Concept of the effective potential in describing the motion of ions in a quadrupole mass filter

We propose a generalization of the effective potential theory for the motion of particles in a rapidly oscillating electric field for the stability parameters lying near the boundary of the diagram where the standard effective potential theory is inapplicable. We derive the dynamic equations describing the variation of the envelope of ion oscillations for the motion of ions near the stability vertex of the first zone of the quadrupole mass filter. We reduce them to the form of the Hamilton equations for oscillations of a material particle in the field of potential forces. We obtain expressions for the effective potential well. It is shown that in spite of the high kinetic energy of oscillations, the depth of the effective potential well for ions in the quadrupole is less than 1 eV in the case of filtration with a mass resolution exceeding 200 units. The acceptance of the mass filter is calculated as a function of the stability parameters and the resolving power.     

Stability of two-ion crystals in the Paul trap: A comparison of exact and pseudopotential calculations

The stability of two-ion crystals in a Paul trap with a dc component in the quadrupole potential has been studied with the use of the monodromy matrix. The pseudopotential model predicts crystals with the ions at rest either along the trap axis or in the radial plane. The solutions of the full equations of motion disagree with the predictions of the pseudopotential model when the radial and axial secular frequencies are nearly degenerate: the crystal is either unstable (as first noted by Emmertet al.) or exists in a previously unanticipated configuration in which the ions lie at an angle to the trap axes. A bifurcation diagram near the edge of the crystalline stability range does not support a frequency-doubling route to chaos.Dedicated to H. Walther on the occasion of his 60th birthday     

Buckling of single layer graphene sheet based on nonlocal elasticity and higher order shear deformation theory

Higher order shear deformation theory (HSDT) is reformulated using the nonlocal differential constitutive relations of Eringen. The equations of motion of the nonlocal theories are derived. The developed equations of motion have been applied to study buckling characteristics of nanoplates such as graphene sheets. Navier's approach has been used to solve the governing equations for all edges simply supported boundary conditions. Analytical solutions for critical buckling loads of the graphene sheets are presented. Nonlocal elasticity theories are employed to bring out the small scale effect on the critical buckling load of graphene sheets. Effects of (i) nonlocal parameter, (ii) length, (iii) thickness of the graphene sheets and (iv) higher order shear deformation theory on the critical buckling load have been investigated. The theoretical development as well as numerical solutions presented herein should serve as reference for nonlocal theories as applied to the stability analysis of nanoplates and nanoshells.     

On a kinetic approach to the modulational stability of envelope solitons in a relativistic plasma in an external electric field

Summary The formation of envelope solitons is discussed in a relativistic plasma under the influence of a fluctuating electric field. We use the kinetic-theory approach for our analysis. Due to the larger inertia, only the electrons are considered to be relativistic and the ions to be nonrelativistic. A NLS equation is derived describing the motion of the solitary wave. This NLS equation actually comes from an approximation of a pair of equations which can be considered to be a relativistic generalisation of the Zakharov equation. We next discuss the exact form of the envelope solitary-wave solution of the NLS equation and the modulation stability of such a wave. When the density, momentum and energy of such wave packets are fixeda priori, conditions are derived for the parameters of the problem from such stability consideration.     

A geometric theory for scroll wave filaments in anisotropic excitable media

Scroll waves are an important example of self-organisation in excitable media. In cardiac tissue, scroll waves of electrical activity underlie lethal ventricular arrhythmias and fibrillation. They rotate around a topological line defect which has been termed the filament. Numerical investigation has shown that anisotropy can substantially affect the dynamics of scroll waves. It has recently been hypothesised that stationary scroll wave filaments in cardiac tissue describe geodesics in a space whose metric is the inverse diffusion tensor. Several computational studies have validated this hypothesis, but until now no quantitative theory has been provided to study the effects of anisotropy on scroll wave filaments. Here, we review in detail the recently developed covariant formalism for scroll wave dynamics in general anisotropy and derive the equations of motion of filaments. These equations are fully covariant under general spatial coordinate transformations and describe the motion of filaments in a curved space whose metric tensor is the inverse diffusion tensor. Our dynamic equations are valid for thin filaments and for general anisotropy and we show that stationary filaments obey the geodesic equation. We extend previous work by allowing spatial variations in the determinant of the diffusion tensor and the reaction parameters, leading to drift of the filament.     

Dynamic analysis of a rectangular plate subjected to multiple forces moving along a circular path

A multi-degree-of-freedom (m.d.o.f.) system excited by a rough moving surface has been developed to study friction-induced oscillations. The normal degrees of freedom allow for oscillatory normal forces, while the normal-tangential coupling of friction produces parametric excitation in the slipping equations of motion. After a modal change of variables, first order averaging has been used to produce a set of autonomous equations of motion. Eigenvalue analysis of the averaged equations has produced stability predictions for the steady sliding position. Numerical integration of the original system of equations has verified the existence of locally unstable oscillations for a system excited by a rough surface input. The combination of velocity-dependent friction and a harmonically varying normal force have been shown to produce large-amplitude oscillations, in some cases leading to stick-slip responses.     

Numerical solution of differential-algebraic equations in mechanical systems simulation

The numerical solution of the differential-algebraic equations of motion of mechanical systems offers many computational challenges. In this paper we describe progress which has been made in understanding the formulation of the equations of motion from the viewpoint of numerical stability, and outline some of the difficulties which must be resolved for efficient and reliable numerical methods in real-time simulation of mechanical systems.     

The use of stability bands to improve the performance of quadrupole mass filters

The possibility of increasing the resolving power of quadrupole mass filters has been discussed. It has been shown that the limitations associated with the finite time of flight imposed by Von Zahn’s rule are modified while using the islands of stability that appear when quadrupole is excited by the additional signals. By calculation of the exponential increment of growth of the oscillation amplitude the effect of the acceleration of mass separation and improvement of the peak shape, when the islands of stability are used for ion filtering, is explained. The case of the excitation by two signals at different frequencies has been studied theoretically. The conditions under which suppression of the first order resonance for one of the directions of motion is obtained. The direct modeling of the peak shape of the mass filter shows the possibility of obtaining a resolution of 10,000 with a time of flight of ions through the quadrupole of 100 cycles of the main RF supply, and low sensitivity of the new operating mode to the nonlinear field distortions in the quadrupoles with rods of circular cross sections.     

快速C60离子团在固体中的库仑爆炸过程Ⅱ分子动力学模拟

研究了快速C60 离子团与固体材料的相互作用过程 .借助于线性介电响应理论及等离子 极点近似介电函数 ,推导出作用在团簇中单个离子上的动力学相互作用力 ,并建立了一套描述离子团中单个离子运动的方程组 .通过数值求解运动方程组 ,可以发现 ,对于高速C60 离子团在固体中穿行时 ,由于动力学相互作用力的影响 ,使得库仑爆炸图形呈现出很强的非球对称性 ,即离子团中的导航离子群爆炸得较快 ,而尾随离子群则保持相对地稳定     

Monte Carlo Simulations of the Influence of Ion‐Neutral Collisions on the Ion Currents Collected by Electrostatic Probes

We have carried out Monte Carlo simulation of the motion of Ar⁺ ions in the space charge sheath surrounding a cylindrical Langmuir probe. The ion currents to the probe have been calculated from these simulations and the percentages of ions crossing the sheath boundary that are collected by the probe have been determined. It has been shown that the collisions of ions with neutral helium gas atoms in the sheath increase the percentage of ions collected by the probe above that predicted by collisionless orbital motion limited current (OMLC) theory at lower helium pressure and decrease this percentage below the OMLC theory prediction at higher helium pressure. It has been shown also that the ion current almost does not depend on probe radius at higher helium pressures. The results of the simulations have been compared with recent Langmuir probe measurements made in flowing afterglow plasmas and with other probe theories.     

快速C60离子团在固体中的库仑爆炸过程Ⅰ——球壳层模型

研究了快速C₆₀离子团在固体中穿行时的库仑爆炸过程.假定离子团中离子之间位置矢量的取向是随机的,并且采用球壳模型描述C₆₀离子团的结构.借助于线性介电响应理论和等离子-极点近似介电函数,推导出C₆₀离子团自能的解析表达式.通过数值求解描述离子团半径变化的运动方程,可以发现自能中的“尾效应”可以降低C₆₀离子团的库仑爆炸速度,甚至可以稳定C₆₀离子团的结构. 关键词： 离子团 库仑爆炸 球壳模型     

快速C60离子团在固体中的库仑爆炸过程Ⅱ——分子动力学模拟

研究了快速Ｃ₆₀离子团与固体材料的相互作用过程.借助于线性介电响应理论及等离子-极点近似介电函数,推导出作用在团簇中单个离子上的动力学相互作用力,并建立了一套描述离子团中单个离子运动的方程组.通过数值求解运动方程组,可以发现,对于高速Ｃ₆₀离子团在固体中穿行时,由于动力学相互作用力的影响,使得库仑爆炸图形呈现出很强的非球对称性,即离子团中的导航离子群爆炸得较快,而尾随离子群则保持相对地稳定. 关键词： 离子团 库仑爆炸 动力学相互作用     

Nitrogen-14 nuclear quadrupole resonance study of hydrazine monohydrate

¹⁴N NQR in hydrazine monohydrate has been investigated from 4.2 K to 140 K. A molecular motion with an activation energy of about 7.5 kcal/mol became active at about 120 K. Echo envelope modulation due to intramolecular dipolar coupling was observed.     

Three-dimensional modelling and dynamic analysis of an automatic ball balancer in an optical disk drive

Dynamic behaviours and stability of an automatic ball balancer (ABB) in an optical disk drive are analyzed based on the proposed three-dimensional dynamic model. For dynamic analysis, the feeding deck with the ball balancer and a spindle motor is modelled as a rigid body with six degrees of freedom. The nonlinear equations of motion are derived using Lagrange's equation in order to describe the translational and rotational motions of the system. From the derived nonlinear equations, the linearized equations of motion in the neighbourhood of a balanced equilibrium position are obtained by the perturbation method. These equations are coupled, linear, differential equations with time-dependent periodic coefficients, from which the stability of the system is analyzed by using the Floquet theory. Finally, the time responses are computed to verify the results of the stability analysis, and to investigate the balancing performance of the ABB.     

快速C60离子团在固体中的库仑爆炸过程Ⅰ球壳层模型

研究了快速C60 离子团在固体中穿行时的库仑爆炸过程 .假定离子团中离子之间位置矢量的取向是随机的 ,并且采用球壳模型描述C60 离子团的结构 .借助于线性介电响应理论和等离子 极点近似介电函数 ,推导出C60 离子团自能的解析表达式 .通过数值求解描述离子团半径变化的运动方程 ,可以发现自能中的“尾效应”可以降低C60 离子团的库仑爆炸速度 ,甚至可以稳定C60 离子团的结构     

The averaging principle and the diagram technique

Rae and Davidson have found a striking connection between the averaging method generalised by Kruskal and the diagram technique used by the Brussels school in statistical mechanics. They have considered conservative systems whose evolution is governed by the Liouville equation. In this paper we have considered a class of dissipative systems whose evolution is governed not by the Liouville equation but by the last-multiplier equation of Jacobi whose Fourier transform has been shown to be the Hopf equation. The application of the diagram technique to the interaction representation of the Jacobi equation reveals the presence of two kinds of interactions, namely the transition from one mode to another and the persistence of a mode. The first kind occurs in the treatment of conservative systems while the latter type is unique to dissipative fields and is precisely the one that determines the asymptotic Jacobi equation. The dynamical equations of motion equivalent to this limiting Jacobi equation have been shown to be the same as averaged equations.     

激光场对快速分子离子与固体相互作用的影响

利用线性化的流体力学方程和泊松方程，描述了在强激光场作用下快速分子离子在固体中产生的电激发过程，并推导出分子离子中两个离子之间的动力学相互作用势和相互作用力的一般表达式.通过数值求解离子的运动方程，研究了激光场的参量对分子离子库仑爆炸过程和能量损失的影响. 关键词： 激光场 分子离子 库仑爆炸 能量损失     

Dynamics of bright soliton in a spin–orbit coupled spin-1 Bose–Einstein condensate

We have investigated the dynamics of bright solitons in a spin–orbit coupled spin-1 Bose–Einstein condensate analytically and numerically. By using the hyperbolic sine function as the trial function to describe a plane wave bright soliton with a single finite momentum, we have derived the motion equations of soliton's spin and center of mass, and obtained its exact analytical solutions. Our results show that the spin–orbit coupling couples the soliton's spin with its center-of-mass motion, the spin oscillations induced by the exchange of atoms between components result in the periodical oscillation of center-of-mass, and the motion of center of mass of soliton can be viewed as a superposition of periodical and linear motions. Our analytical results have also been confirmed by the direct numerical simulations of Gross–Pitaevskii equations.     

GREEN FUNCTION THEORY AND ITS GLOBAL STRUCTURE

The Green function theory is successful in many fields of theoretical physics and the Bogoliubov-Gor'kov theory system is its important branch that involves many theoretical methods. In the last twenty years many papers have been published, but as all the equations of motion are coupled and their number is infinite, its global structure problem has not been investigated as yet. This paper is devoted to the study of its global structure, the exact decoupling problem, and the uniqueness and completeness problems. Some higher order spectral representation theorems and exact relationships between higher and lower order Green functions are obtained. Thus the equations of motion are decoupled exactly. In this paper it is proved that after cutting off the equations of motion are decoupled exactly and the solution of these equationsystemsmay not be unique. It is also proved that if there is one solution satisfying all the Green function's equations, then there must be a solution set, all of them satisfy all the equations and its number is infinite and the differences between them are arbitrary. By adding some limitations to ImG(x) at the regal axis a uniqueness theorem is proved.