Multiscale lattice Boltzmann approach to modeling gas flows

For multiscale gas flows, kinetic-continuum hybrid method is usually used to balance the computational accuracy and efficiency. However, the kinetic-continuum coupling is not straightforward since the coupled methods are based on different theoretical frameworks. In particular, it is not easy to recover the non-equilibrium information required by the kinetic method which is lost by the continuum model at the coupling interface. Therefore, we present a multiscale lattice Boltzmann (LB) method which deploys high-order LB models in highly rarefied flow regions and low-order ones in less rarefied regions. Since this multiscale approach is based on the same theoretical framework, the coupling precess becomes simple. The non-equilibrium information will not be lost at the interface as low-order LB models can also retain this information. The simulation results confirm that the present method can achieve model accuracy with reduced computational cost

The Norm of the Learning-Disability Checklist for Elementary and Middle School Children (in Chinese)

The Learning-Disabilities Checklist for Elementary and Middle School Children was administered to 1067 subjects in Shanghai. The data analyses brought us the following: 1) The mean and standard deviation of each variable of raw data; 2) There were significant age differences and sex differences for each variable; 3) The reliability and validity of this test was up to the criteria of psychometrology; 4) A Shanghai norm was made

The entanglement in one-dimensional random XY spin chain with Dzyaloshinskii-Moriya interaction

The impurities of exchange couplings, external magnetic fields and Dzyaloshinskii--Moriya (DM) interaction considered as Gaussian distribution, the entanglement in one-dimensional random $XY$ spin systems is investigated by the method of solving the different spin-spin correlation functions and the average magnetization per spin. The entanglement dynamics at central locations of ferromagnetic and antiferromagnetic chains have been studied by varying the three impurities and the strength of DM interaction. (i) For ferromagnetic spin chain, the weak DM interaction can improve the amount of entanglement to a large value, and the impurities have the opposite effect on the entanglement below and above critical DM interaction. (ii) For antiferromagnetic spin chain, DM interaction can enhance the entanglement to a steady value. Our results imply that DM interaction strength, the impurity and exchange couplings (or magnetic field) play competing roles in enhancing quantum entanglement.Comment: 12 pages, 3 figure

Galilean invariance of lattice Boltzmann models

It is well-known that the original lattice Boltzmann (LB) equation deviates from the Navier-Stokes equations due to an unphysical velocity dependent viscosity. This unphysical dependency violates the Galilean invariance and limits the validation domain of the LB method to near incompressible flows. As previously shown, recovery of correct transport phenomena in kinetic equations depends on the higher hydrodynamic moments. In this Letter, we give specific criteria for recovery of various transport coefficients. The Galilean invariance of a general class of LB models is demonstrated via numerical experiments

Multi-component lattice-Boltzmann model with interparticle interaction

A previously proposed [X. Shan and H. Chen, Phys. Rev. E {\bf 47}, 1815, (1993)] lattice Boltzmann model for simulating fluids with multiple components and interparticle forces is described in detail. Macroscopic equations governing the motion of each component are derived by using Chapman-Enskog method. The mutual diffusivity in a binary mixture is calculated analytically and confirmed by numerical simulation. The diffusivity is generally a function of the concentrations of the two components but independent of the fluid velocity so that the diffusion is Galilean invariant. The analytically calculated shear kinematic viscosity of this model is also confirmed numerically.Comment: 18 pages, compressed and uuencoded postscript fil

Effect of next-nearest neighbor coupling on the optical spectra in bilayer graphene

We investigate the dependence of the optical conductivity of bilayer graphene (BLG) on the intra- and inter-layer interactions using the most complete model to date. We show that the next nearest-neighbor intralayer coupling introduces new features in the low-energy spectrum that are highly sensitive to sample doping, changing significantly the ``universal'' conductance. Further, its interplay with interlayer couplings leads to an anisotropy in conductance in the ultraviolet range. We propose that experimental measurement of the optical conductivity of intrinsic and doped BLG will provide a good benchmark for the relative importance of intra- and inter-layer couplings at different doping levels.Comment: 5 pages, 5 figure