Crossed Beam Experiment on the Validity of Born-Oppenheimer Approximation in Cl(2P)+D2→DCl+D Reaction

The reaction of chlorine atom Cl(2P)(Cl(2P3/2)and Cl^*(2P1/2))with D2 was investigated at collision energy from 4.5 kcal/mol to 6.5 kcal/mol with a high-resolution crossed molecular beam apparatus using the technique of D-atom Rydberg tagging detection.The contribution from the spin-orbit excited reaction Cl^*(2P1/2)+D2,which is prohibited by Born-Oppenheimer(BO)approximation,was observed.Collision-energy dependence of differential cross sections(DCSs)near the backward scattering direction was measured.The BOforbidden reaction Cl^*+D2 was found to be dominant at lower collision energy.As collision energy increases,reactivity of BO-allowed reaction Cl+D2 increases much faster than that of BO-forbidden reaction and becomes dominant at higher collision energy.Our experiment indicates that the additional energy of spin-orbit excitation in Cl^*facilitates BO-forbidden reaction to pass through the barrier at lower collision energy,while BO approximation is still valid at collision energy near and above the reaction barrier.This tendency of reactivity of Cl/Cl^*+D2 is similar to the isotopic reaction of Cl/Cl^*+H2.

The Born-Oppenheimer Approximation Revisited

We present an improved Born-Oppenheimer method for the treatment of molecules. Our development is based on taking into account a portion of the kinetic energy which was inadvertently omitted by Born and Oppenheimer. Our theory replaces the set of standard atom-atom potentials by an evolution operator. In particular, in contrast to the traditional Born-Oppenheimer method our amended basis describes the so-called Wannier phenomenon which deforms potential surfaces, and traps one or more threshold electrons into an unstable equilibrium. Within our framework that trapping manifests itself as a Fresnel distribution. Finally we discover a π/2 phase jump in the evolution operator caused by the diffraction of a two-electron wave from a potential ridge.

Geometric Phase Approach to Dielectricity Based on the Born-Oppenheimer Approximation

Macroscopic polarization differences in crystal dielectrics have been accurately treated by certain authors using the geometric phase approach.However,in their treatments the explicit meaning of the slowly varying parameters was not explored.In this paper we restudy the problem under the Born-Oppenheimer approximation.It turns out that the coordinates of nuclei in the system can be taken as the slowly varying parameters.In addition,our treatment is no longer restricted to the case of null electric held.

Study of the structures of four-quark states in terms of the Born-Oppenheimer approximation

In this work, we use the Born-Oppenheimer approximation, where the potential between atoms can be approximated as a function of distance between the two nuclei, to study the four-quark bound states. By this approximation, Heitler and London calculated the spectrum of the hydrogen molecule, which includes two protons （heavy） and two electrons （light）. Cenerally, the observed exotic mesons Zb（10610）, ZD（10650）, Zc（3900） and Zc（4020） （Zc（4025）） may be molecular states made of two physical mesons and/or diquark-anti-diquark structures. Analogous to the Heitler-London method for calculating the mass of the hydrogen molecule, we investigate whether there exist energy minima for these two structures. Contrary to the hydrogen molecule case where only the spin-triplet possesses an energy minimum, there exist minima for both of these states. This implies that both molecule and tetraquark states can be stable objects. Since they have the same quantum numbers, however, the two states may mix to result in the physical states. A consequence would be that partner exotic states co-existing with ZD（10610）, Zb（]0650）, Zc（3900） and Zc（4020） （Zc（4025）） are predicted and should be experimentally observed.

Born-Oppenheimer approximation of quantized cavity-atom system and localization control of atomic tunneling

The generalized Born-Oppenheimer approximation theory is applied to the localization control of state tunneling of a two-level atom in a cavity field with single mode. The nonadiabatic effect of tunneling of atomic chiral states in coherent cavity field is analyzed quantitatively and the condition for realizing localization is given strictly. Besides, the influence of variation in temperature on tunneling of atomic state is discussed.

Evolutionary Safe Padé Approximation Scheme for Dynamical Study of Nonlinear Cervical Human Papilloma Virus Infection Model

This study proposes a structure-preserving evolutionary framework to find a semi-analytical approximate solution for a nonlinear cervical cancer epidemic(CCE)model.The underlying CCE model lacks a closed-form exact solution.Numerical solutions obtained through traditional finite difference schemes do not ensure the preservation of the model’s necessary properties,such as positivity,boundedness,and feasibility.Therefore,the development of structure-preserving semi-analytical approaches is always necessary.This research introduces an intelligently supervised computational paradigm to solve the underlying CCE model’s physical properties by formulating an equivalent unconstrained optimization problem.Singularity-free safe Padérational functions approximate the mathematical shape of state variables,while the model’s physical requirements are treated as problem constraints.The primary model of the governing differential equations is imposed to minimize the error between approximate solutions.An evolutionary algorithm,the Genetic Algorithm with Multi-Parent Crossover(GA-MPC),executes the optimization task.The resulting method is the Evolutionary Safe PadéApproximation(ESPA)scheme.The proof of unconditional convergence of the ESPA scheme on the CCE model is supported by numerical simulations.The performance of the ESPA scheme on the CCE model is thoroughly investigated by considering various orders of non-singular Padéapproximants.

The Degree of Approximation by(E,q)(C,α,β)Means in Orlicz Spaces

In this paper,we study the trigonometric approximation problems of functions which belong to the Lipαclass,the Lip(ξ(t))class,and the W(L_(M)^(*);ξ(t))class in Orlicz spaces by using the tools Hölder inequality in Orlicz spaces,the second mean value theorem for integrals,and(E,q)(C,α,β)means etc.At the same time,we give the corresponding degree of approximation.

Determining Hubbard U of VO_(2) by the quasi-harmonic approximation

Vanadium dioxide VO_(2) is a strongly correlated material that undergoes a metal-to-insulator transition around 340 K.In order to describe the electron correlation effects in VO_(2), the DFT+U method is commonly employed in calculations.However, the choice of the Hubbard U parameter has been a subject of debate and its value has been reported over a wide range. In this paper, taking focus on the phase transition behavior of VO_(2), the Hubbard U parameter for vanadium oxide is determined by using the quasi-harmonic approximation(QHA). First-principles calculations demonstrate that the phase transition temperature can be modulated by varying the U values. The phase transition temperature can be well reproduced by the calculations using the Perdew–Burke–Ernzerhof functional combined with the U parameter of 1.5eV. Additionally,the calculated band structure, insulating or metallic properties, and phonon dispersion with this U value are in line with experimental observations. By employing the QHA to determine the Hubbard U parameter, this study provides valuable insights into the phase transition behavior of VO_(2). The findings highlight the importance of electron correlation effects in accurately describing the properties of this material. The agreement between the calculated results and experimental observations further validates the chosen U value and supports the use of the DFT+U method in studying VO_(2).

Saddlepoint Approximation Method in Reliability Analysis:A Review

The escalating need for reliability analysis(RA)and reliability-based design optimization(RBDO)within engineering challenges has prompted the advancement of saddlepoint approximationmethods(SAM)tailored for such problems.This article offers a detailed overview of the general SAM and summarizes the method characteristics first.Subsequently,recent enhancements in the SAM theoretical framework are assessed.Notably,the mean value first-order saddlepoint approximation(MVFOSA)bears resemblance to the conceptual framework of the mean value second-order saddlepoint approximation(MVSOSA);the latter serves as an auxiliary approach to the former.Their distinction is rooted in the varying expansion orders of the performance function as implemented through the Taylor method.Both the saddlepoint approximation and third-moment(SATM)and saddlepoint approximation and fourth-moment(SAFM)strategies model the cumulant generating function(CGF)by leveraging the initial random moments of the function.Although their optimal application domains diverge,each method consistently ensures superior relative precision,enhanced efficiency,and sustained stability.Every method elucidated is exemplified through pertinent RA or RBDO scenarios.By juxtaposing them against alternative strategies,the efficacy of these methods becomes evident.The outcomes proffered are subsequently employed as a foundation for contemplating prospective theoretical and practical research endeavors concerning SAMs.The main purpose and value of this article is to review the SAM and reliability-related issues,which can provide some reference and inspiration for future research scholars in this field.

Gamma Approximation Based Multi-Antenna Covert Communication Detection

Covert communication technology makes wireless communication more secure,but it also provides more opportunities for illegal users to transmit harmful information.In order to detect the illegal covert communication of the lawbreakers in real time for subsequent processing,this paper proposes a Gamma approximation-based detection method for multi-antenna covert communication systems.Specifically,the Gamma approximation property is used to calculate the miss detection rate and false alarm rate of the monitor firstly.Then the optimization problem to minimize the sum of the missed detection rate and the false alarm rate is proposed.The optimal detection threshold and the minimum error detection probability are solved according to the properties of the Lambert W function.Finally,simulation results are given to demonstrate the effectiveness of the proposed method.

Relaxed Stability Criteria for Time-Delay Systems:A Novel Quadratic Function Convex Approximation Approach

This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.

An Overview of Sequential Approximation in Topology Optimization of Continuum Structure

This paper offers an extensive overview of the utilization of sequential approximate optimization approaches in the context of numerically simulated large-scale continuum structures.These structures,commonly encountered in engineering applications,often involve complex objective and constraint functions that cannot be readily expressed as explicit functions of the design variables.As a result,sequential approximation techniques have emerged as the preferred strategy for addressing a wide array of topology optimization challenges.Over the past several decades,topology optimization methods have been advanced remarkably and successfully applied to solve engineering problems incorporating diverse physical backgrounds.In comparison to the large-scale equation solution,sensitivity analysis,graphics post-processing,etc.,the progress of the sequential approximation functions and their corresponding optimizersmake sluggish progress.Researchers,particularly novices,pay special attention to their difficulties with a particular problem.Thus,this paper provides an overview of sequential approximation functions,related literature on topology optimization methods,and their applications.Starting from optimality criteria and sequential linear programming,the other sequential approximate optimizations are introduced by employing Taylor expansion and intervening variables.In addition,recent advancements have led to the emergence of approaches such as Augmented Lagrange,sequential approximate integer,and non-gradient approximation are also introduced.By highlighting real-world applications and case studies,the paper not only demonstrates the practical relevance of these methods but also underscores the need for continued exploration in this area.Furthermore,to provide a comprehensive overview,this paper offers several novel developments that aim to illuminate potential directions for future research.

Nonlinear Filtering With Sample-Based Approximation Under Constrained Communication:Progress, Insights and Trends

The nonlinear filtering problem has enduringly been an active research topic in both academia and industry due to its ever-growing theoretical importance and practical significance.The main objective of nonlinear filtering is to infer the states of a nonlinear dynamical system of interest based on the available noisy measurements. In recent years, the advance of network communication technology has not only popularized the networked systems with apparent advantages in terms of installation,cost and maintenance, but also brought about a series of challenges to the design of nonlinear filtering algorithms, among which the communication constraint has been recognized as a dominating concern. In this context, a great number of investigations have been launched towards the networked nonlinear filtering problem with communication constraints, and many samplebased nonlinear filters have been developed to deal with the highly nonlinear and/or non-Gaussian scenarios. The aim of this paper is to provide a timely survey about the recent advances on the sample-based networked nonlinear filtering problem from the perspective of communication constraints. More specifically, we first review three important families of sample-based filtering methods known as the unscented Kalman filter, particle filter,and maximum correntropy filter. Then, the latest developments are surveyed with stress on the topics regarding incomplete/imperfect information, limited resources and cyber security.Finally, several challenges and open problems are highlighted to shed some lights on the possible trends of future research in this realm.

Design of a 14-Bit 1 MS/s Successive Approximation Analog-to-Digital Converter

A 14-bit successive approximation analog-to-digital converter (SAR ADC) with capacitive calibration has been designed based on the SMIC. 18 μm CMOS process. The overall architecture is in fully differential form to eliminate the effect caused by common mode noise. Meanwhile, the digital-to-analog converter (DAC) is a two-stage structure, which can greatly reduce the area of the capacitor array compared with the traditional DAC structure. The capacitance calibration module is mainly divided into the mismatch voltage acquisition phase and the calibration code backfill phase, which effectively reduces the impact of the DAC mismatch on the accuracy of the SAR ADC. The design of this paper is based on cadence platform simulation verification, simulation results show that when the sampling rate is 1 MS/s, the power supply voltage is 5 V and the reference voltage is 4.096 V, the effective number of bits (ENOB) of the ADC is 13.49 bit, and the signal-to-noise ratio (SNR) is 83.3 dB.

Wave equation tomographic velocity inversion method based on the Born/Rytov approximation

This paper discusses Born/Rytov approximation tomographic velocity inversion methods constrained by the Fresnel zone. Calculations of the sensitivity kernel function and traveltime residuals are critical in tomographic velocity inversion. Based on the Bom/Rytov approximation of the frequency-domain wave equation, we derive the traveltime sensitivity kemels of the wave equation on the band-limited wave field and simultaneously obtain the traveltime residuals based on the Rytov approximation. In contrast to single-ray tomography, the modified velocity inversion method improves the inversion stability. Tests of the near- surface velocity model and field data prove that the proposed method has higher accuracy and Computational efficiency than ray theory tomography and full waveform inversion methods.

APPROXIMATION TECHNIQUES FOR APPLICATION OF GENETIC ALGORITHMS TO STRUCTURAL OPTIMIZATION

Although the genetic algorithm (GA) has very powerful robustness and fitness, it needs a large size of population and a large number of iterations to reach the optimum result. Especially when GA is used in complex structural optimization problems, if the structural reanalysis technique is not adopted, the more the number of finite element analysis (FEA) is, the more the consuming time is. In the conventional structural optimization the number of FEA can be reduced by the structural reanalysis technique based on the approximation techniques and sensitivity analysis. With these techniques, this paper provides a new approximation model-segment approximation model, adopted for the GA application. This segment approximation model can decrease the number of FEA and increase the convergence rate of GA. So it can apparently decrease the computation time of GA. Two examples demonstrate the availability of the new segment approximation model.

Strong Uniqueness of Best Approximations from RS-sets in Banach Spaces

The problem of strong uniqueness of best approximation from an RS set in a Banach space is considered. For a fixed RS set G and an element x∈X , we proved that the best approximation g * to x from G is strongly unique.

The Order of Approximation by Complex Rational Type Interpolating Operators at Fejer's Points

In this paper, supose Γ be a boundary of a Jordan domain D and Γ satisfied Альпер condition, the order that rational type interpolating operators at Fejer's points of f(z)∈C(Γ) converge to f(z) in the sense of uniformly convergence is obtained.

Dynamics of Rabi model under second-order Born Oppenheimer approximation

We apply the second-order Born-Oppenheimer （BO） approximation to investigate the dynamics of the Rabi model, which describes the interaction between a two-level system and a single bosonic mode beyond the rotating wave approxi- mation. By comparing with the numerical results, we find that our approach works well when the frequency of the two-level system is much smaller than that of the bosonic mode.

非Born-Oppenheimer近似一对双原子分子振动光谱的修正

为提高Born Oppenheimer(BO)近似的精确度 ,修正BO近似所得到的令人不太满意的结果 ,此文在电子与原子核之间引入一个位相差 ,并利用小参数微扰法推导出了双原子分子核振动的波函数及红外能谱的计算公式 。