Magnetostatic relations including fluctuation fields - the local expansion

Using the approach of local expansion, we analyze the magnetostatic relations in the case of conventional turbulence. The turbulent relations are obtained consisten tly for themomentum equation and induction equation of both the average and fluctuation relations.In comparison with the magnetostatic relations as discussed usually, turbulent fluctuationfields produce forces, one of which 1/(4π)(α1×B0)×B0 may have parallel and perpendicular components in the direction of magnetic field, the other of which 1/(4π)K×B0 is introduced by the boundary value of turbulence and is perpendicular to the magnetic field. In the case of 2-dimensional configuration of magnetic field, the basic equation will be reduced into a second-order elliptic equation, which includes some linear and nonlinear terms introduced by turbulent fluctuation fields. Turbulent fields may change the configuration of magnetic field and even shear it non-uniformly. The study on the influence of turbulent fields is significant since they are observed in many astrophysical environments.

The magnetostatic relations including fluctuation fields

The influences of the fluctuation fields are important in many astrophysical environments as shown by the observations, and can not be neglected. On the basis of the first-order smoothing approximation, in the present paper, we demonstrate the magnetostatic equations for both the cases of the conventional turbulence aud the random waves, and discuss the consistent conditions of the equations. In the static problem, the fluctuation Lorentz force(▽×δB)×δB influences the large-scale configurations of magnetic field. To study this influence in detail is quite necessary for the explanations of the observation features, especially for the astrophysical environments where the magnetic fields, including the fluctuation fields, are the dominant factors in the equilibrium of momentum and energy.

Relations veritables et curieuses de l'isle de Madagascar et du Bresil : avec l'histoire de la derniere guerre faite au Bresil, entre les portugais & les hollandois : trois relations d'Egypte, e une du royaume de Perse

‘Relations veritables et curieuses de l'Isle de Madagascar, et du Bresil’, de responsabilidade do livreiro Augustin Courbé, foi redigida em parte por Morisot, de DiJon, com base em documentos fornecidos pelos irmãos Dupuy. A obra, composta por dois volumes reunidos em um tomo, contém diversos relatos. Muita confusão existe acerca dessa edição de Courbé, seja relativamente ao número de volumes da obra, seja quanto à autoria dos relatos. Borba de Moraes a firma que "esses erros decorrem da raridade do trabalho completo". O primeiro volume, apresentado sob o titulo geral ‘Relations veritables et curieuses de l’Isle de Madagascar, et du Bresil’, contém os trabalhos ‘Relation du voyage de François Couché...: De la religion, moeurs, et façons de faire de ceux de I'Lsle de Madagascar: colloque entre le madagascarois et le françois...’, e ‘Re1ation du voyage de Roulox Baro’. O segundo volume é intitulado ‘Histoire des derniers troubles du Bresil entre les hollandois et les portugais’ e foi escrito por Pierre Moreau, cujo texto ocupa as 212 páginas iniciais. Além deste, constam do volume ‘Trois relations d'Egypte et autres memoires...’ e a ‘Relation d'um voyage de Perse’. Prod uzida a partir da observação dos fatos ocorridos durante o período de sua permanência em Pernambuco durante a ocupação pelos holandeses, a obra de Moreau é de capital importância para o estudo da situação socioeconômica de Pernambuco sob o domínio holandês. A edição de A. Courbé, conhecido livreiro que se estabeleceu em Paris de 1629 a 1660, teve o projeto das ilustrações a cargo de Jean Picard, oriundo de uma famosa família de gravadores, cujo nome aparece no primeiro volume apenas, segundo Borba de Moraes