Theoretical investigation of unstable axial mass-selective extraction of ions from a nonlinear trap

The unstable axial mass-selective extraction of ions from a three-dimensional quadrupole ion trap is studied theoretically. A method for mapping the ion coordinates over the period of the RF power-supply voltage is developed with allowance for nonlinear distortions of the quadrupole potential. Equations for the envelope of ion oscillations are derived in the form of the equation of motion of a material point in the field of effective forces. The effect of the “delayed extraction” of ions in the presence of negative even field harmonics is explained. The positive even harmonics of the distorted quadrupole potential are shown to be favorable for ion extraction. The dynamics of the extracted ions is investigated.     

Characteristics of electrical field and ion motion in surface-electrode ion traps

In this article, we calculated the potential function of the surface-electrode ion trap (SEIT) by using Green's function method, optimized trap size, obtained the coefficients of the multipoles and analyzed ion trajectories in the RF potential. The optimized SEIT not only increases its trapping well depth by a factor of about 15, but also has relatively good linearity of the field (or large quadrupole component). The current design of SEIT can work well either as the ion guide for ion transmission or as the ion trap for ion confinement. Our research can be used to calculate the potential function in the SEIT with different device parameters, understand ion motions in the traps and optimize instrument performance. The method for calculating potential function can be expanded to planar and halo ion traps.     

The application of homotopy analysis method to solve a generalized Hirota–Satsuma coupled KdV equation

Here, an analytic technique, namely the homotopy analysis method (HAM), is applied to solve a generalized Hirota–Satsuma coupled KdV equation. HAM is a strong and easy-to-use analytic tool for nonlinear problems and dose not need small parameters in the equations. Comparison of the results with those of Adomian's decomposition method (ADM) and homotopy perturbation method (HPM), has led us to significant consequences. The homotopy analysis method contains the auxiliary parameter ?, which provides us with a simple way to adjust and control the convergence region of solution series.     

Analytic approximations of Von Krmn plate under arbitrary uniform pressure—equations in integral form

Analytic approximations of the Von Krmn's plate equations in integral form for a circular plate under external uniform pressure to arbitrary magnitude are successfully obtained by means of the homotopy analysis method(HAM), an analytic approximation technique for highly nonlinear problems. Two HAM-based approaches are proposed for either a given external uniform pressure Q or a given central deflection, respectively. Both of them are valid for uniform pressure to arbitrary magnitude by choosing proper values of the so-called convergence-control parameters c_1 and c_2 in the frame of the HAM. Besides, it is found that the HAMbased iteration approaches generally converge much faster than the interpolation iterative method. Furthermore, we prove that the interpolation iterative method is a special case of the first-order HAM iteration approach for a given external uniform pressure Q when c_1 =.θ and c_2 =-1, where θ denotes the interpolation iterative parameter. Therefore, according to the convergence theorem of Zheng and Zhou about the interpolation iterative method, the HAM-based approaches are valid for uniform pressure to arbitrary magnitude at least in the special case c_1 =.θ and c_2 =-1. In addition, we prove that the HAM approach for the Von Krmn's plate equations in differential form is just a special case of the HAM for the Von Krmn's plate equations in integral form mentioned in this paper. All of these illustrate the validity and great potential of the HAM for highly nonlinear problems,and its superiority over perturbation techniques.     

7Li NMR investigation of Li-Li pair ordering in the paraelectric phase of weakly substitutionally disordered K(1-x)Li(x)TaO3

Breaking of the average cubic symmetry in Li-doped potassium tantalate was observed with quadrupole-perturbed 7Li NMR at temperatures (150-400?K) far above the nominal glass transition temperature (≈50 K for Li concentration x=0.03). The observed spectrum consists of contributions from both isolated Li ions (i.e., with no nearest-neighbor Li) and from Li-Li pairs. The isolated Li ions move among six equivalent off-center sites in a potential having cubic symmetry. These have zero average electric field gradient and, hence, exhibit no quadrupole splitting. In addition, very low intensity, but well resolved, quadrupole satellites having a temperature-dependent splitting were observed. This splitting indicates that the various Li-Li pair configurations are not all equally probable. These are the first direct observations of biased Li ion ordering that persists in the paraelectric phase at temperatures high above the glass phase.     

Employing a spheroidal global potential to estimate the quadrupole deformation of nuclei

A spheroidal global shell potential is constructed on the basis of the optical model whose global parameters are extracted from experimental data on nucleon-nucleus scattering. This potential is used to estimate the quadrupole deformation of a large number of light, intermediate, and heavy nuclei in the mass-number range 10 ? A ? 240. The results are compared with the results of similar calculations for the Nilsson potential and with the estimates of the quadrupole deformation that follow from data on the static quadrupole moments of the nuclei considered in the present study.     

Measurement of the electric quadrupole moment of the 4d2D5/2 level in 88Sr+

The quadrupole moment of the 4d (2)D(5/2) level in 88Sr+ has been measured to be 2.6(3)ea(2)(0), where a(0) is the Bohr radius and e the elementary charge. A single laser-cooled strontium ion was confined in an end cap trap with a variable dc quadrupole potential, and measurements were made on the 5s (2)S(1/2)-4d (2)D(5/2) transition at 674 nm using a femtosecond optical frequency comb. This work shows that measurements of the unperturbed 88Sr+ transition frequency with sub-Hz uncertainty are possible and is important in understanding the reproducibility of ion trap optical frequency standards.     

Identification of glucosinolates in capers by LC-ESI-hybrid linear ion trap with Fourier transform ion cyclotron resonance mass spectrometry (LC-ESI-LTQ-FTICR MS) and infrared multiphoton dissociation

An liquid chromatography-mass spectrometry method using electrospray ionization in negative ion mode coupled with a hybrid quadrupole linear ion trap and Fourier transform ion cyclotron resonance (FTICR) mass spectrometer was applied to characterize of intact glucosinolates (GLSs) in crude sample extracts of wild bud flowers of Capparis spinosa (Capparis species, family Capparaceae). Structural information of GLSs was obtained upon precursor ions' isolation within the FTICR trapping cell and subsequent fragmentation induced by infrared multiphoton dissociation (IRMPD). Such a fragmentation was found very useful in terms of chemical identification of all precursor ions [M-H](-) including sulfur-rich GLSs reported here for the first time. Along with most common GLSs already found in capers such as glucocapparin, isopropyl/n-propyl-GLS, mercapto-glucocapparin, and two indolic GLS, i.e., 4-hydroxyglucobrassicin and glucobrassicin, the occurrence of the uncommon glycinyl-glucocapparin as well as two sulfur-rich GLSs is reported. IRMPD showed an increased selectivity towards disulfide bond cleavages with thiol migration, suggesting the side chain structure of non-targeted compounds, i.e., disulfanyl-glucocapparin and trisulfanyl-glucocapparin. Glucocapparin [2.05?±?0.25?mg/g, dry weight (dw)] was the most abundant GLS, followed by glucobrassicin (232?±?18?μg/g, dw) and 4-hydroxyglucobrassicin (89?±?12?μg/g, dw). All other compounds were present at very low content ranging from 0.5 to 1.5?μg/g dw. Copyright ? 2012 John Wiley & Sons, Ltd.     

交通拥堵相变问题的同伦分析法

利用同伦分析法研究了一类基于洛伦兹系统的交通拥堵相变问题的非线性方程. 通过选取不同的初始解和不同的线性算子,分别得到了问题的近似解和相应的残留误差. 通过与前人结果的比较得出,在研究该类问题时同伦分析法优于微分变换法; 在应用同伦分析法时,要选取尽可能接近原算子线性部分作为线性算子. 本文还给出了一种新的初始解选取方法(双同伦分析法). 数值模拟的结果证实了理论分析的正确性. 关键词： 同伦分析法 交通拥堵 近似解 残留误差     

Application of Homotopy Analysis Method for Solving Systems of Volterra Integral Equations

In this paper, we prove the convergence of homotopy analysis method (HAM). We also apply the homotopy analysis method to obtain approximate analytical solutions of systems of the second kind Volterra integral equations. The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of series solutions. It is shown that the solutions obtained by the homotopy-perturbation method (HPM) are only special cases of the HAM solutions. Several examples are given to illustrate the efficiency and implementation of the method.     

Solutions of Heat-Like and Wave-Like Equations with Variable Coefficients by Means of the Homotopy Analysis Method

We employ the homotopy analysis method （HAM） to obtain approximate analytical solutions to the heat-like and wave-like equations. The HAM contains the auxiliary parameter h, which provides a convenient way of controlling the convergence region of series solutions. The analysis is accompanied by several linear and nonlinear heat-like and wave-like equations with initial boundary value problems. The results obtained prove that HAM is very effective and simple with less error than the Adomian decomposition method and the variational iteration method.     

Application of the homotopy analysis method for the Gross-Pitaevskii equation with a harmonic trap

<正>The Homotopy analysis method(HAM) is adopted to find the approximate analytical solutions of the GrossPitaevskii equation,a nonlinear Schrodinger equation is used in simulation of Bose-Einstein condensates trapped in a harmonic potential.Comparisons between the analytical solutions and the numerical solutions have been made.The results indicate that they fit very well with each other when the atomic interaction is weak.     

微重力环境下无限长柱体内角毛细流动解析近似解研究

应用同伦分析法研究无限长柱体内角毛细流动解析近似解问题,给出了级数解的递推公式.不同于其他解析近似方法,该方法从根本上克服了摄动理论对小参数的过分依赖,其有效性与所研究的非线性问题是否含有小参数无关,适用范围广.同伦分析法提供了选取基函数的自由,可以选取较好的基函数,更有效地逼近问题的解,通过引入辅助参数和辅助函数来调节和控制级数解的收敛区域和收敛速度,同伦分析法为内角毛细流动问题的解析近似求解开辟了一个全新的途径.通过具体算例,将同伦分析法与四阶龙格库塔方法数值解做了比较,结果表明,该方法具有很高的计算精度.     

The splitting of giant multipole states of deformed nuclei

A vibrating potential model is applied to deformed nuclei with a deformed harmonic oscillator potential in order to discuss the splitting of isoscalar giant quadrupole states. Eigenfrequencies of the collective states are estimated to be $\text{√2ω(1 ?}\text{1}\text{3}\text{δ)}$, $\text{√2ω(1 ?}\text{1}\text{6}\text{δ)}\text{and}\text{√2ω(1 +}\text{1}\text{3}\text{δ)}\text{fo and 2}{}^{\mathrm{+}}$ modes, respectively. The splitting of isovector dipole and isovector quadrupole states is also studied according to a schematic model as proposed by Bohr and Mottelson. It is shown that. isovector dipole states are split, as in a hydrodynamic model, while isovector quadrupole states with the same scaling factors as those of isoscalar quadrupole modes.     

同伦分析法在求解非线性演化方程中的应用

利用同伦分析法求解了(2+1)维改进的 Zakharov-Kuznetsov方程, 得到了它的近似周期解,该解与精确解符合很好. 结果表明，同伦分析法在求解高维非线性演化方程时, 仍然是一种行之有效的方法. 同时,还对该方法进行了一定的扩展， 经过扩展后的方法能够更方便地求解更多非线性演化方程的高精度近似解析解. 关键词： 同伦分析法 改进的 Zakharov-Kuznetsov方程 周期解     

实际射频阱中多极势分量的计算和消除

采用边界元方法,计算了当实际射频阱出现帽极开孔、环极开环带以及轴向存在装配误差时阱内电势的多极分量,并给出其随孔径大小变化的规律。结果表明在一定条件下,某些非线性因素可以部分抵消从而产生较为理想的四极势     

BaSnF4 fast ion conductor: Variations versus the method of preparation and anomalous temperature variation of the quadrupole splitting

A new method of preparation of high performance fluoride ion conductor, BaSnF₄, by water leaching of newly discovered barium tin(II) chloride fluorides, has been designed, and the materials have been studied and compared to the solid prepared by the usual dry method. The unit-cell parameters and crystallite dimensions were found to vary with the method of preparation. In addition, the crystallite dimensions were found to be highly anisotropic for the samples obtained by the wet method. The Mössbauer spectrum is made of a large tin(II) quadrupole doublet, and a broad tin(IV) oxide peak due to surface oxidation. The tin(II) spectrum is in agreement with covalently bonded tin(II) having a strongly stereoactive lone pair. An unusually high dependence of the quadrupole splitting at low temperatures was observed (5.8 times larger than for α-SnF₂).     

An optimized ion trap geometry to measure quadrupole shifts of ~(171)Yb~+ clocks

We propose a new ion-trap geometry to carry out accurate measurements of the quadrupole shifts in the ~(171)Yb ion.This trap will minimize the quadrupole shift due to the harmonic component of the confining potential by an order of magnitude.This will be useful to reduce the uncertainties in the clock frequency measurements of the 6s ~2S_(1/2)→4f~(13)6s~2 ~2F_(7/2)and 6s ~2S_(1/2)→5d~2D_(3/2) transitions,from which we can deduce the precise values of the quadrupole moments(0s) of the 4f~(13)6s~2 ~2F_(7/2) and 5d~2D_(3/2) states.Moreover,it may be able to affirm the validity of the measured 0 value of the4f~(13)6s~2~2F_(7/2) state,for which three independent theoretical studies defer almost by one order of magnitude from the measurement.We also calculate 0s using the relativistic coupled-cluster(RCC) method.We use these 0 values to estimate the quadrupole shift that can be measured in our proposed ion trap experiment.     

非线性演化方程孤立波的同伦分析法求解

利用同伦分析法求解了Burgers方程，得到了其扭结形孤立波的近似解析解，该解非常接近于相应的精确解.结果表明，同伦分析法可用来求解非线性演化方程的孤立波解.同时，也对所用方法进行了一定扩展，得到了Kadomtsev-Petviashvili(KP)方程的钟形孤立子解.经过扩展后的方法能够更方便地用于求解更多非线性演化方程的高精度近似解析解. 关键词： Burgers方程 同伦分析法 KP方程 孤立波解     

外加直流电场作用下高阶弱非线性复合介质的电势分布

利用同伦分析方法, 研究了一类由柱形杂质随机嵌入基质所形成的、电场和电流密度满足J = σ E + χ |E|²E + η|E|⁴E 形式本构关系的高阶弱非线性复合介质在外加直流电场作用下的电势分布问题. 首先利用模函数展开法, 将本构方程及边界条件化成了一系列非线性常微分方程的边值问题; 再利用同伦分析方法进行求解, 给出了电势在基质和杂质区域的渐近解析解. 关键词： 高阶弱非线性复合介质 模函数展开法 同伦分析方法 电势分布