Spectral Properties of Effective Dynamics from Conditional Expectations

The reduction of high-dimensional systems to effective models on a smaller set of variables is an essential task in many areas of science. For stochastic dynamics governed by diffusion processes, a general procedure to find effective equations is the conditioning approach. In this paper, we are interested in the spectrum of the generator of the resulting effective dynamics, and how it compares to the spectrum of the full generator. We prove a new relative error bound in terms of the eigenfunction approximation error for reversible systems. We also present numerical examples indicating that, if Kramers–Moyal (KM) type approximations are used to compute the spectrum of the reduced generator, it seems largely insensitive to the time window used for the KM estimators. We analyze the implications of these observations for systems driven by underdamped Langevin dynamics, and show how meaningful effective dynamics can be defined in this setting.     

Generating Multidirectional Variable Hidden Attractors via Newly Commensurate and Incommensurate Non-Equilibrium Fractional-Order Chaotic Systems

This article investigates a non-equilibrium chaotic system in view of commensurate and incommensurate fractional orders and with only one signum function. By varying some values of the fractional-order derivative together with some parameter values of the proposed system, different dynamical behaviors of the system are explored and discussed via several numerical simulations. This system displays complex hidden dynamics such as inversion property, chaotic bursting oscillation, multistabilty, and coexisting attractors. Besides, by means of adapting certain controlled constants, it is shown that this system possesses a three-variable offset boosting system. In conformity with the performed simulations, it also turns out that the resultant hidden attractors can be distributively ordered in a grid of three dimensions, a lattice of two dimensions, a line of one dimension, and even arbitrariness in the phase space. Through considering the Caputo fractional-order operator in all performed simulations, phase portraits in two- and three-dimensional projections, Lyapunov exponents, and the bifurcation diagrams are numerically reported in this work as beneficial exit results.     

Determining Liquid Structure from the Tail of the Direct Correlation Function

In important early work, Stell showed that one can determine the pair correlation function h(r) of the hard-sphere fluid for all distances r by specifying only the tail of the direct correlation function c(r) at separations greater than the hard-core diameter. We extend this idea in a very natural way to potentials with a soft repulsive core of finite extent and a weaker and longer ranged tail. We introduce a new continuous function T(r) which reduces exactly to the tail of c(r) outside the (soft) core region and show that both h(r) and c(r) depend only on the out projection of T(r): i.e., the product of the Boltzmann factor of the repulsive core potential times T(r). Standard integral equation closures can thus be reinterpreted and assessed in terms of their predictions for the tail of c(r) and simple approximations for its form suggest new closures. A new and very efficient variational method is proposed for solving the Ornstein–Zernike equation given an approximation for the tail of c. Initial applications of these ideas to the Lennard-Jones and the hard-core Yukawa fluid are discussed.     

Full-wave modeling of piezoelectric transducers for SAW acousto-optical interactions

In this paper we present an accurate and efficient numerical method for a rigorous full-wave analysis of interdigital transducers (IDT) for the excitation of surface acoustic waves on the piezoelectric substrate of acousto-optical devices. The problem is formulated in terms of an integral equation that is solved by the method of moments. The transducer input admittance and the power coupling factors to both surface and bulk waves are computed. Numerical results for some configurations of X-Y LiNbO₃ IDT for acousto-optic applications are in very good agreement with measured data. It is pointed out that bulk wave excitation may be a serious limitation in the design of efficient, wide band transducers for acousto-optical devices.     

ENDOR spectroscopic and molecular orbital study of the dynamical properties of the side chain in radical anions of ubiquinones Q-1, Q-2, Q-6, and Q-10

The dynamics of the side chain of the radical anions of ubiquinones Q-1 (2,3-dimethoxy-5-methyl-6-[3-methyl-2-butenyl]-1,4-benzoquinone), Q-2, Q-6, and Q-10 have been investigated using electron nuclear double-resonance (ENDOR) spectroscopy. When radicals are produced in the liquid phase, secondary radicals are also formed. The EPR spectra of these additional radicals overlap with the radical of interest. ENDOR spectroscopy was found to be capable for studying the dynamical properties of such conditions. The temperature dependence of the isotropic hyperfine coupling constants of the beta- and gamma-protons of the side chain was measured. The activation energy of the rotation and other dynamical properties of the side chain were calculated assuming that rotation can be modeled by the classical two-jump model. The rotation energy barrier for Q-1 was also determined by the hybrid Hartree-Fock/density functional method UB3LYP with the 6-31G(d) basis set. Calculated results were in good agreement with the experimental results. Despite the numerous parameters affecting the ENDOR linewidth ENDOR spectroscopy was shown to be a potential method for studying the dynamical properties of the mixtures of the radicals. Prominent forbidden transitions appear in the ENDOR spectra when alkali ions are present in the sample. From these transitions measured ENDOR-induced EPR spectra showed an additional doublet and phase transition in electron Zeeman frequency.     

Uniqueness and clustering properties of Gibbs states for classical and quantum unbounded spin systems

We consider quantum unbounded spin systems (lattice boson systems) in -dimensional lattice space Z. Under appropriate conditions on the interactions we prove that in a region of high temperatures the Gibbs state is unique, is translationally invariant, and has clustering properties. The main methods we use are the Wiener integral representation, the cluster expansions for zero boundary conditions and for general Gibbs state, and explicitly -dependent probability estimates. For one-dimensional systems we show the uniqueness of Gibbs states for any value of temperature by using the method of perturbed states. We also consider classical unbounded spin systems. We derive necessary estimates so that all of the results for the quantum systems hold for the classical systems by straightforward applications of the methods used in the quantum case.     

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通过计算得出EAST快动探针交换装置所用材料的理论厚度,运用CATIA绘图软件建立交换装置4mm盒形和筒形结构设计模型。将模型导入ANSYS软件进行前期处理和网格划分,运用有限元法对模型进行整体强度分析,获得了最大应力和应变数据。通过增加设计壁厚,建立了5mm不带加强筋筒形和盒形结构进行了有限元分析。通过对分析结果的优化和比较,得到5mm筒形不带加强筋方案的最大应力和应变最小,结构设计最优。最后,对模型制造了预研件并进行真空捡漏测试,测试结果满足设计要求。     

旋转粗糙目标微运动特征识别技术

基于动态散斑技术的微运动特性识别在目标探测领域具有重要的研究价值.以粗糙面散射理论为基础,研究了旋转粗糙凸体目标的动态散斑时间相关函数,给出了旋转圆锥体目标动态散斑时间相关函数.将数值结果与相同条件下实验结果进行比较,验证了圆锥体目标时间相关长度的有效性.利用粒子群算法,反演出旋转圆锥体的旋转角速度和视线角.结果表明,该方法可识别旋转圆锥体范围为20°—90°之间的视线角值和范围为0.5—6 r/min的角速度值,为微运动特征识别提供理论和实验依据.     

基于$lt;i$gt;J$lt;/i$gt;积分的颗粒煤岩单轴压缩下裂纹扩展研究

颗粒煤岩是由众多离散的煤岩颗粒组成的固态多层次多结构物质,具有煤岩与颗粒物质的双重性质,其裂纹扩展规律可以从煤岩力学特性和颗粒物质多尺度特性进行研究. 首先,从能量角度对线弹性材料受压破坏,裂纹扩展产生原因进行了阐述,指出线弹性阶段裂纹的扩展动力源自应变能的释放. 然后,通过物理实验和数值试验从宏观和细观两方面对颗粒煤岩受压破裂过程中裂纹扩展做了进一步研究,结果表明:颗粒煤岩完全破裂后,底部会形成一个锥形堆,裂纹的扩展随着煤岩颗粒粒径的减小而减缓,部分裂纹扩展会出现突变点,且裂纹无光滑性;由于煤岩颗粒粒径等引起介质的非均匀性对裂纹扩展有重要的影响,均质度系数越大裂纹起裂时间越晚,声发射能量释放在裂纹扩展的轻度、中度和深度三个不同阶段逐渐变得频繁、剧烈. 研究结果将有利于进一步研究岩土类颗粒材料受压破裂过程的裂纹扩展规律. 关键词： J积分')" href="#">J积分 颗粒煤岩 单轴压缩 裂纹扩展     

基于粒子群优化算法的船舶动力定位云模型控制器设计

云模型控制理论是智能控制学科的新兴领域,因此如何扩展云模型的应用范围并使其走向工程化实用化成为其研究重点。针对船舶运动模型具有不确定性和外部扰动随机性等特点,尝试将云模型应用于船舶动力定位的控制过程中。由于云模型控制器存在参数难以整定的问题,提出了基于粒子群算法的优化设计方法。针对标准粒子群优化算法容易出现早熟收敛的问题,引入自适应粒子群优化算法。仿真研究表明云模型控制及粒子群优化的可行性和有效性。