Nanoscale detection of faint machinery vibration using the NV center in diamond

We propose a novel method for detection of the faint machinery vibration at the nanometer resolution based on the spin magnetic resonant effect. A suspension magnet acts as a vibration sensor to transfer the vibration signals as the magnetic field fluctuation to excite the spin magnetic resonance. Due to the high sensitivity of the magnetic field of the nitrogen-vacancy center in diamond, the theoretical detection limit of mechanical vibration is as high as 5.7 nm, and the actual measurement resolution reached 12.8 nm, and proved the potential for further improvement to ∼pm resolution. The feasibility of this method is verified by dynamic tests. This method provides a novel approach for the detection of micro-mechanical vibrations.     

Near wake properties of axisymmetric bluff body flows

Experiments have been made to measure some of the near wake properties of axisymmetric bluff body flows with fixed points of separation, including the detention or residence time of fluid borne scalar entities, base pressure coefficient, wake bubble length parameter and shape parameter. Measurements were made in smooth and turbulent air flow for Reynolds number in the range 2×10³<Re<4×10⁴. The results for a given bluff body were found to be uniquely controlled by a free-stream turbulence parameter. The data for all the shapes of bluff body in the class under consideration were found to collapse into unique inter-relationships by the introduction of the face pressure coefficient as a quantitative measure of “bluffness”. This paper was originally presented at the 14th International Congress of Theoretical and Applied Mechanics, Delft (August–September, 1976).     

Archimedean operator-theoretic Positivstellensätze

We prove a general archimedean positivstellensatz for hermitian operator-valued polynomials and show that it implies the multivariate Fejer-Riesz theorem of Dritschel-Rovnyak and positivstellensätze of Ambrozie-Vasilescu and Scherer-Hol. We also obtain several generalizations of these and related results. The proof of the main result depends on an extension of the abstract archimedean positivstellensatz for ?-algebras that is interesting in its own right.     

重积分和线面积分中的一个典型题目

针对授课班级出错率较高的一道曲面积分题目,给出四种解法.分析出错的原因在于练习不够外,主要是对重积分概念理解不够透彻.     

Multiple scattering of elastic waves by pinned dislocation segments in a continuum

The coherent propagation of elastic waves in a solid filled with a random distribution of pinned dislocation segments is studied to all orders in perturbation theory. It is shown that, within the independent scattering approximation, the perturbation series that generates the mass operator is a geometric series that can thus be formally summed. A divergent quantity is shown to be renormalizable to zero at low frequencies. At higher frequencies said quantity can be expressed in terms of a cut-off with dimensions of length, related to the dislocation length, and physical quantities can be computed in terms of two parameters, to be determined by experiment. The approach used in this problem is compared and contrasted with the scattering of de Broglie waves by delta-function potentials as described by the Schrödinger equation.     

初始啁啾补偿光纤色散效应的适用范围

以啁啾高斯脉冲在单模光纤中的传输为例,分别就线性初始啁啾对光纤二阶和三阶色散的补偿进行了系统的理论分析和数值计算,结果表明：线性初始啁啾对光纤的二阶色散（线性色散）有一定的补偿作用,但不能有效地用于三阶色散的补偿.     

Stable model equations for long water waves

In this paper, a sequel to two others [1, 2], some extensions and improvements of this earlier work are presented. Among these are: A more precise version of the proof of the basic canonical theorem, some considerations on conservation laws and their relation, a more complete treatment of the stability of the models, especially with respect to the wave amplitude, a short treatment of the Lagrangian version of the theory, a stable discrete model which might be useful for numerical experiments and an extension of the method to the case of slowly varying water depth.     

Sigmoids as precursors of solar eruptions

Coronal mass ejections (CMEs) appear to originate preferentially in regions of the Sun's corona that are sigmoidal, i.e., have sinuous S or reverse-S shapes. Yohkoh solar X-ray images have been studied before and after a modest number of Earth-directed (halo) CMEs. These images tend to show sigmoidal shapes before the eruptions and arcades, cusps, and transient coronal holes after. Using such structures as proxies, it has been shown that there is a relationship between sigmoidal shape and tendency to erupt. Regions in the Sun's corona appear sigmoidal because their magnetic fields are twisted. Some of this twist may originate deep inside the Sun. However, it is significantly modulated by the Coriolis force and turbulent convection as this flux buoys up through the Sun's convection zone. As the result of these phenomena, and perhaps subsequent magnetic reconnection, magnetic flux ropes form. These flux ropes manifest themselves as sigmoids in the corona. Although there are fundamental reasons to expect such flux ropes to be unstable, the physics is not as simple as might first appear, and there exist various explanations for instability. Many gaps need to be filled in before the relationship between sigmoids and CMEs is well enough understood to be a useful predictive tool     

Coaxial configuration of the dielectric Cherenkov maser

The linearized Lorentz force, continuity equation, and Maxwell's equations are used to calculate the system dispersion relation for a coaxial configuration of the dielectric Cherenkov maser. The system consists of two coaxial conductors lined with dielectric and an annular relativistic electron beam, which propagates between the two liners. The dispersion relation for the beam and dielectric-lined coaxial waveguide structure and the no-beam system that describes the dependence of the generated frequency on the coaxial waveguide parameters are presented. Using the linearized dispersion relation, the growth rate for the beam-TM_0n waveguide mode instability is calculated in the strong-coupling tenuous beam limit     

Effect of the laser axial modes on the coherence length of the laser beam

The effect of the presence of the axial modes within the spectral halfwidth of a laser spectral line on the visibility of its interference fringes is represented. It is found in case of axial modes with equal spectral halfwidths that the dominant factor in determining the coherence length of the laser beam is the spectral halfwidth of its axial mode and not the spectral halfwidth of the laser line. For the case of a laser beam with axial modes of different spectral halfwidths, the calculation shows a coherence length, closer to the mode with the smaller halfwidth.