The fifth interaction: universal long range force between spins

In this paper we present a review of our investigations on universal long range force between spins mediated by a massless axial vector gauge field which we name as “axial photon”. The invariance of the Lagrangian field theory of particles, possessing spin degrees of freedom, under local Lorentz transformations, necessitates the introduction of such an axial vector gauge field which interacts with spin current of the particles. Classical as well as quantum dynamics of electrons interacting with photon and axial photon are worked out. The new interaction is found to be asymptotically free. It is shown thatqed can be made finite if the coupling strengths of electron to photon and axial photon can be made equal. Experimental consequences of the existence of axial photon are discussed and the strength of the interaction is estimated by comparing predictions of the theory with experiments.     

Principal component analysis of shear strain effects

Shear stresses are always present during quasi-static strain imaging, since tissue slippage occurs along the lateral and elevational directions during an axial deformation. Shear stress components along the axial deformation axes add to the axial deformation while perpendicular components introduce both lateral and elevational rigid motion and deformation artifacts into the estimated axial and lateral strain tensor images. A clear understanding of these artifacts introduced into the normal and shear strain tensor images with shear deformations is essential. In addition, signal processing techniques for improved depiction of the strain distribution is required. In this paper, we evaluate the impact of artifacts introduced due to lateral shear deformations on the normal strain tensors estimated by varying the lateral shear angle during an axial deformation. Shear strains are quantified using the lateral shear angle during the applied deformation. Simulation and experimental validation using uniformly elastic and single inclusion phantoms were performed. Variations in the elastographic signal-to-noise and contrast-to-noise ratios for axial deformations ranging from 0% to 5%, and for lateral deformations ranging from 0 to 5° were evaluated. Our results demonstrate that the first and second principal component strain images provide higher signal-to-noise ratios of 20 dB with simulations and 10 dB under experimental conditions and contrast-to-noise ratio levels that are at least 20 dB higher when compared to the axial and lateral strain tensor images, when only lateral shear deformations are applied. For small axial deformations, the lateral shear deformations significantly reduces strain image quality, however the first principal component provides about a 1–2 dB improvement over the axial strain tensor image. Lateral shear deformations also significantly increase the noise level in the axial and lateral strain tensor images with larger axial deformations. Improved elastographic signal and contrast-to-noise ratios in the first principal component strain image are always obtained for both simulation and experimental data when compared to the corresponding axial strain tensor images in the presence of both axial and lateral shear deformations.     

谱域光学相干层析系统中基于解卷积方法的像质优化

谱域光学相干层析（spectral domain optical coherence tomography, 简记为SD-OCT）系统的轴向点扩散函数（point spread function, 简记为PSF）并不具备空不变特性,无法直接应用于解卷积运算.为实现SD-OCT系统成像质量基于解卷积算法的优化,本文采用数值校正后的轴向扫描信号和轴向有效PSF来实施基于Lucy-Richardson算法的解卷积运算,进而实现了SD-OCT系统中图像质量尤其是轴向分辨率的改善.本文理论分析了SD-OCT系统中导致轴向有效PSF随成像深度增大而下降和图像模糊的因素,阐述了利用解卷积算法实现图像质量优化的过程,基于建立的SD-OCT系统实施了不同成像深度位置处PSF的标定,并利用离散轴向位置处PSF的峰值拟合了轴向有效PSF的调制函数.利用调制函数对所有轴向扫描信号进行数值校正,然后根据轴向有效PSF进行解卷积算法.典型样品的解卷积图像重建结果表明,提出的解卷积方法能有效提高系统的轴向分辨率,同时有效抑制系统灵敏度随成像深度增大而下降的趋势. 关键词： 谱域光学相干层析 Lucy-Richardson解卷积 有效点扩散函数     

谱域光学相干层析系统中基于解卷积方法的像质优化

谱域光学相干层析（spectral domain optical coherence tomography, 简记为SD-OCT）系统的轴向点扩散函数（point spread function, 简记为PSF）并不具备空不变特性,无法直接应用于解卷积运算.为实现SD-OCT系统成像质量基于解卷积算法的优化,本文采用数值校正后的轴向扫描信号和轴向有效PSF来实施基于Lucy-Richardson算法的解卷积运算,进而实现了SD-OCT系统中图像质量尤其是轴向分辨率的改善.本文理论分析了SD-OCT系统中导致轴向有效PSF随成像深度增大而下降和图像模糊的因素,阐述了利用解卷积算法实现图像质量优化的过程,基于建立的SD-OCT系统实施了不同成像深度位置处PSF的标定,并利用离散轴向位置处PSF的峰值拟合了轴向有效PSF的调制函数.利用调制函数对所有轴向扫描信号进行数值校正,然后根据轴向有效PSF进行解卷积算法.典型样品的解卷积图像重建结果表明,提出的解卷积方法能有效提高系统的轴向分辨率,同时有效抑制系统灵敏度随成像深度增大而下降的趋势.     

Double-walled carbon nanotube with surrounding elastic medium under axial pressure

In this paper, the buckling behavior and critical axial pressure of double-walled carbon nanotubes (DWCNTs) with surrounding elastic medium are investigated. A double-shell (circular cylindrical shell) model is presented and the effects of surrounding elastic medium on the outer tube and the van der Waals forces between two adjacent tubes are taken into account. The analysis and the numerical solution method are based on the classical theory of plates and shells and the Galerkin method. Equations are derived for the critical axial forces and pressures of DWCNTs; the critical axial forces and pressures are calculated for different axial half sine wavenumbers and circumferential sine wavenumbers and compared with those for single-walled carbon nanotubes (SWCNTs).Results indicate that the critical axial force of a DWCNT is higher than that of an SWCNT, but the critical axial pressure of a DWCNT is lower than the critical axial pressure of a SWCNT. Although the critical axial force of a DWCNT decreases as the axial half sine wavenumbers increase, it rises as the circumferential sine wavenumbers increase.     

Topological invariants and the dynamics of an axial vector torsion field

A generalized theory of gravitation is discussed which is based on a Riemann-Cartan space-time,U ₄, with an axial vector torsion field. Besides Einstein's equations determining the metric of theU ₄, a system of nonlinear field equations is established coupling an axial vector source current to the axial vector torsion field. The properties of the solutions of these equations are discussed assuming a London-type condition relating the axial current and torsion field. To characterize the solutions use is made of the Euler and Pontrjagin forms and the associated quadratic curvature invariants for theU ₄ space-time. It is found that there exists for a Riemann-Cartan space-time a relation between the zeros of the axial vector torsion field and the singularities of the Pontrjagin invariant, which is analogous to the well-known Hopf relation between the zeros of vector fields and the Euler characteristic.     

轴向多光阱微粒捕获与实时直接观测技术

传统的光镊技术使用单个物镜同时进行光学捕获与显微成像,使得捕获与成像区域被限制在物镜焦平面附近,无法同时观察到沿光轴方向(即Z向)捕获的多个微粒.本文提出一种轴平面(XZ平面)GerchbergSaxton迭代算法来产生沿轴向分布的多光阱阵列,将轴平面成像技术与光镊结合,实现了沿轴向对二氧化硅微球的多光阱同时捕获与实时观测.通过视频分析法测量了多个二氧化硅微球在轴向光镊阵列中的布朗运动,并标定了光阱刚度.本文提出的轴向多光阱微粒捕获与实时观测技术为光学微操纵提供了一个新的观测视角和操纵方法,为生物医学、物理学等相关领域研究提供了一种新的技术手段.     

Deformation analysis of an incompressible composite cylindrical tube subjected to end axial loads and internal constraint

In this paper,the problem of axially symmetric deformation is examined for a composite cylindrical tube under equal axial loads acting on its two ends,where the tube is composed of two different incompressible neo-Hookean materials.Significantly,the implicit analytical solutions describing the deformation of the tube are proposed.Numerical simulations are given to further illustrate the qualitative properties of the solutions and some meaningful conclusions are obtained.In the tension case,with the increasing axial loads or with the decreasing ratio of shear moduli of the outer and the inner materials,it is proved that the tube will shrink more along the radial direction and will extend more along the axial direction.Under either tension or compression,the deformation along the axial direction is obvious near the two ends of the tube,while in the rest,the change is relatively small.Similarly,for a large domain of the middle part,the axial elongation is almost constant;however,the variation is very fast near the two ends.In addition,the absolute value of the axial displacement increases gradually from the central cross-section of the tube and achieves the maximum at the two endpoints.     

Inhomogeneous two-dimensional structures in liquid crystals

Localized axisymmetric inhomogeneous states with a continuous distribution of the director field can exist in nematics. Such structures are compressed into dense filaments under the influence of a magnetic or electric field. It is hypothesized that the given states can be achieved in filamentary nematic textures. This model is an alternative to the conventional disclination model. Two types of lattices of axial structures can exist in the entire range of existence of the modulated state. Axial structures with a kernel of finite radius can exist in cylindrical capillaries. The structure and equilibrium dimensions of the axial states are easily altered over a wide range under the influence of an applied field. The feasibility of utilizing isolated axial structures and lattices of such structures in optical data processing and imaging devices is discussed. The most promising outlook in this regard is for modulated states and axial structures in chiral liquid crystals exhibiting spontaneous polarization. Zh. éksp. Teor. Fiz. 113, 1675–1697 (May 1998)     

Identifying multiple axial load patterns using measured vibration data

Multiply redundant frames possess as many linearly independent axial load patterns as their degree of static indeterminacy. Any state of equilibrium can be described as the linear sum of these axial load patterns. As a frame is loaded in the multiple patterns, the changes in member axial loads affect the frame frequencies and mode shapes in a complicated way through geometric stiffening. By representing this behaviour in a finite element model (FEM), it is possible to measure the dynamic characteristics of a physical frame, update the axial loads in the FEM until the difference between measured and model frequencies is minimised and thus infer the member axial loads. What is updated is the factors on the axial load patterns and this is done iteratively using traditional model updating (Newton's method). Thus, all member axial loads can be identified using just a set of updating parameters equal in number to the degree of static indeterminacy. A numerical simulation and, for the first time, an implementation on a physical realisation of a multiply redundant frame using measured vibration data are presented herein and show that member loads can be identified to an encouraging degree of accuracy. Beneficial strategies such as formulating the problem on an orthonormal basis for the axial load patterns and a ‘modal tagging’ scheme, which helps to conserve the strength of the necessary, but otherwise typically compromised, pairing of mode shapes of the FEM to those measured, are discussed.     

Three-dimensional shear in granular flow

The evolution of granular shear flow is investigated as a function of height in a split-bottom Couette cell. Using particle tracking, magnetic-resonance imaging, and large-scale simulations, we find a transition in the nature of the shear as a characteristic height H* is exceeded. Below H* there is a central stationary core; above H* we observe the onset of additional axial shear associated with torsional failure. Radial and axial shear profiles are qualitatively different: the radial extent is wide and increases with height, while the axial width remains narrow and fixed.     

Effect of interactive damping on vibration sensitivities of a scanning near-field optical microscope probe

The effect of interactive damping on the sensitivity of flexural and axial vibration modes of scanning near-field optical microscope (SNOM) with a tapered optical fiber probe has been analyzed. The interaction of the SNOM probe with a sample surface is modeled by a combination of a spring and a dashpot in the flexural direction and a similar combination in the axial direction. An approximate form for the sensitivities of both modes was derived by using the Rayleigh–Ritz method. The results show that the interactive damping will decrease the sensitivities of both flexural and axial vibration modes when the contact stiffness is low. The more the damping effect, the lower the sensitivities are. In addition, when the contact stiffness was low, the flexural sensitivity of the tapered probe slightly increased as the tapered angle decreased. However, the axial sensitivity apparently decreased as the tapered angle decreased. When the contact stiffness became higher, the sensitivities of both flexural and axial vibration modes increased as the tapered angle increased. PACS 68.35.Ja; 07.79.Fc; 61.16.Ch     

Experimental investigation of a compact relativistic magnetron with axial TE11 mode radiation

As one of the relativistic electron tubes having compact configuration and high efficient output, the relativistic magnetron with direct axial radiation is very attractive in pulsed power and high power microwave fields for industrial and military applications. In this paper, the experimental investigation of a relativistic magnetron with axial TE11 mode radiation is reported. Under a total length of - 0.3 m, volume of - 0.014 m3, working at an applied voltage of 508 kV and a magnetic field of - 0.31 T, the relativistic magnetron radiates a microwave of 540 MW with the TE11 mode at 2.35 GHz in the axial direction. The power conversion efficiency is 15.0%. After a lot of shots, the detected amplitudes of microwaves are nearly the same. The fluctuations of wave amplitudes are less than 0.3 dB.     

Optimisation of axially segmented liners for aeroengine broadband noise

A practical two-stage method for optimising an acoustic liner divided into axial segments for aeroengine broadband noise is presented. The principles are explained based on a three segment design but extension to more segments is straightforward. Initially, the optimisation focuses on the material properties of the individual segments. The second stage determines the optimum axial segment lengths and the optimum permutation of segments along the duct by evaluating the fully scattered acoustic field. This method is deployed to optimise an absorber for a broadband source noise of bandwidth 900 Hz-1.8 kHz. The axial order of the segments is found to have a dramatic influence on the optimum axial segment lengths. In the case study, comparisons with optimised uniform liners over this frequency range demonstrate only a small noise reduction. A simple optimisation that neglects scattering between axial segments significantly overestimates the available attenuation and provides a poor estimate of the optimum segment lengths.     

Estimation of the Axial Dispersion Effect on Supercritical Fluid Extraction from Bidisperse Packed Beds

The general hydrodynamic equations of a mathematical model for supercritical fluid extraction are derived within the framework of the continuum mechanics approach. The shrinking core concept is used to describe the mass transfer on the solid-liquid interface. The complete system of macroscopic differential mass-balance equations is reduced to a one-dimensional approximation and accounts for the axial dispersion effect. Correlation formulas available in the literature are used to calculate the axial dispersion coefficient for the conditions of supercritical CO₂ filtration. The effect of axial dispersion on the characteristics of the macroscopic process is analyzed for the typical laboratory-scale extraction conditions in the framework of the suggested model. The numerical simulations demonstrate that the difference between the values of the current mass of accumulated extract calculated in terms of the complete approach, which accounts for the axial dispersion, and the one related to the simplified model (in which the axial dispersion is neglected), is less than 10%. The same comparison is made for the outlet concentrations of the target compounds; the difference reaches 200%.     

Structure of the axial intensity minima in the Fresnel diffraction on a circular opening and superluminous effects

The “classical” problem of plane-wave diffraction by a circular opening is inspected with one particular interest to check the existence of axial zeroes of amplitude, which can produce a specific type of phase singularities. We investigate the problem using paraxial and nonparaxial solutions of scalar wave equation based on Hankel transform. The main result of investigation is the detection of the absence of any exact amplitude zeroes in the Fresnel diffraction field. Instead, sharp phase variations localized at the regions of axial amplitude minima with longitudinal and transversal dimensions of the order of one wavelength are revealed. These phase variations influence on the phase velocity, which drops up to c/2 in the point of axial amplitude minimum. Also, superluminous effects of wavefront propagation are discussed.     

Vibration and buckling of a double-beam system under compressive axial loading

On the basis of the Bernoulli–Euler beam theory, the properties of free transverse vibration and buckling of a double-beam system under compressive axial loading are investigated in this paper. It is assumed that the two beams of the system are simply supported and continuously joined by a Winkler elastic layer. Explicit expressions are derived for the natural frequencies and the associated amplitude ratios of the two beams, and the analytical solution of the critical buckling load is obtained. The influences of the compressive axial loading on the responses of the double-beam system are discussed. It is shown that the critical buckling load of the system is related to the axial compression ratio of the two beams and the Winkler elastic layer, and the properties of free transverse vibration of the system greatly depend on the axial compressions.     

Axial anomaly at finite temperature and finite density

TheU(1) axial anomaly in a hot fermion medium is investigated by using the real time Green's function method. After calculating the lowest order triangle diagrams, we find that finite temperature as well as finite fermion density does not affect the axial anomaly. The higher order corrections for the axial anomaly are discussed.     

Nuclear anapole moment and axial neutral current in nuclei

Nuclear anapole moments and axial neutral currents are calculated for a set of nuclei. The accuracy of the leading approximation is studied in detail. The core polarization renormalizing both the anapole moment and the axial current is treated in the random-phase approximation with effective forces. Parameters of parity-violating nuclear forces are discussed. The experimental value of the anapole moment of the ¹³³Cs nucleus as extracted from data with allowance for axial-current renormalization is found to be κ=0.39±0.06.     

The canonical problem of the fluid-conveying pipe and radiation of the knowledge gained to other dynamics problems across Applied Mechanics

The basic dynamics of pipes conveying fluid is reviewed, establishing why this system has become a model dynamical problem. The paper then discusses the radiation of the experience gained in studying this problem into other areas of Applied Mechanics, particularly other problems in fluid-structure interactions involving slender structures and axial flows; specifically the dynamics of (i) quasi-cylindrical bodies in axial flow or towed in quiescent fluid; (ii) cylindrical shells containing or immersed in axial flow; and (iii) plates in axial flow. Applications, some of them wholly unexpected when the work was done, are noted throughout.