A unified gas kinetic scheme for transport and collision effects in plasma

In this study, the Vlasov-Poisson equation with or without collision term for plasma is solved by the unified gas kinetic scheme (UGKS). The Vlasov equation is a differential equation describing time evolution of the distribution function of plasma consisting of charged particles with long-range interaction. The distribution function is discretized in discrete particle velocity space. After the Vlasov equation is integrated in finite volumes of physical space, the numerical flux across a cell interface and source term for particle acceleration are computed to update the distribution function at next time step. The flux is decided by Riemann problem and variation of distribution function in discrete particle velocity space is evaluated with central difference method. A electron-ion collision model is introduced in the Vlasov equation. This finite volume method for the UGKS couples the free transport and long-range interaction between particles. The electric field induced by charged particles is controlled by the Poisson's equation. In this paper, the Poisson's equation is solved using the Green's function for two dimensional plasma system subjected to the symmetry or periodic boundary conditions. Two numerical tests of the linear Landau damping and the Gaussian beam are carried out to validate the proposed method. The linear electron plasma wave damping is simulated based on electron-ion collision operator. Compared with previous methods, it is shown that the current method is able to obtain accurate results of the Vlasov-Poisson equation with a time step much larger than the particle collision time. Highly non-equilibrium and rarefied plasma flows, such as electron flows driven by electromagnetic field, can be simulated easily.Comment: 33 pages, 13 figure

Urban Planning in China Shanghai: City Planning "With a Human Face" The Case of the Gubei Pedestrian Promenade (GPP): The Pedestrianisation of a Densely Populated Area

International audienceEver since Expo 2010 was held in Shanghai, the city has been trying to present an image of itself as having the capacity to offer amenities that are more environmentally friendly and that contribute to an improved quality of life. This article aims to show that a locally-enacted facility – far from the much-publicised monumental developments – can constitute a high point of urban activity, an example that contributes to cultivating the sought-after identity of a modern city concerned about the sustainability of its actions. Thanks to a singular grouping of actors from the public, semi-public, and private sectors, the Gubei Pedestrian Promenade (GPP) in the western district of Changning laid the principles of a sustainable urban planning programme ten years before the publication of Shanghai’s New City Plan, resetting the ways for building the city. From today’s perspective, this initiative could be seen as a manifestation of this new way of imagining the cit