Computer Physics Reports最新文献

This paper reviews a method to calculate steady, axisymmetric wind models with frozen-in magnetic fields, as a straightforward extension of the one-dimensional model developed by Weber and Davis. The wind solution along the magnetic field is given by an algebraic equation (the Bernoulli equation) for the density. There appear two critical points, the slow mode and the fast mode critical points. The shape of the magnetic field should be determined in such a way that the force-balance across the field is satisfied. This requirement leads to a second-order partial differential equation for the magnetic stream function. This equation is singular at the Alfvén point, and an additional constraint is introduced there to obtain a regular solution. A numerical scheme is developed following this basic formulation, and examples of solutions are presented. The basic feature of the solution is the poleward deflection of the flow due to the build-up of toroidal magnetic field in the wind. The magnetic winds from rotating objects are therefore collimated along the rotation axis.

The very different spatial and temporal scales inherent in the dissipative MHD model impose severe requirements on the numerical simulations, which have to be met by appropriate methods. The numerical approximation discussed is based on the finite-element method, where space-time discretization and semi-discretization are included. Specific advanced methods, such as adaptive mesh, multigrid, normal-mode analysis and semi-implicit schemes are presented. Important features of present and future supercomputers are being addressed.

We review a number of models which are currently being considered for coronal heating, but we consider also heating of the chromosphere which requires nearly as much energy as the active corona, and more energy than coronal holes or the quiet corona. There are basically two types of models, which are motivated by a variety of observations. (1) Models which invoke MHD waves generated by the convective motions are motivated by observations of the ubiquitous presence of Alfvén waves in the solar wind. There is evidence that these waves heat and accelerate the solar wind protons and heavy ions. The solar wind thus provides one example of wave heating. Waves have the advantage of being able to heat the chromosphere and photospheric magnetic flux tubes on their way to the corona. MHD turbulence (as observed in the solar wind) or resonance absorption seem to provide adequate dissipation mechanisms. A problem with wave theories is that the waves tend to be reflected by the steep Alfén speed gradient in the chromosphere and transition region, but it is estimated that adequate energy fluxes can enter the open corona, or closed coronal loops if global loop resonances can be excited. Short coronal loops (L≲10⁴ km) can also receive adequate wave energy fluxes even if the loop resonances are not excited, but a problem exists with getting enough energy into intermediate length loops (L≈10⁴-5×10⁴ km) since their resonant frequencies are possibly to high to be excited. (2) Models which invoke the gradual buildup of coronal magnetic energy due to random walks of the photospheric flux tubes, and the subsequent release of that energy via current sheet information and reconnection, are supported by observations indicating that localized impulsive heating and dynamic events occur in the transition region and corona. These models cannot explain the chromospheric heating or the coronal heating on open field lines. They require substantial random walks of the photospheric footpoints, which still need to observationally verified. A third possibility, which has not been studied in detail, is that the chromospheric and coronal heating is associated with emergence and cancellation of magnetic flux. All types of models are ripe for further studies using numerical simulations, and along the way we shall offer several suggestions for fruitful numerical studies.

The memory function approach is discussed with respect to the representation of computer generated time correlation functions. Single-particle and collective properties of the Lennard-Jones fluid are considered, and the usefulness of directly evaluated memory functions and model memory functions is discussed. The scatterirng functions analysis is restricted to the medium and small wave vector range in order to demonstrate the approximate hydrodynamic behaviour of these functions, that can be exploited to determine transport coefficients. Furthermore, the method of determining thermal transport coefficients via a single Gaussian memory function is presented in direct comparison with molecular dynamics results. Experimental aspects are considered. Finally a limited comparison of results for the Lennard-Jones and the hard sphere fluids is given.

A review is given of statistical methods which are applied to the distributions of various quantities in atomic spectra. The fundamental laws discovered by nuclear physicists are first recalled. Then, applications to quantum numbers, level energies and electric-dipolar line strengths are described, with many examples from the literature.