Formalism of rotating-wave approximation in high-spin system with quadrupole interaction

We investigate the rotating wave approximation applied in the high-spin quantum system driven by a linearly polarized alternating magnetic field in the presence of quadrupole interactions.The conventional way to apply the rotating wave approximation in a driven high-spin system is to assume the dynamics being restricted in the reduced Hilbert space.However,when the driving strength is relatively strong or the driving is off resonant,the leakage from the target resonance subspace cannot be neglected for a multi-level quantum system.We propose the correct formalism to apply the rotating wave approximation in the full Hilbert space by taking this leakage into account.By estimating the operator fidelity of the time propagator,our formalism applied in the full Hilbert space unambiguously manifests great advantages over the conventional method applied in the reduced Hilbert space.

Zero-Magnetic-Field Spin Splitting of Polaron＇s Ground State Energy Induced by Rashba Spin-Orbit Interaction

We study theoretically the ground state energy of a polaron near the interface of a polar-polar semiconductor by considering the Rashba spin-orbit （SO） coupling with the Lee-Low-Pines intermediate coupling method. Our numerical results show that the Rashba SO interaction originating from the inversion asymmetry in the heterostructure splits the ground state energy of the polaron. The electron area/density and vector dependence of the ratio of the SO interaction to the total ground state energy or other energy composition are obvious. One can see that even without any external magnetic field, the ground state energy can be split by the Rashba SO interaction, and this split is not a single but a complex one. Since the presents of the phonons, whose energy gives negative contribution to the polaron＇s, the spin-splitting states of the polaron are more stable than electron＇s.

An Approach to Continuous Approximation of Pareto Front Using Geometric Support Vector Regression for Multi-objective Optimization of Fermentation Process

The approaches to discrete approximation of Pareto front using multi-objective evolutionary algorithms have the problems of heavy computation burden, long running time and missing Pareto optimal points. In order to overcome these problems, an approach to continuous approximation of Pareto front using geometric support vector regression is presented. The regression model of the small size approximate discrete Pareto front is constructed by geometric support vector regression modeling and is described as the approximate continuous Pareto front. In the process of geometric support vector regression modeling, considering the distribution characteristic of Pareto optimal points, the separable augmented training sample sets are constructed by shifting original training sample points along multiple coordinated axes. Besides, an interactive decision-making(DM)procedure, in which the continuous approximation of Pareto front and decision-making is performed interactively, is designed for improving the accuracy of the preferred Pareto optimal point. The correctness of the continuous approximation of Pareto front is demonstrated with a typical multi-objective optimization problem. In addition,combined with the interactive decision-making procedure, the continuous approximation of Pareto front is applied in the multi-objective optimization for an industrial fed-batch yeast fermentation process. The experimental results show that the generated approximate continuous Pareto front has good accuracy and completeness. Compared with the multi-objective evolutionary algorithm with large size population, a more accurate preferred Pareto optimal point can be obtained from the approximate continuous Pareto front with less computation and shorter running time. The operation strategy corresponding to the final preferred Pareto optimal point generated by the interactive DM procedure can improve the production indexes of the fermentation process effectively.

Dynamic Response of Fluid-Single Leg Gravity Platform-Soil Interaction System

An approximate method is presented to investigate the earthquake response of the fluid-single leg (shortened for S. L.) gravity platform-soil interaction system. By assuming a suitable form of the velocity potential of the radiation waves and by using the motion equation and the boundary conditions, the unknown coefficients can be obtained. Thereafter the function of frequency for the interaction system may also be obtained. In this paper, the difference of the system dynamic response between rigid foundation is analyzed and the influences of the various foundation geometric dimension and the various water-depth on the hydrodynamic loading and dynamic response of the system is illustrated.

The Effect of Hyperon-Hyperon Interaction on Neutron Stars

The equations ofstate of the neutron star matter are calculated in the relativistic mean-field approximation witl different hyperon coupling constants. The properties of neutron stars are studied by solving the OppenheimerVolkoff equation. It manifests the properties of neutron stars - change explicitly as different hyperon coupling constants are concerned.

Spin-Spin Interactions in Gauge Theory of Gravity, Violation of Weak Equivalence Principle and New Classical Test of General Relativity

For a long time, it has been generally believed that spin-spin interactions can only exist in a theory where Lorentz symmetry is gauged, and a theory with spin-spin interactions is not perturbatively renormalizable. But this is not true. By studying the motion of a spinning particle in gravitational field, it is found that there exist spin-spin interactions in gauge theory of gravity. Its mechanism is that a spinning particle will generate gravitomagnetic field in space-time, and this gravitomagnetic field will interact with the spin of another particle, which will cause spin-spin interactions. So, spin-spin interactions are transmitted by gravitational field. The form of spin-spin interactions in post Newtonian approximations is deduced. This result can also be deduced from the Papapetrou equation. This kind of interaction will not affect the renormalizability of the theory. The spin-spin interactions will violate the weak equivalence principle, and the violation effects are detectable. An experiment is proposed to detect the effects of the violation of the weak equivalence principle.

MEAN-FIELD LIMIT OF BOSE-EINSTEIN CONDENSATES WITH ATTRACTIVE INTERACTIONS IN R^2

Starting with the many-body SchrSdinger Hamiltonian in R2, we prove that the ground state energy of a two-dimensional interacting Bose gas with the pairwise attractive interaction approaches to the minimum of the Gross-Pitaevskii energy functional in the mean- field regime, as the particle number N → ∞ and however the scattering length → 0. By fixing N｜k｜, this leads to the mean-field approximation of Bose-Einstein condensates with attractive interactions in R^2.

Relativistic symmetries with the trigonometric Pschl-Teller potential plus Coulomb-like tensor interaction

The Dirac equation is solved to obtain its approximate bound states for a spin-1/2 particle in the presence of trigonometric Poeschl-Teller （tPT） potential including a Coulomb-like tensor interaction with arbitrary spin-orbit quantum number κ using an approximation scheme to substitute the centrifugal terms κ（κ± i 1）r^-2. In view of spin and pseudo-spin （p-spin） symmetries, the relativistic energy eigenvalues and the corresponding two-component wave functions of a particle moving in the field of attractive and repulsive tPT potentials are obtained using the asymptotic iteration method （AIM）. We present numerical results in the absence and presence of tensor coupling A and for various values of spin and p-spin constants and quantum numbers n and κ. The non-relativistic limit is also obtained.

Post-collision interactions and the polarization effect in (e, 2e) collisions of helium

A modified distorted-wave Born approximation （DWBA） method is used to calculate the triple differential cross sections （TDCSs） in a coplanar asymmetric geometry for the electron impact single ionization of a He （ls2） atom at intermediate and lower energies. The post-collision interaction and the polarization effect in （e, 2e） collisions of helium are considered in the calculations. The polarization potentials from the damping method and density functional theory （DFT） are compared. Theoretical results are compared with the recent experimental data.

SOLITARY WAVES IN STRATIFIED FLUIDS AND THEIR INTERACTION

A systematic procedure is proposed for obtaining solutions for soli- tary waves in stratified fluids. The stratification of the fluid is assumed to be expo- nential or linear. Its comparison with existing results for an exponentially stratified fluid shows agreement, and it is found that for the odd series of solutions the direc- tion of displacement of the streamlines from their asymptotic levels is reversed when the stratification is changed from exponential to linear. Finally the interaction of solitary waves is considered, and the Korteweg-de Vries equation and the Boussinesq equation are derived. Thus the known solutions of these equations can be rehed upon to provide the answers to the interaction problem.

Electron-Phonon Interaction in an Annular Quantum Dot

The confined longitudinal-optical （LO） phonon and surface-optical （SO） phonon modes of a free-standing annular cylindrical quantum dot are derived within the framework of dielectric continuum approximation. It is found that there exist two types of SO phonon modes： top SO （TSO） mode and side SO（SSO） mode in a cylindrical quantum annulus. Numerical calculation on CdS annulus system has been performed. Results reveal that the two different solutions of SSO mode distribute mainly at the inner or outer surfaces of the annulus. The dispersion relations and the coupling intensions of phonons in a quantum annulus are compared with those in a cylindrical quantum dot. It is found that the dispersion relations of the two different structures are similar, but the coupling intension of the phonon-electron interaction in quantum annulus is larger than that in quantum dot. The Hamiltonians describing the free phonon modes and their interactions with electrons in the system are also derived.

Quantum-Chemical Estimating Interaction of <i>sp²</i>-Carbon Nanoclusters with PE and PP Oligomers

The purpose of this work was to examine the interaction of graphene-like nanoclusters with fragments of polymers of the same nature, but somewhat different structure, for example, polyethylene (PE) and polypropylene (PP) by means of quantum chemistry. By method of density functional theory with the exchange-correlation functional B3LYP, the basis set 6 - 31 G (d, p) and the Grimme’s dispersion correction, the energy values have been calculated of interaction between nanocarbon fragments and oligomers of PE and PP, the most probable structures of their intermolecular complexes being optimized. A graphene-like plane of 40 carbon atoms and 16 atoms of hydrogen was chosen as a model for the surface of the graphene and carbon nanotubes (CNT). In order to take into account the dimensional effect of the surface of the nanotube fragment model on the interaction energy, in addition to the above described, two larger models were used, with the general formula C54H18 and C96N24. It has been found that the interaction energy of nanocarbon fragment with an oligomer of PP is greater, compared with PE, which is consistent with the experimental data on melting temperatures of pure polymers and nanotube-polymer composites. The polymer with a surface of nanocarbon fragment forms an intermolecular complex not bound covalently and retained by intermolecular dispersion forces. Oligomers of polymeric matters and carbon surfaces in formed nanocomplex are placed closer to each other than separate polymeric links between them.

Assessment of Advanced xDH@B3LYP Methods in Describing Various Potential Energy Curves Driven byπ-π,CH/π,and SH/πNon-Bonded Interactions

Accurate description of potential energy curves driven by nonbonded interactions remains a great challenge for pure density functional approximations(DFAs).It is because the Rdecay behavior of dispersion cannot be intrinsically captured by the(semi)-local ingredients and the exact-exchange used in the popular hybrid DFAs.Overemphasizing the accuracy on the equilibrium region for the functional construction would likely deteriorate the overall performance on the other regions of potential energy surfaces.In consequence,the empirical dispersion correction becomes the standard component in DFAs to treat the non-bonded interactions.In this Letter,we demonstrate that without the use of empirical dispersion correction,doubly hybrid approximations,in particular two recently proposed rev XYG3 and XYG7 functionals,hold the promise to have a balanced description of non-bonded interactions on the whole potential energy curves for several prototypes ofπ-π,CH/π,and SH/πinteractions.The error of rev XYG3 and XYG7 for non-bonded interactions is around 0.1 kcal/mol,and their potential energy curves almost coincide with the accurate CCSD(T)/CBS curves.

The Primordial Principle of Self-Interaction

The Standard Model of Particle Physics treats four fields—the gravitational, electromagnetic, weak and strong fields. These fields are assumed to converge to a single field at the big bang, but the theory has failed to produce this convergence. Our theory proposes one primordial field and analyzes the evolution of this field. The key assumption is that only the primordial field exists—if any change is to occur, it must be based upon self-interaction, as there is nothing other than the field itself to interact with. This can be formalized as the Principle of Self-interaction and the consequences explored. I show that this leads to the linearized Einstein field equations and discuss the key ontological implications of the theory.

Range of applicability of real mode superposition approximation method for seismic response calculation of non-classically damped industrial buildings

An industrial building is a non-classically damped system due to the different damping properties of the primary structure and equipment.The objective of this paper is to quantify the range of applicability of the real model superposition approximation method to the seismic response calculation of industrial buildings.The analysis using lumped mass-and-shear spring models indicates that for the equipment-to-structure frequency ratiosγf>1.1 orγf<0.9,the non-classical damping effect is limited,and the real mode superposition approximation method provides accurate estimates.For 0.9<γf<1.1,the system may have a pair of closely spaced frequency modes,and the non-zero off-diagonal damping terms have a non-negligible effect on the damping ratios and mode shape vectors of these modes.For 0.9<γf<1.1 and the equipment-to-structure mass ratiosγm<0.07,the real mode superposition approximation method results in large errors,while the approximation method can provide an accurate estimation for 0.9<γf<1.1 andγm>0.07.Furthermore,extensive parametric analyses are conducted,where both steel structures and reinforced concrete structures with equipment with various damping ratios are considered.Finally,the finite element analysis of a five-story industrial building is adopted to validate the proposed range of applicability.

On the van der Waals interaction of carbon nanotubes as electromechanical nanothermometers

Electromechanical carbon nanothermometers are devices that work based on the interactions and relative mo- tions of double-walled carbon nanotubes （DWCNTs）. In this paper, the mechanics of carbon nanotubes （CNTs） con- stituting two welt-known configurations for nanothermome- ter, namely shuttle configuration and telescope configuration are fully investigated. Lennard-Jones （LJ） potential func- tion along with the continuum approximation is employed to investigate van der Waals （vdW） interactions between the in- teracting entities. Accordingly, semi-analytical expressions in terms of single integrals are obtained for vdW interactions. Acceptance condition and suction energy are studied for the shuttle configuration. In addition, a universal potential en- ergy is presented for the shuttle configuration consisting of two finite CNTs. Also, for the telescope configuration, ex- tensive studies are performed on the distributions of potential energy and interaction force for various radii and lengths of CNTs. It is found that these geometrical parameters have a considerable effect on the potential energy.

基于储层砂岩孔隙结构的地震岩石物理模型

在实验室内对新疆车排子地区春光油田沙湾组储层砂岩样品进行了系统地震岩石物理实验,在确定储层砂岩中不同孔隙类型组成条件下,基于非接触模型综合考虑储层砂岩孔隙度以及孔隙形状对于干燥岩石骨架弹性性质的影响,并利用实验结果对模型参数进行标定进而建立表征目标储层岩石骨架地震弹性性质的岩石物理模型,模型结果与实验结果吻合良好。依据实验及模型结果,利用喷射流作用模型替代传统Gassmann方程进行流体替换,同样能够较好地对超声频率实验结果进行解释。

LLM-105的分子间相互作用和热力学性质

应用第一性原理可以计算含能材料0 K下的结构和物理性质,但温度效应的缺失通常会导致计算数据与实验结果产生偏差.同时,与温度相关的热力学参数是含能材料在宏观和介观尺度下建模的关键输入.为此,本文以高能低感炸药1-氧-2,6-二氨基-3,5-二硝基吡嗪(LLM-105)为研究体系,基于准简谐近似,采用色散修正的密度泛函理论研究温度加载下LLM-105的分子间相互作用和热力学性质.晶格参数和热膨胀系数的演化表明LLM-105分子间相互作用具有强烈的各向异性,其中b轴方向(分子层间)的膨胀率远高于ac平面(分子层内).Hirshfeld表面及其指纹图分析进一步证实LLM-105的分子间相互作用主要取决于O···H构成的氢键.结合Mulliken布居数和结构分析,温度加载下氢键相互作用的变化可诱发硝基旋转,并使得C—NO_(2)键的强度明显减弱,为高温分解反应的触发键提供了理论依据.此外,本文计算了等容和等压条件下的热容、熵以及等温和绝热条件下的体模量等基础热力学参数.其中绝热条件下的体模量与实验值吻合,同时体模量随温度的演化反映了LLM-105在温度加载下的软化行为.上述理论研究可用于构建含能材料在介观和宏观尺度下的模型,也为测量原子分子水平下的热力学性质提供了重要的参考价值.

基于多点触摸的协作机器人近似最优人机交互控制算法

针对人机交互系统中现有方法无法准确捕捉用户的操作意图,动态环境适应性较差,导致人机交互精准性不佳的问题,为提高协作机器人在作业过程中的人机交互精准性,提出一种基于多点触摸的近似最优人机交互控制方法.首先,基于人机交互的多点触摸动作匹配,建立交互手势动作序列图像传导函数,提取交互手势特征,分析图像相似度特征分量,根据像素值得出动作判断的模糊度集合,以实现对多点触摸动作的匹配,从而准确捕捉用户的操作意图;其次,考虑机器人运动条件和摩擦力因素,建立摩擦力近似最优约束方程,以保证机器人移动交互的平衡性和稳定性;最后,获取交互手臂的期望响应,利用Lagrange方程描述多点触摸条件下的人机交互状态,建立交互动作动力学方程,引入交互控制变量,利用自适应模糊控制体系输出近似最优控制结果,以提高动态环境适应性,并根据实际情况调整控制策略,更好地满足人机交互的需求.实验结果表明,该方法能有效完成人机交互控制,识别率高达94%以上,控制时延误差较小,为0.03×10^(-3)s,且迭代收敛速度快,具有更好的控制效果.

基于隔离非线性法-黏弹性人工边界的结构高效抗震分析方法

黏弹性人工边界是解决土-结构动力相互作用问题的有效手段之一,但其在分析过程中通常需要进行大量的非线性动力时程计算,效率较低。建立采用黏弹性人工边界求解土-结构动力相互作用问题控制方程求解的高效计算方法,为此,引入隔离非线性法高效求解思想,构造基于隔离非线性法-黏弹性人工边界的非线性土-结构动力相互作用分析模型,推导的动力控制方程在形式上与固定边界的隔离非线性动力控制方程基本一致,仅需将黏弹性人工边界的弹簧-阻尼器元件的刚度直接集成到近场土-结构模型的初始刚度矩阵与阻尼矩阵上即可。此外,结合Woodbury公式与组合近似法提出了改进Woodbury近似法,该改进方法能同时降低控制方程求解的时间复杂度与空间复杂度,实现了黏弹性人工边界求解土-结构动力相互作用问题动力控制方程的高效求解。研究方法同时保留了黏弹性人工边界与隔离非线性法的优点,数值算例验证了所提方法的正确性与高效性。