Resonant tunneling in step-barrier structures is investigated by using the transfer-matrix technique. The formulas for the transmission coefficient and the current density are derived when taking into account the coupling between components of the motion of an electron in directions parallel and perpendicular to the interfaces. By making a detailed comparison of resonant tunneling among single square-barrier structures, asymmetric double-barrier structures, and step-barrier structures, the tunneling properties in step-barrier structures are revealed. It is shown that the global behavior of step-barrier structures obtained resembles that of asymmetric double-barrier structures, and step-barrier structures are superior to both single- and double-barrier structures in many aspects. In comparison to asymmetric double-barrier structures, step-barrier structures have several features, such as a wider negative-differential resistance region, easier fabrication, high-speed response, and a relatively lower transmission coefficient and current peak-to-valley ratios. Moreover, higher resonant bias is required in order to obtain optimal transmission resonances in the step-barrier structure. The results shown in this work not only shed new light on the physics of resonant tunneling in electric-barrier structures but are also helpful in designing quantum devices based on step-barrier tunneling structures.

从理论和数值模拟两个方面分析了ESWL中的非线性的动力学焦点和实际焦点的位置，给出三种典型的动力学焦点的数值结果，说明非线性动力学焦点和实际焦点一般不是几何焦点,指出正确确定实际焦点在ESWL技术中的重要性。

The floating zone technique is promising to realize large, high-quality crystals under microgravity. Thermocapillary flow, which is the dominant convection in a floating zone under microgravity, has been widely reported in the literature to be extremely sensitive to the Prandtl number Pr: In the present study, the effect of Pr on steady thermocapillary convection is re-evaluated based on both analytical and numerical solutions. The results indicate that an approximate similarity of temperature and velocity structures in a large Pr range is realized under suitable conditions, fixing the Marangoni number Ma; in steady two-dimensional regime.

The mixed buoyancy-thermocapillary flow in a half-zone liquid bridge with the dynamic Bond number Bd≈α(1) is investigated numerically by the finite volume method. The similarities of temperature and velocity structures are realized under conditions of fixed Marangoni and Rayleigh numbers in steady two-dimensional regime for a suitable Prandtl number range.

Three-dimensional oscillatory thermocapillary convection in silicone oil liquid bridge is studied numerically by means of finite volume method (FVM). The results reveal the existence of two different oscillatory modes: pulsating and rotating oscillations. Close to the onset of oscillation, the pulsating oscillatory convection is observed. With the increment of Marangoni number Ma, the pulsating oscillatory convection is replaced by rotating oscillatory convection, where the temperature and velocity fields demonstrate the characteristics of rotation. An approximately linear relationship between Ma and dimensionless main frequency f*=fH2χ1 is found for As=4.0 in periodic oscillatory regime. This relationship becomes a little more complex for As=1.0.