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Topological superfluid state is different from the normal superfluid one due to the excitation energy gap on the boundary. How to obtain the topological superfluid state by using spin–orbit coupling to control the s-waves paired mass-imbalanced Fermi gas is a recent novel topic. In this paper, we study the topological superfluid phase diagram of two-dimensional mass-imbalanced Fermi gas with Rashba spin–orbit coupling at zero temperature. We find that due to the competition among mass imbalance, pairing interaction and spin–orbit coupling, there is a double-well structure in the thermodynamic potential, which affects the properties of the ground state of the system. We comprehensively give the phase diagrams of the system on the plane of spin–orbit coupling and chemical potential, and the phase diagrams on the plane of the reduced mass ratio and two-body binding energy. This study not only points out the stable region of topological superfluid state of mass-imbalanced Fermi gas, but also provides a detailed theoretical basis for better observation of topological superfluid state in experiments.

In this paper we report on the effect of an InxGa1-xN continuously graded buffer layer on an InGaN epilayer grown on a GaN template. In our experiment, three types of buffer layers including constant composition, continuously graded composition, and the combination of constant and continuously graded composition are used. Surface morphologies, crystalline quality, indium incorporations, and relaxation degrees of InGaN epilayers with different buffer layers are investigated. It is found that the InxGa1-xN continuously graded buffer layer is effective to improve the surface morphology, crystalline quality, and the indium incorporation of the InGaN epilayer. These superior characteristics of the continuously graded buffer layer can be attributed to the sufficient strain release and the reduction of dislocations.

We use a simple and controllable method to fabricate GaN-based light-emitting diodes (LEDs) with 22° undercut sidewalls by the successful implementation of the inductively coupled plasma reactive ion etching (ICP-RIE). Our experiment results show that the output powers of the LEDs with 22° undercut sidewalls are 34.8 mW under a 20-mA current injection, 6.75% higher than 32.6 mW, the output powers of the conventional LEDs under the same current injection.

Noether—Mei symmetry of a discrete mechanico-electrical system on a regular lattice is investigated. Firstly, the Noether symmetry of a discrete mechanico-electrical system is reviewed, and the motion equations and energy equations are derived. Secondly, the definition of Noether—Mei symmetry for the system is presented, and the criterion is derived. Thirdly, conserved quantities induced by Noether—Mei symmetry with their existence conditions are obtained. Finally, an example is discussed to illustrate the results.

Based on the complex variable moving least-square (CVMLS) approximation and a local symmetric weak form, the complex variable meshless local Petrov—Galerkin (CVMLPG) method of solving two-dimensional potential problems is presented in this paper. In the present formulation, the trial function of a two-dimensional problem is formed with a one-dimensional basis function. The number of unknown coefficients in the trial function of the CVMLS approximation is less than that in the trial function of the moving least-square (MLS) approximation. The essential boundary conditions are imposed by the penalty method. The main advantage of this approach over the conventional meshless local Petrov—Galerkin (MLPG) method is its computational efficiency. Several numerical examples are presented to illustrate the implementation and performance of the present CVMLPG method.

In this paper, we investigate whether the Lie symmetry can induce the Mei conserved quantity directly in a nonconservative Hamilton system and a theorem is presented. The condition under which the Lie symmetry of the system directly induces the Mei conserved quantity is given. Meanwhile, an example is discussed to illustrate the application of the results. The present results have shown that the Lie symmetry of a nonconservative Hamilton system can also induce the Mei conserved quantity directly.