Multi-channel scattering problems: an analytically solvable model

We have proposed a general method for finding an exact analytical solution for the multi-channel scattering problem in the presence of a delta function coupling. Our solution is quite general and is valid for any set of potentials, if the uncoupled diabatic potential has an exact solution. We have also discussed a few examples, where our method can easily be applied.     

Curve crossing problem with Gaussian type coupling: analytically solvable model

We give a general method for finding an exact analytical solution for the two state curve crossing problem. The solution requires the knowledge of the Green's function for the motion on the uncoupled potentials. We use the method to find the solution of the problem in the case of parabolic potentials coupled by Gaussian interaction. Our method is applied to this model system to calculate the effect of curve crossing on the electronic absorption spectrum and the resonance Raman excitation profile.     

Efimov effect in an analytically solvable model

The Efimov effect is demonstrated in a model consisting of two heavy particles and a light one when the light-heavy interaction leads to a zero-energy two-body bound state. The model is solved in the Born-Oppenheimer approximation with the light-heavy interaction taken to be a separable S-wave potential of Yamaguchi form. It is demonstrated that in the case of a- two-body zero-energy bound state the binding energy of the light particle in the two-center potential exactly yields an effective $\text{1}\text{r}{}^2$ potential for the relative motion of the heavies. If the light-heavy mass ratio is made small enough, infinitely many bound states (the Efimov effect) are obtained. The approach to this limit is studied and the nature of the potential for large scattering length is obtained. An upper bound for the number of bound states is calculated using a result of Bargmann and Calogero and Efimov's $\text{ln}\text{(}\text{a}\text{r}{}_0\text{)}$ result is found. We note that the long-range effect arises from the large extent of the bound state, the pair wave function being essentially $\text{exp}\text{(?}\text{r}\text{a}\text{)}$ when the scattering length a is large.     

Electromagnetically induced alpha-emission in an analytically solvable model

Alpha emission induced byγ-absorption or inelastic electron scattering on²⁰Ne is examined in an analytically solvable model. The exact results are compared with an approximation recently proposed by Fliessbach. The model is used as a testing case to decide which definition of alpha-spectroscopic amplitudes is appropriate. A method for handling center of mass effects is presented.     

Proton radioactivity with analytically solvable potential

The phenomenon of proton emission is treated as a process of asymmetric fission through a one-dimensional potential barrier developed due to combined effects of the Coulomb potential, centrifugal potential and various renormalization processes. The barrier is simulated to an asymmetric, smooth and analytically solvable potential with adjustable depth, shape and range. The half-lives of proton emitters in the mass range A = 105–171 have been calculated using exact expression for the transmission coefficients. Good agreement with the experimental data is obtained by the adjustment of just one parameter in all the cases.      

Level crossing in a two-photon Jaynes—Cummings model

In this paper,the energy spectrum of the two-photon Jaynes-Cummings model(TPJCM) is calculated exactly in the non-rotating wave approximation(non-RWA),and we study the level-crossing problem by means of fidelity.A narrow peak of the fidelity is observed at the level-crossing point,which does not appear at the avoided-crossing point.Therefore fidelity is perfectly suited for detecting the level-crossing point in the energy spectrum.     

Glass-glass transition and new dynamical singularity points in an analytically solvable p-spin glasslike model

We introduce and analytically study a generalized p-spin glasslike model that captures some of the main features of attractive glasses, recently found by mode coupling investigations, such as a glass-glass transition line and dynamical singularity points characterized by a logarithmic time dependence of the relaxation. The model also displays features not predicted by the mode coupling scenario that could further describe the attractive glasses behavior, such as aging effects with new dynamical singularity points ruled by logarithmic laws or the presence of a glass spinodal line.     

Photodissociation of iodocyclohexane at 266 and 277 nm: Energy partitioning and curve crossing analysis

The photodissociation dynamics of iodocyclohexane (C₆H₁₁I) at 266 and 277 nm has been investigated by ion velocity imaging technique. The velocity distributions, angular distributions and relative quantum yields are obtained for I (²P_3/2) (denoted I) and I (²P_1/2) (denoted I*) fragments. The energy partitioning shows that about 70% of the available energy goes into the internal excitation of the photofragments for both dissociation channels. From the angular distributions, we found the value of the anisotropy parameter β for I* at the corresponding excitation wavelength was less than that for I. Based on the measured angular distributions and relative quantum yields, the relative fractions of each excited state to the products are determined. The curve crossing probabilities between the ³Q₀ and ¹Q₁ states are determined 0.503 at 266 nm and 0.443 at 277 nm.     

The CA model for traffic-flow at the grade roundabout crossing

The cellular automaton model is suggested to describe the traffic-flow at the grade roundabout crossing. After the simulation with computer, the fundamental properties of this model have been revealed. Analysing this kind of road structure, this paper transforms the grade roundabout crossing with inner-roundabout-lane and outer-roundabout-lane into a configuration with many bottlenecks. Because of the self-organization, the traffic flow remains unblocked under a certain vehicle density. Some results of the simulation are close to the actual design parameter.     

An analytically solvable model of confined electrons in a magnetic field and its relation to Landau diamagnetism

Here we present analytic results for the Slater sum and the magnetic moment for arbitrary magnetic field strengths for an assembly of harmonically confined, but initially free, electrons. The relevance of the results to the generalized Landau diamagnetism of such confined electrons is emphasized.     

Novel solvable many-body problems

Novel classes of dynamical systems are introduced, including many-body problems characterized by nonlinear equations of motion of Newtonian type (“acceleration equals forces”) which determine the motion of points in the complex plane. These models are solvable, namely their con?guration at any time can be obtained from the initial data by algebraic operations, amounting to the determination of the zeros of a known time-dependent polynomial in the independent variable z. Some of these models are multiply periodic, isochronous or asymptotically isochronous; others display scattering phenomena.     

Investigation of privatization by level crossing approach

Privatization — a political as well as an economic policy — is generally defined as the transfer of a property or the responsibility for it from the public to the private sector. But privatization is not merely the transfer of the ownership and efficiency of the market should be considered. A successful privatization program induces better profitability and efficiency, higher output, more investment, etc. The main method of privatization is through introducing new stocks to the market to motivate competition. However, for a successful privatization the capability of a market for absorbing the new stock should also be considered. Without paying attention to this aspect, privatization through the introduction of new stocks may lead to reduced market efficiency. We study, based on the complexity theory and in particular the concept of Level Crossing, the effect of the stages of the development, activity, risk, and the waiting times for special events on the privatization.     

多通道同步数据采集器设计

设计了一种基于CPLD的多通道同步数据采集存储系统,能够实现多通道同步数据采集和数据存储。系统设计采用多通道数据的同步实时采集、存储以及坏块检测技术。多通道同步数据采集模块能够同时采集多路相关信号并准确存储,便于后续数据分析计算。系统可满足多通道同步数据采集存储要求,且性能安全可靠。     

便携式多通道数据采集系统设计

在EAST全超导托卡马克核聚变放电实验中,某些信号需要低功耗、便捷的进行独立同步采集与分析;而现有的大型采集系统并不能满足此需求,所以需要设计一套低功耗的、便携式的多通道数据采集系统来保障EAST实验的顺利进行。系统具有界面友好、性能稳定等诸多优点。在LabVIE软件编程环境中,系统能够实现对多达32路信号的同步采集、实时显示、数据存储、数据分析以及历史数据回放等功能。经过实验测试,该系统运行稳定可靠,完全满足EAST实验的数据采集需求。     

平面环行交叉路口交通流的研究

从道路结构出发,对具有内、外环道的平面环形交叉路口建立了具有多个道路瓶颈的元胞自动机模型,对平面环行交叉路口的交通流进行研究.计算机模拟结果表明,环形交叉路口的内环道中与入环车道接壤处是最容易发生阻塞的地方,内环道中车辆之间的非线性相互作用的效应随刹车概率的增大而增强,流量随之减小;而转向概率的增加有助于提高系统交通流量. 关键词： 平面环形交叉路口 元胞自动机模型 瓶颈 自组织     

Exact solution to the curve crossing problems of two linear diabatic potentials by transfer matrix method

In the present work we have reported a simple exact analytical solution to the curve crossing problem of two linear diabatic potentials by transfer matrix method. Our problem assumes the crossing of two linear diabatic potentials which are coupled to each other by an arbitrary coupling (in contrast to linear potentials in the vicinity of crossing points) and for numerical calculation purposes this arbitrary coupling is taken as Gaussian coupling which is further expressed as a collection of Dirac delta functions. Further we calculated the transition probability from one diabatic potential to another by the use of this method.     

基于FPGA的多通道超声波测距系统设计

超声波测距是一种非接触式连续测量方法,具有电路简单、测量精度高等优点。传统的测距系统多采用单片机实现,无法满足现代测距实时性、立体化、多向性的要求;因此设计了一种基于FPGA的多通道超声波测距系统,所有通道同时进行检测与处理,系统具有较高的扩展性。硬件部分采用US_100超声波传感器实现了超声信号的发射与接收,采用京微雅格C192芯片对回波信号进行检测和处理,实现了从2厘米到4米的距离的精确测量,测量结果送入LCD12864进行显示。软件设计采用Verilog HDL语言在Primace编辑环境下进行开发,在Modelsim软件下进行仿真,并通过HR3开发板验证了全部设计功能。测试结果表明：该测距系统运行稳定可靠,测量精度高。