Diffusion analogy and shock capturing for solving aerodynamic equations

Improving the resolution of the shock is one of the most important subjects in computational aerodynamics. In this paper the behaviour of the solutions near the shock is discussed and the reason of the oscillation production is investigated heuristically. According to the differential approximation of the difference scheme the so-called diffusion analogy equation and the diffusion analogy coefficient are defined. Four methods for improving the resolution of the shock are presented using the concept of diffusion analogy.

Diffusion sliding rate in the binary gaseous mixture

radiation incident upon a test cell filled with gaseous SF6 has

Characteristics of a CW HF chemical-laser calculated from a simplified two-dimensional model

A two-dimensional simplified model of an HF chemical laser is introduced. Using an implicit finite difference scheme, the solution of two adjacent parallel streams with diffusion mixing and chemical reaction is generated. A contour of mixing and reaction boundary is obtained without presupposition. The distribution of the HF(v) concentrations, gas temperature and the optical small signal gain (alpha sub V, J) on the flowing plane (X, Y) are presented. Compared with the solution solved directly from a set of Navier-Stokes equations, the results of these two methods agree with each other qualitatively. The influences of the different velocity, temperature (T sub 0) and composition of the two streams on the small signal gain after the nozzle exit are investigated. It is interesting that for larger J with a fixed v, the peaks of alpha sub v-T sub 0 profiles move towards higher T sub 0. The computing method is simple and only a short computing time is needed.

Microscopic theory of chemical-reaction rate

In this paper we deduce the formulae for rate-constant of microreaction with high resolving power of energy from the time-dependent Schrdinger equation for the general case when there is a depression on the reaetional potential surface (when the depression is zero in depth, the case is reduced to that of Eyring). Based on the assumption that Bolzmann distribution is appropriate to the description of reactants, the formula for the constant of macrorate in a form similar to Eyring's is deduced and the expression for the coefficient of transmission is given. When there is no depression on the reactional potential surface and the coefficient of transmission does not seriously depend upon temperature, it is reduced to Eyring's. Thus Eyring's is a special case of the present work.

Numerical-Value Perturbation Method with Application of Solving Convective-Diffusion Integral Equation

The convective--diffusion equation is of primary importance in such fields as fluid dynamics and heat transfer hi the numerical methods solving the convective-diffusion equation, the finite volume method can use conveniently diversified grids (structured and unstructured grids) and is suitable for very complex geometry The disadvantage of FV methods compared to the finite difference method is that FV-methods of order higher than second are more difficult to develop in three-dimensional cases. The second-order central scheme (2cs) offers a good compromise among accuracy, simplicity and efficiency, however, it will produce oscillatory solutions when the grid Reynolds numbers are large and then very fine grids are required to obtain accurate solution. The simplest first-order upwind (IUW) scheme satisfies the convective boundedness criteria, however. Its numerical diffusion is large. The power-law scheme, QMCK and second-order upwind (2UW) schemes are also often used in some commercial codes. Their numerical accurate are roughly consistent with that of ZCS. Therefore, it is meaningful to offer higher-accurate three point FV scheme. In this paper, the numerical-value perturbational method suggested by Zhi Gao is used to develop an upwind and mixed FV scheme using any higher-order interpolation and second-order integration approximations, which is called perturbational finite volume (PFV) scheme. The PFV scheme uses the least nodes similar to the standard three-point schemes, namely, the number of the nodes needed equals to unity plus the face-number of the control volume. For instanc6, in the two-dimensional (2-D) case, only four nodes for the triangle grids and five nodes for the Cartesian grids are utilized, respectively. The PFV scheme is applied on a number of 1-D problems, 2~Dand 3-D flow model equations. Comparing with other standard three-point schemes, The PFV scheme has much smaller numerical diffusion than the first-order upwind (IUW) scheme, its numerical accuracy are also higher than the second-order central scheme (2CS), the power-law scheme (PLS), the QUICK scheme and the second-order upwind(ZUW) scheme.

Surface-Bound Selectin-Ligand Binding Is Regulated By Carrier Diffusion

Two-dimensional (2D) kinetics of receptor-ligand interactions governs cell adhesion in many biological processes. While the dissociation kinetics of receptor-ligand bond is extensively investigated, the association kinetics has much less been quantified. Recently receptor-ligand interactions between two surfaces were investigated using a thermal fluctuation assay upon biomembrane force probe technique (Chen et al. in Biophys J 94:694-701, 2008). The regulating factors on association kinetics, however, are not well characterized. Here we developed an alternative thermal fluctuation assay using optical trap technique, which enables to visualize consecutive binding-unbinding transition and to quantify the impact of microbead diffusion on receptor-ligand binding. Three selectin constructs (sLs, sPs, and PLE) and their ligand P-selectin glycoprotein ligand 1 were used to conduct the measurements. It was indicated that bond formation was reduced by enhancing the diffusivity of selectin-coupled carrier, suggesting that carrier diffusion is crucial to determine receptor-ligand binding. It was also found that 2D forward rate predicted upon first-order kinetics was in the order of sPs > sLs > PLE and bond formation was history-dependent. These results further the understandings in regulating association kinetics of surface-bound receptor-ligand interactions.

Structural and optical properties of YAG : Ce3+ phosphors by sol-gel combustion method

High-quality Ce3+-doped Y3Al5O12 (YAG:Ce3+) phosphors were synthesized by a facile sol-gel combustion method. In this sol-gel combustion process, citric acid acts as a fuel for combustion, traps the constituent cations and reduces the diffusion length of the precursors. The XRD and FT-IR results show that YAG phase can form through sintering at 900 degrees C for 2 h. This temperature is much lower than that required to synthesize YAG phase via the solid-state reaction method. There were no intermediate phases such as YAlO3 (YAP) and Y4Al2O9 (YAM) observed in the sintering process. The average grain size of the phosphors sintered at 900-1100 degrees C is about 40 nm. With the increasing of sintering temperature, the emission intensity increases due to the improved crystalline and homogeneous distribution of Ce3+ ions. A blue shift has been observed in the Ce3+ emission spectrum of YAG:Ce3+ phosphors with increasing sintering temperatures from 900 to 1200 degrees C. It can be explained that the decrease of lattice constant affects the crystal field around Ce3+ ions. The emission intensity of 0.06Ce-doped YAG phosphors is much higher than that of the 0.04Ce and 0.02Ce ones. The red-shift at higher Ce3+ concentrations may be Ce-Ce interactions or variations in the unit cell parameters between YAG:Ce3+ and YAG. It can be concluded that the sol-gel combustion synthesis method provides a good distribution of Ce3+ activators at the molecular level in YAG matrix. (c) 2005 Elsevier B.V. All rights reserved.

The effect of diffusion and overhangs/vacancies on the microstructure of zig-zag thin film

Basing on some growth models of thin film, we have investigated the growth mechanism of glancing angle deposition (GLAD) film. The simulation verifies that the overhangs/vacancies also contribute to the columnar growth as well as the self-shadowing effect for GLAD thin film. Besides, we have studied the effect of the deposition rate, surface and bulk diffusions on the microstructure of thin film using the time-dependent Monte Carlo method. The results show that the surface and bulk diffusions can significantly enhance the packing density of thin film in GLAD growth, and the increase of the deposition rate induce the moderate decrease of the packing density. (c) 2006 Elsevier B.V. All rights reserved.