Zhong Zeng

Resonant tunneling in step-barrier structures under an applied electric field

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.

Direct numerical simulation of oscillatory Marangoni convection in cylindrical liquid bridges

A three-dimensional oscillatory Marangoni (thermocapillary) convection with Prandtl number Pr=16.0849 and Marangoni number Ma=3.30508×104 in a large aspect ratio (As=H/R) range, As=0.2–4, in a silicone oil liquid bridge with a non-deformable cylindrical surface is investigated by the finite volume method. The azimuthal wave numbers 1, 2, 3, 4, 5, 6, 10 and 16 are obtained for different aspect ratios, As. The dimensionless main frequency of periodic or quasi-periodic temperature oscillations strongly depends on aspect ratio, As. increases with the increment of As with approximately a bi-linear relation, and its gradient for As=0.2–1 is less than that for As>1. The periodic and quasi-periodic oscillations are found to depend on aspect ratio, As, for fixed Pr and Ma.

Three-dimensional oscillatory thermocapillary convection in liquid bridge under microgravity

Abstract 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*=fH2ϰ−1 is found for As=4.0 in periodic oscillatory regime. This relationship becomes a little more complex for As=1.0.

Three-dimensional oscillatory convection of LiCaAlF6 melts in Czochralski crystal growth

Abstract Three-dimensional (3D) unsteady mixed thermal buoyancy, Marangoni and forced convection of LiCaAlF 6 (LiCAF) melts (Prandtl number Pr ≈1.4) are investigated numerically for model set up typically for Czochralski crystal growth. With increasing crystal rotation rate, convection evolves from steady axisymmetric to three-dimensional oscillatory convection with varying spatio-temporal features. The details of the oscillatory convection structures are presented.

Usefulness of experiments with model fluid for thermocapillary convection—effect of Prandtl number on two-dimensional thermocapillary convection

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.

Marangoni convection in model of floating zone under microgravity

Marangoni convection in a half-zone model, a simplification of the floating zone model, is steady and axisymmetric for Marangoni number Ma5Mac, but the azimuthal flow after instability (Ma>Mac) breaks the axial-symmetry, and m-foldsymmetry of the flow pattern is observed. The symmetry number m (azimuthal wave number) depends strongly on the aspect ratio, As (As=height/radius), of the half-zone. Based on the results of numerical simulation, the nature of the correlation between m andAs is investigated # 2001 Elsevier Science B.V. All rights reserved.

Simulation of self-assemblies of colloidal particles on the substrate using a lattice Boltzmann pseudo-solid model

Abstract A simulation study on the self-assemblies of colloidal particles partially immersed in a fluid layer on the substrate is carried out. To take the full solid–fluid interactions into account, a novel modeling approach for colloidal particles, called pseudo-solid model (PSM) is introduced in the framework of lattice Boltzmann (LB) model for multi-component fluids. A typical phenomenon in the fluid layer due to the lateral capillary forces, namely the attraction of two colloidal particles with the same affinity is numerically demonstrated, while the influence of particle distance and surface tension as well as the so-called many-body effects are investigated. Furthermore, the formation of self-assemblies of colloidal particles on the substrate is simulated under different coverage ratios and interfacial tensions. Results show good agreement with previous studies, proving the potential of LB-PSM as a simulation model to provide further insight into the self-organizing process of colloidal particles.

Size effect on quasibound states and negative differential resistances in step-barrier structures

Abstract Electronic states and tunneling properties in step-barrier structures have been investigated. The results indicate that there exists quasibound states in step-barrier structure both at zero bias and under an applied bias. Size effect on negative-differential resistances is examined and the condition for obtaining larger current peak-to-valley ratios has been discussed.

Consistent lattice Boltzmann methods for incompressible axisymmetric flows.

In this work, consistent lattice Boltzmann (LB) methods for incompressible axisymmetric flows are developed based on two efficient axisymmetric LB models available in the literature. In accord with their respective original models, the proposed axisymmetric models evolve within the framework of the standard LB method and the source terms contain no gradient calculations. Moreover, the incompressibility conditions are realized with the Hermite expansion, thus the compressibility errors arising in the existing models are expected to be reduced by the proposed incompressible models. In addition, an extra relaxation parameter is added to the Bhatnagar-Gross-Krook collision operator to suppress the effect of the ghost variable and thus the numerical stability of the present models is significantly improved. Theoretical analyses, based on the Chapman-Enskog expansion and the equivalent moment system, are performed to derive the macroscopic equations from the LB models and the resulting truncation terms (i.e., the compressibility errors) are investigated. In addition, numerical validations are carried out based on four well-acknowledged benchmark tests and the accuracy and applicability of the proposed incompressible axisymmetric LB models are verified.

A comparative study of lattice Boltzmann models for incompressible flow

Abstract For incompressible flow, a comparative study on the four lattice Boltzmann (LB) models, the standard model, the He–Luo model, Guo’s model, and the present model, is performed. Theoretically, the macroscopic equations derived from the involved LB models are compared by the Chapman–Enskog analysis. Then, the analytical framework proposed in M. Junk’s work is applied to investigate the finite difference stencils and the equivalent moment systems pertaining to the concerned LB models. Conclusions are drawn from the theoretical derivations that the truncated error terms, which differ among the concerned LB models, have effects on the accuracy of the modeled deviatoric stress. Moreover, the cavity flow in two dimensions is adopted as a benchmark test to confirm the theoretical demonstrations. The resulting velocity fields from the present model are more in line with the reference solutions in the region of high deviatoric stress than other three LB models, which is consistent with the theoretical expectations and is further confirmed by the comparisons of the truncation error terms. In addition, we also conclude from the numerical tests that the present model has the advantage of better convergence efficiency but suffers from the worse stability.