一维谐振子势阱中二全同粒子的空间关联

针对一维谐振子势阱中由两个全同粒子组成的体系,假设其空间波函数分别具有以下3种交换对称性:1)没有交换对称性,2)对于交换是反对称情况,3)对于交换是对称情况,讨论了二粒子空间相对位置的分布概率.并由此将量子力学教材中自由粒子情况下的结论推广至一维谐振子束缚态情形,即两个全同粒子无论是处于自由态还是束缚态,在空间波函数交换对称的情况下,两个粒子靠拢的概率最大,而交换反对称情况下,两个粒子靠近(r→0)的概率趋于零.论文结论有助于加深对量子力学中全同粒子交换对称性及其物理效应的理解.     

单杠结构差分离散系统的振动反问题

研究组合结构中的杆-梁-杆组合单支结构,或称单杠结构的模态反问题,从数学上证明单杠结构差分离散系统固有振动的刚度矩阵的符号振荡性,并导出其频率和振型的一些定性性质.在此基础上,探讨由两组位移或应变振型及相应频率构造物理参数的条件和方法,给出两个计算实例.讨论结构参数关于其几何对称轴具有对称性的条件下的模态反问题,并给出计算实例.计算结果表明,上述反问题提法合理,解法正确.     

带全动翼尖飞翼布局的颤振规律

现代战斗机的任务性能要求满足高速、高机动、隐身、轻量化等多目标,无尾飞翼布局飞机的气动效率高,具有良好的机动性、低可探测性和飞发一体化优势。该布局采用翼身融合、多操纵面和全动翼尖的结构设计。全动翼尖机翼新型结构使得其气动弹性问题突出,其中全动翼尖结构和各个操纵面之间的耦合作用,使得颤振问题尤为突出。采用线性颤振法和模态跟踪技术研究全动翼尖机翼的颤振问题,通过研究发现,无尾飞翼布局飞机结构的颤振耦合类型主要有3种：机翼对称一弯和全动翼尖对称旋转耦合型(对称耦合型)、机翼反对称一弯和全动翼尖反对称旋转耦合型(反对称耦合型)及机身模态参与的颤振型。通过研究发现,反对称耦合型的颤振速度要低于对称耦合型,而在机身模态参与的颤振结果中,机身和机翼的耦合颤振速度高于前两者,机身和全动翼尖的耦合颤振速度低于前两者。影响对称耦合型颤振的主要结构因素有机翼弯曲刚度和全动翼尖旋转刚度,而影响反对称耦合型颤振的主要有机翼弯曲刚度、机身转动惯量和全动翼尖旋转刚度。总之,全动翼尖结构是造成无尾飞翼布局飞机容易发生颤振的内在因素。     

空间波函数的对称性对氦原子双光子双电离过程中电子关联的影响

通过数值求解含时薛定谔方程,研究了氦原子具有对称空间波函数的1s2s 1S态和具有反对称空间波函数的1s2s 3S态分别作为初态的双光子双电离过程. 结果表明,对于初态为单重态1s2s 1S的双光子双电离过程,两个电离电子的能量分布随激光脉冲持续时间的增加呈现由单峰到双峰的变化,这里的单峰和双峰分别意味着两个电离电子主要携带相等和不等的能量;然而对于初态为三重态1s2s 3S的双光子双电离过程,两个电离电子的能量分布随激光脉冲持续时间的增加总是保持双峰结构. 这些结果表明当原子的初态处于反对称空间波函数时,两电子的空间密度分布具有较少的重叠,从而导致电子在超短激光脉冲中电离时电子关联能无法平均分配.     

外伸梁差分离散系统的模态反问题

研究外伸梁模态的反问题,即由两组位移模态或应变模态及相应的频率构造外伸梁差分离散模型物理参数的方法,讨论反问题解存在的充要条件.提出算法并用算例验证.结果表明,由应变模态构造外伸梁的物理参数比用位移模态构造梁的物理参数精度要高.     

多电子体系波函数的构造问题

我们知道,多电子体系的波函数 Ψ(r1s1,r2s2,…rnsn)对任何一对粒子的位置和自旋参量的同时对调,必须是反对称的.本文讨论当体系的哈密顿量H0不包含粒子间相互作用时,如何构造H0的反对称本征函数 H0Ψ=EΨ的问题.这一问题在微扰论中构造零级近似波函数时也要遇到. 有的书上说,当自旋与轨道相互作用可以忽略时,体系的波函数可以写为 Ψ(r1s1,r2s2,…rnsn) =φ(r1,r2,…rn)x(s1,s2,…sn) (1)然后取对称的φ和反对称的x相乘,反对称的中和对称的x相乘,所得的都是体系的反对称波函数. 这种方法对于两个电子的体系无疑是正确的.但当。>3时.这种…     

Paul阱中共线三离子体系的经典动力学

研究了在Paul阱囚禁场赝势作用下共线构形的三离子体系经典动力学特性.尽管这是一个非线性体系，但不存在混沌，即体系在任何能量下运动都是规则的，而相空间则由两个轨迹为对称和反对称周期(或准周期)轨道的KAM不变环面构成.体系的两条最简单的周期轨道S和A的周期随能量E的下降而增大，并在E趋于体系的最小值E_min=3.0时分别为反对称和对称谐振动. 关键词：     

构造哈密尔顿系统jet辛差分格式的生成函数法

考虑哈密尔顿系统的保结构算法,在经典哈密尔顿系统的jet辛算法的基础上,给出了一般哈密尔顿系统的jet辛差分格式的定义.并利用带有变系数辛矩阵的一般哈密尔顿系统中的构造辛差分格式的生成函数法的思想,来建立由一般的反对称矩阵所确定的微分二形式与生成函数的关系,再利用哈密尔顿-雅可比方程来构造jet辛的差分格式.     

杆的离散系统的某些混合型振动反问题

研究杆的离散系统的混合型振动反问题,即由给定的部分频谱数据和部分模态数据构造一个杆的离散系统的刚度矩阵和质量矩阵.提出3个此类反问题,给出反问题的解法,讨论反问题的解的存在条件,给出相应的计算实例,并分析这类反问题的潜在价值.     

魔角旋转情形下化学位移各向异性相互作用的反对称分量

核自旋之间的各种各向异性相互作用都能用二阶张量表示,这些张量可分解成各向同性、对称以及反对称分量。本文针对化学位移各向异性相互作用,讨论了反对称分量的NMR性质,指出在MAS情形下,反对称分量对频移和谱宽的贡献仍是二阶小量。反对称分量与对称分量的非久期项对频移和谱宽的影响决定了MAS谱的极限分辨率。文中计算了MAS情形下这两种效应产生的粉末线型。     

Reconstruction of the stiffness of an inhomogeneous elastic plate

The paper discusses the problem of reconstructing the inhomogeneous cylindrical, symmetric stiffness distribution of a round plate using information on the bias function for established oscillations, which is measured at a certain point. A solution is constructed to the direct problem using the Galerkin method and to the inverse problem of reconstructing the stiffness using an iterative approach based on the regularized linearization method. We present the results of calculation experiments on reconstructing different types of functions that show the efficiency of the proposed approach and make it possible to estimate changes in stiffness.     

Approximate solutions of the Liouville equation. II. Stationary variational principles

Stationary variational functionals for the Laplace transform of the Liouville distribution are constructed. The value of the functional is the autocorrelation function that one wishes to compute. It is shown that the functionals may be transformed to a renormalized form. Trial functions not involving the potential explicitly give rise to time-dependent autocorrelation functions determined only by equilibrium spatial correlation functions. Another class of functionals is constructed by independently varying the parity symmetric and antisymmetric parts of the distribution function. Trial functions need only be assumed for one of these—the optimum value of the other one is given exactly. This procedure is used to improve the simplest known theories for velocity and density autocorrelation functions.Work supported by a grant from the National Science Foundation.     

RELIABILITY SENSITIVITY FOR ROTOR-STATOR SYSTEMS WITH RUBBING

On the basis of the dynamic equations of the Jeffcott rotor-stator model with imbalance, the reliability sensitivity of the rotor-stator systems with rubbing is examined. A statistical fourth moment method is developed to determine the first four moments of system response and state function. The distribution function of the system state function is approximately determined by the standard normal distribution functions using the Edgeworth series technique. The reliability and reliability sensitivity are obtained and the effect on reliability and reliability sensitivity of shaft stiffness and damping, stator stiffness and damping, radial clearance and stator radial stiffness is studied. Numerical results are also presented and discussed.     

A model of Jupiter’s magnetodisk

An axially symmetric equilibrium model of Jupiter’s magnetodisk is developed in the MHD approximation that takes the plasma corotation and the centrifugal force into account. The model is constructed for two cases: (1) the magnetodisk plasma is assumed to have a uniform temperature; (2) the plasma pressure is assumed to be an adiabatic function of density. Analytical expressions for the magnetic field, current density, and magnetodisk temperature and thickness distributions are obtained as functions of the system parameters, viz., the radial distribution of plasma pressure in the equatorial plane, the transverse magnetic field in the center of the layer, and the angular velocity of the plasma rotation.     

Symmetry properties of integral equations in the theory of classical fluids

The functional formalism described in a preceding paper, leads to a great number of integral equations for molecular distribution functions. Some of them have a certain symmetry property which, in the case of the pair distribution function includes symmetry with respect to the permutation of particles. This symmetry condition is necessary for any self consistent approximation. Among all integral equations known to date only the PY and the HNC equations satisfy this condition. In this paper we derive some new symmetric equations. Integral equations which are obtained with the help of the Percus method, involvingn-particle distribution functions (n > 2), cannot be symmetric with respect to the interchange of particles.     

Optimal lattice configurations for interacting spatially extended particles

We investigate lattice energies for radially symmetric, spatially extended particles interacting via a radial potential and arranged on the sites of a two-dimensional Bravais lattice. We show the global minimality of the triangular lattice among Bravais lattices of fixed density in two cases: In the first case, the distribution of mass is sufficiently concentrated around the lattice points, and the mass concentration depends on the density we have fixed. In the second case, both interacting potential and density of the distribution of mass are described by completely monotone functions in which case the optimality holds at any fixed density.     

Reduced forms of the Wigner distribution function for the numerical analysis of rotationally symmetric synchrotron radiation

In an effort to provide a computationally convenient approach to the characterization of partially coherent synchrotron radiation in phase space, a thorough discussion of the minimum dimensionality of the Wigner distribution function for rotationally symmetric sources of arbitrary degrees of coherence is presented. It is found that perfectly coherent, perfectly incoherent and partially coherent sources may all be characterized by a three‐dimensional reduced Wigner distribution function, and some special cases are discussed in which a two‐dimensional reduced Wigner distribution function suffices. An application of the dimension‐reducing formalism to the case of partially coherent radiation from a planar undulator and a circularly symmetric electron beam as can be found in linear accelerators is demonstrated. The photon distribution is convolved over a realistic electron bunch, and how the beta function, emittance and energy spread of the bunch affect the total degree of coherence of the radiation is inspected. Finally the cross spectral density is diagonalized and the eigenmodes of the partially coherent radiation are recovered.     

Construction of minimizing sequence of multiparticle functions for calculating the spectrum of an atom

A method for calculating the states of a many-electron atom is proposed based on the representation of the wave function of the atom as a linear combination of multideterminant functions. Determinants are constructed from single-particle hydrogen-like functions in which the positive nuclear charge is replaced by a certain effective charge. For each single-particle function, the effective charge is calculated such that to take into account the interaction of a given electron with the spherically symmetric part of the screening charge distribution of remaining electrons. Examples of constructing approximating sequence of functions are given and results of calculations of energies of stationary states of the He and Li atoms are presented.     

Kinetic description of the Coulomb explosion of a spherically symmetric cluster

The particle distribution function is calculated for the Coulomb explosion of a spherically symmetric charged cluster formed through the interaction of intense ultrashort laser pulses with a cluster gas. The particle density and mean velocity distributions as well as the energy spectra of the accelerated particles are obtained. These characteristics are analyzed in detail for a cold cluster plasma, where the kinetic effects determine the physics of multiple flows emerging after the turnover of the cluster particle velocity profile. We find the boundaries of the multiple-flow regions and study the characteristics of an exploding cluster as a function of its initial density profile. The energy spectra of the accelerated ions are obtained for a cluster plasma with a specified cluster size distribution.     

Solving the Boltzmann equation in a 2-D-configuration and2-D-velocity space for capacitively coupled RF discharges

A new kinetic scheme, the generalized Monte Carlo flux (GMCF) method, provides the electron particle distribution function in phase space, f(ν, μ, r, z, t) (ν: speed, μ: velocity angle, r: radial position, z: axial position, and t: time), for solving the Boltzmann equation in modeling capacitively coupled RP discharges. For a simulation with spatial- and temporal-varying fields in RF discharges, the GMCF method handles the collision terms of the Boltzmann equation by using one transition matrix to compute the collision transition between velocity space cells. An anti-diffusion flux transport scheme is developed to overcome the numerical diffusion in the velocity and configuration spaces. The major advantages of the GMCF method are the increase in resolution in the tail of distribution functions and the decrease of computation time. The GMCF calculation results in terms of microscopic electron distribution function and macroscopic quantities of density, electric field and ionization rate, are presented for RF discharges and compared with other kinetic and fluid simulation and experimental results. The effects of the induced radial electric field in the sheath close to the radial wall in a cylindrically symmetric parallel-plate geometry are discussed