Criticality of the exponential rate of decay for the largest nearest-neighbor link in random geometric graphs

Let n points be placed independently in d-dimensional space according to the density f(x) = A(d)e(-lambda parallel to x parallel to alpha), lambda, alpha > 0, x is an element of R-d, d >= 2. Let d(n) be the longest edge length of the nearest-neighbor graph on these points. We show that (lambda(-1) log n)(1-1/alpha) d(n) - b(n) converges weakly to the Gumbel distribution, where b(n) similar to ((d - 1)/lambda alpha) log log n. We also prove the following strong law for the normalized nearest-neighbor distance (d) over tilde (n) = (lambda(-1) log n)(1-1/alpha) d(n)/log log n: (d - 1)/alpha lambda <= lim inf(n ->infinity) (d) over tilde (n) <= lim sup(n ->infinity) (d) over tilde (n) <= d/alpha lambda almost surely. Thus, the exponential rate of decay alpha = 1 is critical, in the sense that, for alpha > 1, d(n) -> 0, whereas, for alpha <= 1, d(n) -> infinity almost surely as n -> infinity.

Stereospecific total synthesis of (±)-albene via a prochiral precursor

The total synthesis of racemic albene 2 via the prochiral precursor 3, using a stereoselective Claisen rearrangement and an intramolecular diazoketone cyclopropanation as key reactions, is described.

Mechanism of seizure of aluminium-silicon alloys dry sliding against steel

A steel ball was slid on aluminium-silicon alloys at different temperatures. After the coefficient of friction had been measured, the surface shear stress was deconvoluted using a two-term model of friction. The ratio of surface shear stress to bulk hardness was calculated as a function of temperature, silicon content and alloying additions. These results are qualitatively similar to those recorded for pre-seizure specimens slid against an En24 disc in a pin-on-disc machine. This similarity, when viewed in the context of the phenomenon of bulk shear, provides a model for seizure of these alloys.

Effect of hinged leaflets on vortex pair generation

We experimentally study the effect of having hinged leaflets at the jet exit on the formation of a two-dimensional counter-rotating vortex pair. A piston-cylinder mechanism is used to generate a starting jet from a high-aspect-ratio channel into a quiescent medium. For a rigid exit, with no leaflets at the channel exit, the measurements at a central plane show that the trailing jet in the present case is never detached from the vortex pair, and keeps feeding into the latter, unlike in the axisymmetric case. Passive flexibility is introduced in the form of rigid leaflets or flaps that are hinged at the exit of the channel, with the flaps initially parallel to the channel walls. The experimental arrangement closely approximates the limiting case of a free-to-rotate rigid flap with negligible structural stiffness, damping and flap inertia, as these limiting structural properties permit the largest flap openings. Using this arrangement, we start the flow and measure the flap kinematics and the vorticity fields for different flap lengths and piston velocity programs. The typical motion of the flaps involves a rapid opening and a subsequent more gradual return to its initial position, both of which occur when the piston is still moving. The initial opening of the flaps can be attributed to an excess pressure that develops in the channel when the flow starts, due to the acceleration that has to be imparted to the fluid slug between the flaps. In the case with flaps, two additional pairs of vortices are formed because of the motion of the flaps, leading to the ejection of a total of up to three vortex pairs from the hinged exit. The flaps' length (L-f) is found to significantly affect flap motions when plotted using the conventional time scale L/d, where L is the piston stroke and d is the channel width. However, with a newly defined time scale based on the flap length (L/L-f), we find a good collapse of all the measured flap motions irrespective of flap length and piston velocity for an impulsively started piston motion. The maximum opening angle in all these impulsive velocity program cases, irrespective of the flap length, is found to be close to 15 degrees. Even though the flap kinematics collapses well with L/L-f, there are differences in the distribution of the ejected vorticity even for the same L/L-f. Such a redistribution of vorticity can lead to important changes in the overall properties of the flow, and it gives us a better understanding of the importance of exit flexibility in such flows.

A rhodamine-based `turn-on' Al3+ ion-selective reporter and the resultant complex as a secondary sensor for F- ion are applicable to living cell staining

A newly designed fluorescent aluminum(III) complex (L'-Al; 2) of a structurally characterized non-fluorescent rhodamine Schiff base (L) has been isolated in pure form and characterized using spectroscopic and physico-chemical methods with theoretical density functional theory (DFT) support. On addition of Al(III) ions to a solution of L in HEPES buffer (1 mM, pH 7.4; EtOH-water, 1 : 3 v/v) at 25 degrees C, the systematic increase in chelation-enhanced fluorescence (CHEF) enables the detection of Al(III) ions as low as 60 nM with high selectivity, unaffected by the presence of competitive ions. Interestingly, the Al(III) complex (L'-Al; 2) is specifically able to detect fluoride ions by quenching the fluorescence in the presence of large amounts of other anions in the HEPES buffer (1 mM, pH 7.4) at 25 degrees C. On the basis of our experimental and theoretical findings, the addition of Al3+ ions to a solution of L helps to generate a new fluorescence peak at 590 nm, due to the selective binding of Al3+ ions with L in a 1 : 1 ratio with a binding constant (K) of 8.13 x 10(4) M-1. The Schiff base L shows no cytotoxic effect, and it can therefore be employed for determining the intracellular concentration of Al3+ and F-ions by 2 in living cells using fluorescence microscopy.

Study on Post Foundation of Highway Medium Guardrail

目前高速公路中央分隔带波形梁护栏立柱的实际设置中,普遍存在着由于分隔带地基强度低于压实路基,护栏立柱承载能力偏低,护栏的防护性能达不到设计要求的问题。对粘性土地基中立柱的受力情况进行了分析,并对地基为压实土与回填土两种情况进行了对比,给出了中央分隔带中立柱地基的加固方案。

液桥中不同Prandtl数流体的热毛细对流

本文研究从上面加热的液桥中不同 pr 数流体的热表面张力驱动对流。在 Ma 数相同的条件下,不同 pr 数流体液桥中的温度分布和流场结构定性相似,但定量结果不同。小pr数(pr<<1)流体液桥中的粘性边界层远小于热边界层,最大流函数所在位置向冷端偏移,有较大的流动速度。结果表明,Ma 数是描述这种流动的敏感参数。

有涨落效应的磁流体静力学关系

观测表明,在许多天体物理环境中,涨落场具有不可忽略的重要作用.本文在一阶光滑近似条件下,推导了普通湍流和随机波动两种条件下的磁流体静力学方程组,以及这些方程所要求的自洽性条件.在静力学问题中,涨落的洛伦茨力会对大尺度磁场位形有影响.具体研究这种影响对于解释观测的特征是十分必要的,特别是许多天体物理环境中,磁场(包括涨落磁场δB)是决定能量和动量平衡的重要因素.

基于红外热象技术的金属材料疲劳性能研究方法

金属材料的疲劳极限或疲劳寿命等性能是长寿命机械和结构抗疲劳设计的基本数据,探讨效率高、成本低而又准确的试验新方法,成为相关研究者十分感兴趣的课题。材料在循环载荷作用下产生的塑性变形经不断累积会引起疲劳破坏,这个过程所耗的塑性功绝大部分以热量形式耗散,因此寻找热耗散温度变化过程与疲劳极限及寿命之间的关系很有意义。就此问题,文中引入利用先进的红外热成象技术确定金属材料疲劳性能的试验研究方法,主要从原理和试验方法两方面进行介绍,并对45钢的试验过程和现象作较为详细地阐述,得到较准确的疲劳极限值和基于红外热象技术确定疲劳寿命的重要参量M。