Multiple optical trapping based on high-order axially symmetric polarized beams

Multiple optical trapping with high-order axially symmetric polarized beams（ASPBs） is studied theoretically,and a scheme based on far-field optical trapping with ASPBs is first proposed.The focused fields and the corresponding gradient forces on Rayleigh dielectric particles are calculated for the scheme.The calculated results indicate that multiple ultra-small focused spots can be achieved,and multiple nanometer-sized particles with refractive index higher than the ambient can be trapped simultaneously near these focused spots,which are expected to enhance the capabilities of traditional optical trapping systems and provide a solution for massive multiple optical trapping of nanometer-sized particles.

Tight focusing of axially symmetric polarized vortex beams

Tight focusing of axially symmetric polarized vortex beams is studied numerically based on vector diffraction theory. The mathematical expressions for the focused fields are derived. Simulation results show that the focused fields and phase distributions at focus are largely influenced by both the polarization order and topological charge of the incident beams. Moreover, focal spots with flat-topped or tightly-focused patterns can be flexibly achieved by carefully choosing the polar- ization order and the topological charge, which confirms the potential of such beams in wide applications, such as optical tweezers, laser printing, lithography, and material processing.

STED microscopy based on axially symmetric polarized vortex beams

A stimulated emission depletion （STED） microscopy scheme using axially symmetric polarized vortex beams is pro- posed based on unique focusing properties of such kinds of beams. The concept of axially symmetric polarized vortex beams is first introduced, and the basic principle about the scheme is described. Simulation results for several typical beams are then shown, including radially polarized vortex beams, azimuthally polarized vortex beams, and high-order axi- ally symmetric polarized vortex beams. The results indicate that sharper doughnut spots and thus higher resolutions can be achieved, showing more flexibility than previous schemes based on flexible modulation of both phase and polarization for incident beams.

On Axially Symmetric Vibrations of Fluid Filled Poroelastic Spherical Shells

Employing Biot’s theory of wave propagation in liquid saturated porous media, waves propagating in a hollow poroelastic closed spherical shell filled with fluid are studied. The frequency equation of axially symmetric vibrations for a pervious and an impervious surface is obtained. Free vibrations of a closed spherical shell are studied as a particular case when the fluid is vanished. Frequency as a function of ratio of thickness to inner radius is computed in absence of dissipation for two types of poroelastic materials each for a pervious and an impervious surface. Results of previous works are obtained as a particular case of the present study.

Calibration method for electrode gains in an axially symmetric stripline BPM

The four electrodes in the stripline beam position monitor(BPM) for Hefei Light Source(HLS II) storage ring are of axially symmetric type. We have derived a new calibration method of electrode gains for this type stripline BPM. The gain fit error of different data grids was analyzed, and the ±5 mm by ±5 mm grid is the best.The electrode gains of two stripline BPMs(HLS II SR-BD-STLB1 and HLS II SR-BD-STLB2) were obtained based on offline calibrated data. The results show that data after fitting gains are improved, with the electrode gains being between 0.94 and 1.15.

APPROXIMATION OF GENERALIZED BI－AXIALLY SYMMETRIC POTENTIALS WITH FAST RATES OF GROWTH

The paper deals with growth and approximation of solutions (not necessarily entire) of certain elliptic partial differential equations. These solutions are called Generalized Bi-axially Symmetric Potentials (GBSP's). The GBSP's are taken to be regular in a finite hyperball and influence of the growth of their maximum moduli on the rate of decay of their approximation errors in sup norm is studied. The authors obtain the characterizations of the q-type and lower q-type of a GBSP H ∈ HP,0 < R < ∞, in terms of rate of decay of approximation error E.(H,R0), 0 < R0<R <∞.

Multiple 3D optical trapping using higher polarization order axially-symmetric polarized beams

We propose a novel single-beam multiple 3D optical trapping scheme using higher polarization order axially-symmetric polarized beams in an aplanatic focusing system. We calculate numerically the intensity distribution near the focus which presents a multi-focus-spot pattern and provides the possibility of multiple optical trapping. We also calculate the corresponding gradient force distribution near the focus. Finally we introduce a 3D optical chain by combining the single-beam system with a single diffractive optical element.

ANALYTICAL SOLUTION OF AXIAL SYMMETRICAL WALL TEMPERATURE DISTRIBUTION FOR HOLLOW CYLINDER

Using the variable transformation method,the formulae of the axial symmetrical wall temperature distribution during steady heat conduction of a hollow cylinder are derived in this paper.The wall temperature distribution and the wall heat flux distribution in both axial and radial direction can be calculated by the temperature distribution of the liquid medium both inside and outside the cylinder with temperature changing in axial direction.The calculation results are almost consistent with the experience results.The applicative condition of the formulae in this paper consists with most of practice.They can be applied to the engineering calculation of the steady heat conduction.The calculation is simple and accurate.

Global Tangentially Analytical Solutions of the 3D Axially Symmetric Prandtl Equations

In this paper,the authors will prove the global existence of solutions to the three dimensional axially symmetric Prandtl boundary layer equations with small initial data,which lies in H1Sobolev space with respect to the normal variable and is analytical with respect to the tangential variables.The main novelty of this paper relies on careful constructions of a tangentially weighted analytic energy functional and a specially designed good unknown for the reformulated system.The result extends that of Paicu-Zhang in[Paicu,M.and Zhang,P.,Global existence and the decay of solutions to the Prandtl system with small analytic data,Arch.Ration.Mech.Anal.,241(1),2021,403–446].from the two dimensional case to the three dimensional axially symmetric case,but the method used here is a direct energy estimates rather than Fourier analysis techniques applied there.

SELF-SIMILAR SOLUTIONS OF FRACTURE DYNAMICS PROBLEMS ON AXIALLY SYMMETRY

By the theory of complex functions, a penny-shaped crack on axially symmetric propagating problems for composite materials, was studied. The general representations of the analytical solutions with arbitrary index of self-similarity, were presented for fracture elastodynamics problems on axially symmetry by the ways of self-similarity under the ladder-shaped loads. The problems dealt with can be transformed into Riemann-Hilbert problems and their closed analytical solutions are obtained rather simple by this method. After those analytical solutions are utilized by using the method of rotational superposition theorem in conjunction with that of Smirnov-Sobolev, the solutions of arbitrary complicated problems can be obtained.

THE GENERAL SOLUTION ON NONLINEAR AXIAL SYMMETRICAL DEFORMATION OF NONHOMOGENEOUS CYLINDRICAL SHELLS

In this paper, the general solution on nonlinear axial symmetrical deformation of nonhomogeneous cylindrical shells is obtained by step reduction method[1]. The general formula of displacements and stress resultants, which is used to solve the bending problems of nonhomogeneous cylindrical shells under arbitrary axial symmetric loads, is derived. Its uniform convergence is proved. Finally, it is only necessary to solve one set of binary linear algebraic equations. A numerical example is given at the end of the paper which indicates satisfactory results of displacement and stress resultants can be obtained and converge to the exact solution.

A Criterion of Superdeformed Triaxial Shape

Using axially-symmetric and triaxial superdeformed modelsπ[6001/2]band in 165Lu is investigated.The observedγ-transition energies can be reproduced quite well in both models.However,the triaxiality factor F(I)and the ratio of dynamical quadrupole moment Q(l)to Q(2)in axially-symmetric superdeformed model are essentially different from those in triaxial superdeformed model,which may be used to determine the nuclear shape.Precise measurement of the electromagnetic transition probabilities,combined with the information from the energy levels is necessary.Experimental information which may differentiate triaxial superdeformation from axially-symmetric superdeformation is discussed.

Organocatalytic atroposelective construction of axially chiral nonsymmetric biaryltriols and their applications in asymmetric synthesis and heavy metal ion detection

An organocatalytic methodology toward the atroposelective construction of axially chiral nonsymmetric biaryltriols has been successfully developed.A quinine-derived thiourea-catalyzed intramolecular reaction using VQM(vinylidene ortho-quinone methides)intermediates enabled efficient access to a class of axially chiral nonsymmetric biaryltriols with up to 98%yield and 99%ee.

A Review of Results on Axially Symmetric Navier-Stokes Equations,with Addendum by X.Pan and Q.Zhang

In this paper,we give a brief survey of recent results on axially symmetric Navier-Stokes equations(ASNS)in the following categories:regularity criterion,Liouville property for ancient solutions,decay and vanishing of stationary solutions.Some discussions also touch on the full 3 dimensional equations.Two results,closing of the scaling gap for ASNS and vanishing of homogeneous D solutions in 3 dimensional slabs will be described in more detail.In the addendum,two new results in the 3rd category will also be presented,which are generalizations of recently published results by the author and coauthors.

平面薛定谔-泊松系统的轴对称解

研究如下的平面薛定谔-泊松型系统:-Δu+V(x)u+φu=f(x,u),x∈R^(2),Δφ=u^(2),x∈R^(2),其中V∈C(R^(2),[0,∞))是轴对称的。我们考虑非线性项f(x,u)是Trudinger-Moser意义上的次临界指数增长情形,并给出一个非全局性的超四次条件,通过借助一些新的分析技巧和变分方法得到平面薛定谔-泊松系统轴对称解的存在性,在此基础上我们为f(x,u)添加一个对称性条件,得到平面薛定谔-泊松系统多解的存在性。

基于ADAMS的轴对称矢量喷管喷口精度分析

为研究误差对喷口精度的影响,以轴对称矢量喷管为研究对象,利用ADAMS软件的参数化点的功能建立模型并仿真,验证模型有效性;建立衡量喷口精度的指标:偏转角、方位角、喷口面积的测量函数;基于设计研究功能,得出了单一设计变量误差对喷口精度影响的灵敏度;通过ADAMS/Insight模块、蒙特卡洛方法以较快的速度、较少的工作量完成零部件随机设计变量误差的分析。研究结果表明:在随机误差-0.1 mm<μ<0.1 mm的情况下,偏转角仿真值与平均值相对误差为0.675%,方位角为0.847%,喷口面积为0.048%,喷口精度变化较小,可以保证发动机工作范围。

对称配筋钢筋混凝土小偏心受压柱正截面承载力分析

基于平截面假定推导了钢筋混凝土小偏心受压柱离轴力远侧纵向钢筋应力的计算公式,建立对称配筋钢筋混凝土小偏心受压矩形截面柱的正截面承载力计算表达式。采用所建立的表达式与《混凝土结构设计规范》中的计算公式分别分析了矩形截面小偏心受压柱截面配筋和正截面承载力。结果表明,采用《混凝土结构设计规范》中的公式计算得到的纵向钢筋截面面积小于基于平截面假定建立的正截面承载力计算表达式算出的纵向钢筋截面面积,其最大误差可达11.1%;而受压承载力的计算值相近。

轴流通风机镜像对称叶片研究

轴流通风机的叶片对其性能有着重要影响,文中提出了采用镜像对称方法设计制造风机叶片,随后通过研究基于此方法设计制造的叶片,发现镜像对称叶片的轴流通风机性能参数和叶片应力均在要求范围内,但是左旋叶片应力略小于右旋叶片,可供轴流风机及轴流泵等设计制造参考。

一个四分量Camassa-Holm系统的行波解

考虑了一个具有双哈密顿结构、无穷多守恒律的带有任意函数的四分量CH系统,得到了当该系统具有对称行波解时所满足的条件,导出了带有任意函数的尖峰解的显式表达式,通过对解的直接约化得到了一些两分量CH型系统的尖峰解表达式.

充气头型对超空泡轴对称体阻力特性影响的试验研究

为了了解充气空泡对不同头型的空泡特征及对轴对称体阻力特性的影响 ,在高速水洞中试验研究了三种典型头体在不同空泡数下 ,轴对称体上充气空泡的几何特征以及相对应的阻力特性 ,分析了充气数对轴对称体空泡特征与阻力的影响。试验结果表明 ,充气模型的空泡长度、厚度、空泡角随充气量增加而增大 ,从模型头部充气 ,能够产生稳定形状的空泡覆盖模型 ,针对某种特定形状模型 。