Large-time Behavior of Solutions to the Inflow Problem of Full Compressible Navier-Stokes Equations

Large-time behavior of solutions to the inflow problem of full compressible Navier-Stokes equations is investigated on the half line $R^+ =(0,+\infty)$. The wave structure which contains four waves: the transonic(or degenerate) boundary layer solution, 1-rarefaction wave, viscous 2-contact wave and 3-rarefaction wave to the inflow problem is described and the asymptotic stability of the superposition of the above four wave patterns to the inflow problem of full compressible Navier-Stokes equations is proven under some smallness conditions. The proof is given by the elementary energy analysis based on the underlying wave structure. The main points in the proof are the degeneracies of the transonic boundary layer solution and the wave interactions in the superposition wave.Comment: 27 page

Microscopic interface phonon modes in structures of GaAs quantum dots embedded in AlAs shells

By means of a microscopic valence force field model, a series of novel microscopic interface phonon modes are identified in shell quantum dots(SQDs) composed of a GaAs quantum dot of nanoscale embedded in an AlAs shell of a few atomic layers in thickness. In SQDs with such thin shells, the basic principle of the continuum dielectric model and the macroscopic dielectric function are not valid any more. The frequencies of these microscopic interface modes lie inside the gap between the bulk GaAs band and the bulk AlAs band, contrary to the macroscopic interface phonon modes. The average vibrational energies and amplitudes of each atomic shell show peaks at the interface between GaAs and AlAs. These peaks decay fast as their penetrating depths from the interface increase.Comment: 13 pages, 4 figure

Relationship of transport coefficients with statistical quantities of charged particles

In the previous studies, from the Fokker-Planck equation the general spatial transport equation, which contains an infinite number of spatial derivative terms $T_n=\kappa_{nz}\partial^n{F}/ \partial{z^n}$ with $n=1, 2, 3, \cdots$, was derived. Due to the complexity of the general equation, some simplified equations with finite spatial derivative terms have been used in astrophysical researches, e.g., the diffusion equation, the hyperdiffusion one, subdiffusion transport one, etc. In this paper, the simplified equations with the highest order spatial derivative terms up to the first-, second-, third-, fourth-, and fifth-order are listed, and their transport coefficient formulas are derived, respectively. We find that most of the transport coefficients are determined by the corresponding statistical quantities. In addition, we find that the well-known statistical quantities, skewness $\mathcal{S}$ and kurtosis $\mathcal{K}$, are determined by some transport coefficients. The results can help one to use different transport coefficients determined by the statistical quantities, including many that are relatively new found in this paper, to study charged particle parallel transport processes

The effect of solar wind on the charged particles' diffusion coefficients

The transport of energetic charged particles through magnetized plasmas is ubiquitous in interplanetary space and astrophysics, and the important physical quantities are the along-field and cross-field spatial diffusion coefficients of energetic charged particles. In this paper, the influence of solar wind on particle transport is investigated. Using the focusing equation, we obtain along- and cross-field diffusion coefficient accounting for the solar wind effect. For different conditions, the relative importance of solar wind effect to diffusion are investigated. It is shown that when energetic charged particles are close to the sun, for along-field diffusion the solar wind effect needs to be taken into account. These results are important for studying energetic charged particle transport processes in the vicinity of the sun