Semi‐analytical method for departure point determination

A new method for departure point determination on Cartesian grids, the semi‐analytical upwind path line tracing (SUT) method, is presented and compared to two typical departure point determination methods used in semi‐Lagrangian advection schemes, the Euler method and the four‐step Runge–Kutta method. Rigorous comparisons of the three methods were conducted for a severely curving hypothetical flow field and for advective transport in the rotation of a Gaussian concentration hill. The SUT method was shown to have equivalent accuracy to the Runge–Kutta method but with significantly improved computational efficiency. Depending on the case being simulated, the SUT method provides either far greater or equivalent computational efficiency and more certain accuracy than the Euler method. Copyright © 2004 John Wiley & Sons, Ltd.     

Fluorinated comblike homopolymers: The effect of spacer lengths on surface properties

A series of polyacrylate monomers with F‐alkylalkyl [F(CF₂)_n(CH₂)_n′] side groups were prepared by free‐radical polymerization. The effect of the chemical structure on the surface properties of poly(ethylene terephthalate)s was evaluated by variations in the relative length of the fluorocarbon and hydrocarbon units in the side group. The resulting polymers were quite surface‐active in the solid state. The surface and bulk organization was investigated by X‐ray photoelectron spectroscopy analysis. A strong correlation between the bulk organization and surface properties of the polymers was established. The outmost layer, formed from trifluoromethyl groups and some ester functions, suggests that the side chain is arranged irregularly in the polymer–air interface. The length of the lateral chain governs this organization: long fluorinated chains and short hydrocarbon spacers are essential elements of the molecular design for such low‐surface‐energy materials. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 3737–3747, 2005     

Effects of oxidation and surface roughness on contact angle

Contact angle is known to be a parameter that effects boiling. This study was undertaken to measure contact angle of high and low surface tension fluids on copper and aluminum surfaces.Data were taken for polished, oxidized, and rough surfaces. A simple, yet fairly accurate method of measuring the static equilibrium contact angle of a solid/liquid interface is presented. The principles of a line light source and tilting plate were modified and then combined in the design of this apparatus. The angles obtained and their variation with the solid surface properties were in good agreement with previously published data. The contact angle of distilled water o of the organic fluids and refrigerants tested were in the range of 2–5°. Roughness and oxidation reduce the contact angle. If the depth of the roughness is less than 0.5 μm contact angle. The apparatus is fairly simple in construction, is inexpensive, and has good reproductibity. The measured angles were then compared to those measured with the sessile drop method.     

A proposed mechanism for hydrodynamically-controlled onset of significant void in microtubes

Data and analysis have shown that bubble nucleation and ebullition phenomena in microchannels are different than in large channels. The macroscale models and correlations often fail to predict data representing bubble ebullition processes in microchannels. It is hypothesized here that hydrodynamically-controlled onset of significant void in microchannels is due to bubble departure from wall cavities, and the latter process may be controlled by thermocapillary and aerodynamic forces that act on the bubble. Accordingly, the limited available relevant experimental data are semi-analytically modeled, and the soundness of the proposed hypothesis is shown.     

Direct Imaging of Octahedral Distortion in a Complex Molybdenum Vanadium Mixed Oxide

Complex Mo,V‐based mixed oxides that crystallize in the orthorhombic M1‐type structure are promising candidates for the selective oxidation of small alkanes. The oxygen sublattice of such a complex oxide has been studied by annular bright field scanning transmission electron microscopy. The recorded micrographs directly display the local distortion in the metal oxygen octahedra. From the degree of distortion we are able to draw conclusions on the distribution of oxidation states in the cation columns at different sites. The results are supported by X‐ray diffraction and electron paramagnetic resonance measurements that provide integral details about the crystal structure and spin coupling, respectively.     

Bounds for solid angles of lattices of rank three

We find sharp absolute constants C₁ and C₂ with the following property: every well-rounded lattice of rank 3 in a Euclidean space has a minimal basis so that the solid angle spanned by these basis vectors lies in the interval [C₁,C₂]. In fact, we show that these absolute bounds hold for a larger class of lattices than just well-rounded, and the upper bound holds for all. We state a technical condition on the lattice that may prevent it from satisfying the absolute lower bound on the solid angle, in which case we derive a lower bound in terms of the ratios of successive minima of the lattice. We use this result to show that among all spherical triangles on the unit sphere in RN with vertices on the minimal vectors of a lattice, the smallest possible area is achieved by a configuration of minimal vectors of the (normalized) face centered cubic lattice in R³. Such spherical configurations come up in connection with the kissing number problem.     

平板大攻角绕流升力和阻力系数的计算

二维平板或二维对称薄翼型大攻角绕流升力和阻力系数与攻角之间存在的函数关系一般用数据表格的形式给出。本文根据垂直平板绕流阻力实验数据和对称薄翼型全攻角绕流实验数据,分析得到了平板大攻角绕流总压力及其升力分量和阻力分量系数的近似计算公式。结果表明：平板总压力系数约等于攻角正弦值的2倍;总压力的阻力分量系数约等于攻角正弦值平方的2倍;升力分量系数约为攻角2倍的正弦值。计算结果与两组试验数据具有较好的一致性。     

单轴晶体光轴任意取向时非寻常光的折射规律

在单轴晶体光轴任意取向的情形下 ,应用惠更斯原理导出了非寻常光折射方向的普遍计算公式 ,并给出了确定非寻常光线折射面和折射角的具体解。结合几种熟知的特殊情形进行了简要讨论 ,揭示了文中所得到的折射规律较之斯涅尔定律更具有普遍性 ,从而为光学系统中各类单轴晶体光学元件的应用提供了一个理论依据     

Full-Field Determination of Principal-Stress Directions Using Photoelasticity with Plane-Polarized RGB Lights

In this paper, we propose a new three-wavelength method for automatic measurement of principal-stress directions over an entire model on the basis of four-step phase shift method. This method uses four fringe patterns captured by a color charge-coupled devices (CCD) camera corresponding to four angular position arrangements of polaroids in a dark-field plane polariscope. The principal-stress directions can be determined by a single calculation. The method is applied to a circular disc under compression. The principal-stress direction distributions obtained from the proposed method are compared with those obtained from a conventional method and theory. It can be obviously seen that the proposed method accurately yields the principal-stress directions compared with the conventional method.