The energy and angular momentum flux carried by gravitational waves from a spinning rod are calculated exactly in the weak field limit of general relativity. It is shown that contrary to common belief, the energy and angular momentum flux are not proportional and the energy and angular momentum equations governing the evolution of the rod are not identical. The spinning rod does not remain rigid: Its length increases. Both the angular deceleration and the rate of change of length are dependent on the nature of the material of the rod, and these rates are small, as expected. 相似文献
Thienylmercury(II)chloride reacts with [Pd(PPh3)2Cl2], [Pd(PPh3)4] and [Pt(PPh3)4] to afford new compounds containing a metal-2-thienyl linkage. The compound [Pd(PPh3)2(2-C4H3S)Cl] probably has trans stereochemistry.2-Bromothiophen undergoes oxidative addition with [Pd(PPh3)4] and [Pt(PPh3)4], probably via a radical mechanism. With [Pd(CO)(PPh3)3], a carbonyl inserted product is obtained. The bromo-metal(II) complexes have trans stereochemistry. The course of the reaction between 3-methyl-2-bromothiophen and Pd(PPh3)4 is more complex. Thus, there is evidence of some cis bromopalladium(II) compounds amongst the products, also there is good evidence to support the view that some isomerisation of 3-methyl-2-thienyl to 4-methyl-2-thienyl occurs during the reaction, thus giving greater molar quantities of [Pd(PPh3)2(4-CH3-2-C4H2S)Br] than can be accounted for from any initial 4-methyl-2-bromothiophen impurity.The metallation of the thiophen ring, probably in the 4-position, with palladium(II) is described for 3-theylidene-4-methylaniline. 相似文献
A time-dependent box model is developed to calculate oxygen isotope compositions of bone phosphate as a function of environmental and physiological parameters. Input and output oxygen fluxes related to body water and bone reservoirs are scaled to the body mass. The oxygen fluxes are evaluated by stoichiometric scaling to the calcium accretion and resorption rates, assuming a pure hydroxylapatite composition for the bone and tooth mineral. The model shows how the diet composition, body mass, ambient relative humidity and temperature may control the oxygen isotope composition of bone phosphate. The model also computes how bones and teeth record short-term variations in relative humidity, air temperature and δ18O of drinking water, depending on body mass. The documented diversity of oxygen isotope fractionation equations for vertebrates is accounted for by our model when for each specimen the physiological and diet parameters are adjusted in the living range of environmental conditions. 相似文献
Conductive‐tip atomic force microscopy (C‐AFM) is a powerful tool for investigating the electrical characteristics of phase‐change materials commonly used for electronic and optical data storage. We demonstrate the usefulness of this technique by examining the electrical conductivity of crystalline marks recorded with a focused laser pulse on a thin Ge2Sb2Te5 film. 相似文献
Transformation optics, a recent geometrical design strategy of light manipulation with both ray trajectories and optical phase controlled simultaneously, promises an invisibility cloaking device that can render a macroscopic object invisible even to a scientific instrument measuring optical phase. Recent “carpet” cloaks have extended their cloaking capability to broadband frequency ranges and macroscopic scales, but they only demonstrated the recovery of ray trajectories after passing through the cloaks, while whether the optical phase would reveal their existence still remains unverified. In this paper, a phase‐preserved macroscopic visible‐light carpet cloak is demonstrated in a geometrical construction beyond two dimensions. As an extension of previous two‐dimensional (2D) macroscopic carpet cloaks, this almost‐three‐dimensional carpet cloak exhibits three‐dimensional (3D) invisibility for illumination near its center (i.e. with a limited field of view), and its ideal wide‐angle invisibility performance is preserved in multiple 2D planes intersecting in the 3D space. Optical path length is measured with a broadband pulsed‐laser interferometer, which provides unique experimental evidence on the geometrical nature of transformation optics.
In this paper, we applied the polyharmonic splines as the basis functionsto derive particular solutions for the differential operator ∆2 ± λ2. Similar to thederivation of fundamental solutions, it is non-trivial to derive particular solutionsfor higher order differential operators. In this paper, we provide a simple algebraicfactorization approach to derive particular solutions for these types of differentialoperators in 2D and 3D. The main focus of this paper is its simplicity in the sensethat minimal mathematical background is required for numerically solving higherorder partial differential equations such as thin plate vibration. Three numericalexamples in both 2D and 3D are given to validate particular solutions we derived. 相似文献
