physics), North-West University, Potchefstroom Campus, 2015