负载弦之演示教具

介绍一自制的负载弦教具，5颗沿铀向充磁的圆柱状钐钴磁铁穿在细钓鱼线上，作为负载弦之负载质点，再以可调频率的交流电磁化马蹄形电磁铁，使得马蹄形电磁铁对圆柱状钐钴磁铁施与周期性的引力及斥力，启动负载弦的各个简正模式．此自制的负载弦教具可定量演示教科书中理论计算的结果．     

Strong-coupling limit for one-dimensional polarons in a finite box

The strong coupling limit is studied for a Pekar-Fröhlich polaron confined to a one-dimensional (1D) structure. The non-linear effective Schrödinger equation is solved exactly in the case of two different external potentials which imitate a finite size 1D sample: an infinite and a finite deep rectangular well. The ground state and excited states are calculated. We found that taking the limit of a finite size box to an infinitely large box leads to additional solutions which are not found in a treatment on an infinite axis. The additional solutions, which have a 1/n ² discrete spectrum, correspond to polaron states in which the wave function is split up in identical parts which are infinitely apart from each other.     

A Complex Network Model for Analyzing Railway Accidents Based on the Maximal Information Coefficient

It is an important issue to identify important influencing factors in railway accident analysis. In this paper, employing the good measure of dependence for two-variable relationships, the maximal information coefficient (MIC), which can capture a wide range of associations, a complex network model for railway accident analysis is designed in which nodes denote factors of railway accidents and edges are generated between two factors of which MIC values are larger than or equal to the dependent criterion. The variety of network structure is studied. As the increasing of the dependent criterion, the network becomes to an approximate scale-free network. Moreover, employing the proposed network, important influencing factors are identified. And we find that the annual track density-gross tonnage factor is an important factor which is a cut vertex when the dependent criterion is equal to 0.3. From the network, it is found that the railway development is unbalanced for different states which is consistent with the fact.     

Strong-coupling limit for one-dimensional polarons in a finite box

The strong coupling limit is studied for a Pekar-Fröhlich polaron confined to a one-dimensional (1D) structure. The non-linear effective Schrödinger equation is solved exactly in the case of two different external potentials which imitate a finite size 1D sample: an infinite and a finite deep rectangular well. The ground state and excited states are calculated. We found that taking the limit of a finite size box to an infinitely large box leads to additional solutions which are not found in a treatment on an infinite axis. The additional solutions, which have a 1/n ² discrete spectrum, correspond to polaron states in which the wave function is split up in identical parts which are infinitely apart from each other.     

旋转内接悬臂梁的刚柔耦合动力学特性分析

对固结于旋转刚环上内接柔性梁的刚柔耦合动力学特性进行了研究. 在精确描述柔性梁非线性变形基础上, 利用Hamilton变分原理和假设模态法, 在计入柔性梁由于横向变形而引起的轴向变形二阶耦合量的条件下, 推导出一次近似耦合模型. 忽略柔性梁纵向变形的影响,给出一次近似简化模型,引入无量纲变量, 对简化模型做无量纲化处理. 首先分析在非惯性系下内接悬臂梁的动力学响应, 并与外接悬臂梁进行比较; 其次研究内接悬臂梁的稳定性;最后分析内接悬臂梁失稳临界转速的收敛性. 研究发现, 与外接悬臂梁存在动力刚化效应不同,内接悬臂梁存在着动力柔化效应; 给出了内接悬臂梁无条件稳定的临界径长比以及失稳的临界转速的计算方法; 若第一阶固有频率随转速增大而减小,则该内接悬臂梁处于有条件稳定; 随着模态截断数的增加,内接悬臂梁失稳的临界转速减小且有收敛值. 关键词： 内接悬臂梁 一次近似简化模型 动力柔化 临界转速     

On the connection between quantum fields and von Neumann algebras of local operators

The relationship between a standard local quantum field and a net of local von Neumann algebras is discussed. Two natural possibilities for such an association are identified, and conditions for these to obtain are found. It is shown that the local net can naturally be so chosen that it satisfies the Special Condition of Duality. The notion of an intrinsically local field operator is introduced, and it is shown that such an operator defines a local net with which the field is locally associated. A regularity condition on the field is formulated, and it is shown that if this condition holds, then there exists a unique local net with which the field is locally associated if and only if the field algebra contains at least one intrinsically local operator. Conditions under which a field and other fields in its Borchers class are associated with the same local net are found, in terms of the regularity condition mentioned.     

Discovery of a missing disease spreader

This study presents a method to discover an outbreak of an infectious disease in a region for which data are missing, but which is at work as a disease spreader. Node discovery for the spread of an infectious disease is defined as discriminating between the nodes which are neighboring to a missing disease spreader node, and the rest, given a dataset on the number of cases. The spread is described by stochastic differential equations. A perturbation theory quantifies the impact of the missing spreader on the moments of the number of cases. Statistical discriminators examine the mid-body or tail-ends of the probability density function, and search for the disturbance from the missing spreader. They are tested with computationally synthesized datasets, and applied to the SARS outbreak and flu pandemic.     

A singularity-avoiding moving least squares scheme for two-dimensional unstructured meshes

Moving least squares interpolation schemes are in widespread use as a tool for numerical analysis on scattered data. In particular, they are often employed when solving partial differential equations on unstructured meshes, which are typically needed when the geometry defining the domain is complex. It is known that such schemes can be singular if the data points in the stencil happen to be in certain special geometric arrangements, however little research has specifically addressed this issue. In this paper, a moving least squares scheme is presented which is an appropriate tool for use when solving partial differential equations in two dimensions, and the precise conditions under which singularities occur are identified. The theory is used to develop a stencil building algorithm which automatically detects singular stencils and corrects them in an efficient manner, while attempting to maintain stencil symmetry as closely as possible. Finally, the scheme is applied in a convection–diffusion equation solver and an incompressible Navier–Stokes solver, and the results are shown to compare favourably with known analytical solutions and previously published results.     

Lax Pair and Darboux Transformation for a Variable-Coefficient Fifth-Order Korteweg-de Vries Equation with Symbolic Computation

In this paper, we put our focus on a variable-coe~cient fifth-order Korteweg-de Vries （fKdV） equation, which possesses a great number of excellent properties and is of current importance in physical and engineering fields. Certain constraints are worked out, which make sure the integrability of such an equation. Under those constraints, some integrable properties are derived, such as the Lax pair and Darboux transformation. Via the Darboux transformation, which is an exercisable way to generate solutions in a recursive manner, the one- and two-solitonic solutions are presented and the relevant physical applications of these solitonic structures in some fields are also pointed out.     

高精度光电数据采集系统的实验研究

针对光电弱信号检测,采用Σ-ΔAD转换器AD7706和AVR单片机ATmega8515设计了适用于低频量测量的高精度数据采集器,采用Σ-ΔAD转换器ADC16471、AVR单片机ATmega8515、C51单片机C8051F020和以太网控制器RTL8019AS设计了适用于高精度线阵CCD的数据采集器,并分别对两套数据采集器进行了实验研究与性能分析。     

Radiation transport with anisotropic scattering

Reflection and transmission of radiation with anisotropic scattering in considered, using an invariant-imbedding formulation of the transport equation. Extensive numerical calculations show that the results of the transport approximation, in which the scattering kernel is represented by an isotropic part and a forward scattered component, are useful for an isotropic incident source but they are not satisfactory for a monodirectional source, especially in the case of reflection for large and small incident angles. A modified transport approximation is proposed in which singly-scattered radiation is taken into account exactly and higher-order scatterings are obtained from the transport approximation. The results derived from the modified transport approximation are in good agreement with other calculations for the cases considered.     

Many-body spin interactions and the ground state of a dense Rydberg lattice gas

We study a one-dimensional atomic lattice gas in which Rydberg atoms are excited by a laser and whose external dynamics is frozen. We identify a parameter regime in which the Hamiltonian is well approximated by a spin Hamiltonian with quasilocal many-body interactions which possesses an exact analytic ground state solution. This state is a superposition of all states of the system that are compatible with an interaction induced constraint weighted by a fugacity. We perform a detailed analysis of this state which exhibits a crossover between a paramagnetic phase with short-ranged correlations and a crystal. This study also leads us to a class of spin models with many-body interactions that permit an analytic ground state solution.     

Magnetic field effects on the localization of electromagnetic waves in random 1D systems which are almost periodic

The effects of an externally applied magnetic field on the Anderson localization of electromagnetic waves in an alternating layered system of vacuum and semiconducting slabs are studied. Specifically, a waveguide formed from perfectly conducting parallel plates which contain between them an array of vacuum and n-type semiconductor slabs is examined in the presence of an external static magnetic field applied parallel to both the plates and the slab surfaces. The widths of the slabs in the array are random but with a randomness such that the array of slabs is almost periodic, and we study only electromagnetic modes which propagate perpendicular to the slab surfaces. The localization length is obtained by studying the reflection and transmission properties of a finite array of slabs in the limit that it becomes semi-infinite. Two types of system are treated: (i) a reciprocal system which exhibits a localization length that does not depend on the sign of the applied magnetic field, and (ii) a non-reciprocal system which exhibits a localization length that depends on the sign of the applied magnetic field.     

Interionic potentials in alkali halides and their use in simulations of the molten salts

After an outline of work on rare-gas systems, which serves as a target for parallel work on alkali halides, and an initial brief survey of those parts of this parallel work for which results have been obtained, interionic potential models for alkali halides are considered in some detail. The rigid ion potentials of Fumi and Tosi are discussed and then a major part of the section is devoted to deriving a new set of polarizable ion potentials, which incorporate the ideas behind the lattice dynamical shell model. Extensions which include many-body terms in the potentials are considered briefly and finally the information which can be obtained from alkali halide diatomic molecules is discussed.

In the third section methods of computer simulation for ionic liquids are outlined, concentrating on the molecular dynamics method, and some of the properties which can be obtained by analysing the ion trajectories are listed. Results from simulations, including some new work on LiF, NaCl and RbI, are reviewed.     

Coexistence of Coulomb blockade and zero bias anomaly in a strongly coupled nanodot

The current-voltage characteristics through a metallic nanoparticle which is well coupled to a metallic lead are measured. It is shown that the I-V curves are composed of two contributions. One is a suppression of the tunneling conductivity at the Fermi level, and the second is an oscillating feature which shifts with gate voltage. The results indicate that zero-bias anomaly and Coulomb blockade phenomena coexist in an asymmetric strongly coupled zero-dimensional system.     

Theoretical investigation of an electron beam propagating through a wide gap cavity

This paper presents a self-consistent nonlinear theory of the current and energy modulations when an electron beam propagates through an inductively-loaded wide gap cavity. The integro-differential equations axe obtained to describe the modulation of the beam current and kinetic energy. A relativistic klystron amplifier （RKA） model is introduced, which uses an inductively-loaded wide gap cavity as an input cavity. And a numerical code is developed for the extended model based on the equations, from which some relations about the modulated current and modulated energy are numerically given.     

A STUDY ON THE VIBRATION CHARACTERISTICS OF A LARGE SIZE KOREAN BELL

Structural elements which determine the vibration and sound properties of the Korean bell are reviewed. Vibration response characteristics under an impact excitation are investigated by the analysis and experiment. Numerical and experimental methods to predict and tune the vibration and sound properties of a large Korean bell (named the New Bosingak Bell) are introduced. Beat phenomenon, which is a very important sound property of the Korean bell, is analytically examined, and an experimental technique to enhance the beat property is proposed.     

Liquid oxide surface layers in metal combustion

We present a model that allows us to define the combustion concepts of ignition and extinction for those metals which are separated from an ambient oxidizing atmosphere by a liquid layer of their oxide during a stage of pre-ignition. To obtain the definition, the oxide layer is treated as an open system capable of multiple stationary states. Ignition and extinction are then associated with stationary states of the layer that are critical, i.e. which are located on the stability boundary. The model is used for an investigation of the particular cases of aluminium and boron which differ as to how the oxide layer is supported during the pre-ignition stage: at ignition, boron is known to be a solid whereas aluminium is in the liquid state. Both boron and aluminium have a promising potential for a number of applications in rocket propulsion. The model does not require the initial symmetry to be preserved and allows symmetry-breaking to occur, and thus goes beyond other current models of metal ignition and extinction. We demonstrate how this can be used to unravel some of the physical causes which have so far prevented the full realization of the potential of metals for propulsion.     

Adjoint symmetries and the generation of first integrals in non-holonomic mechanics

We discuss a general mechanism by which first integrals of mechanical systems, in particular systems that satisfy non-holonomic constraints, can be obtained from a systematic search for adjoint symmetries. Such an approach has already been used in our earlier work and is re-advocated here in the context of a recent analysis by Giachetta, in which first integrals are generated by vector fields which are not symmetries. Further advantages of our approach are: the fact that an essential projection operator associated to the constraints need not be related to some given fibre metric on the full evolution space, and the specific selection of a connection, which is naturally associated to this projection and the second-order dynamics on the constraint submanifold. The computational aspects of the method are illustrated by some simple examples.