非线性最优控制系统的时程精细计算研究

针对非线性最优控制问题 ,通过一阶 Taylor级数展开 ,得到线性化的动力学方程 ,进而在方程原变量的基础上 ,引入对偶向量 (Lagrange乘子向量 ) ,将动力学方程从 Lagrange体系引入到了 Hamilton体系 ,在全状态下 ,从一个新的角度对非线性最优控制问题进行了描述 ,进一步基于时程精细积分理论 ,对其方程进行了有效的精细求解 ,并通过算例说明了文中方法的有效性     

A new methodology for precise cadmium isotope analyses of seawater

Previous studies have revealed considerable Cd isotope fractionations in seawater, which can be used to study the marine cycling of this micronutrient element. The low Cd concentrations that are commonly encountered in nutrient-depleted surface seawater, however, pose a particular challenge for precise Cd stable isotope analyses. In this study, we have developed a new procedure for Cd isotope analyses of seawater, which is suitable for samples as large as 20 L and Cd concentrations as low as 1 pmol/L. The procedure involves the use of a ¹¹¹Cd–¹¹³Cd double spike, co-precipitation of Cd from seawater using Al(OH)₃, and subsequent Cd purification by column chromatography. To save time, seawater samples with higher Cd contents can be processed without co-precipitation. The Cd isotope analyses are carried out by multiple collector inductively coupled plasma mass spectrometry (MC-ICP-MS). The performance of this technique was verified by analyzing multiple aliquots of a large seawater sample that was collected from the English Channel, the SAFe D1 seawater reference material, and several samples from the GEOTRACES Atlantic intercalibration exercise. The overall Cd yield of the procedure is consistently better than 85% and the methodology can routinely provide ε ^114/110Cd data with a precision of about ±0.5 ε (2sd, standard deviation) when at least 20–30 ng of natural Cd is available for analysis. However, even seawater samples with Cd contents of only 1–3 ng can be analyzed with a reproducibility of about ±3 to ±5 ε. A number of experiments were furthermore conducted to verify that the isotopic results are accurate to within the quoted uncertainty.     

Preparation of porous silica spheres with self-dispersing properties

A sol-gel procedure in a water/oil emulsion was introduced for the synthesis of porous silica spheres. Tetraethoxysilane was used as the silica source. The specific surface area and total pore volume of the product reached 772.3 m2/g and 0.663 cm3/g, respectively. The electrolyte washing process conferred a surface charge to the product, which displayed self-dispersal properties in water. The porous spheres have potential applications in the fields of drug delivery, controlled release capsules, indoor air pollutant scavengers, and hydrogen storage agents. The oil phase, which accounts for over 8O% of the chemical cost of the procedure, could largely be recycled by filtering, standing, and layering. The whole procedure is suitable for application as an industrial process.     

Chaos in an embedded single-walled carbon nanotube

Considering the geometrical nonlinearity of an embedded single-walled carbon nanotube, the analytical condition and the numerical results of chaotic vibration of the carbon nanotube are presented in this paper. Firstly, based on the Galerkin approximation method, a Duffing-type model is derived from the equation of motion that describes the oscillation of the embedded single-walled carbon nanotube clamped at both ends under a transverse load. And then, the Melnikov function of the Duffing-type model is derived. From the Melnikov function, the analytical condition of the chaos in the nanotube is obtained. Finally, a structure-preserving difference scheme for the original oscillating model is constructed based on the generalized multi-symplectic framework and the chaotic vibration of the nanotube is reproduced to verify the accuracy and the validity of the analytical condition. The analytical condition obtained in this paper gives some guidance on the property studying and the structure designing of some carbon nanotube devices.     

Preparation of porous TiO2/silica composites without any surfactants

TiO₂-SiO₂ composites, with high specific surface area (up to 308 m²/g), large pore volume, and narrow distribution with average pore sizes of 3.2 nm, have been synthesized from wollastonite and titanium sulfate in the absence of any surfactants. Calcium sulfate, a microsolubility salt, plays an important role in the formation of pores in this porous TiO₂/silica composite. The microstructure and chemical composition of composite were characterized by X-ray diffractometry (XRD), transmission electron microscopy (TEM) equipped with energy-dispersive X-ray spectroscopy (EDX), X-ray photoelectron spectrometer (XPS) and N₂ adsorption and desorption analysis. The as-prepared porous titanium dioxide-silicon dioxide composites with high specific surface area and well-crystallized anatase contents were used as an efficient photocatalyst.     

Three-dimensional ZnS/reduced graphene oxide/polypyrrole composite for high-performance supercapacitors and lithium-ion battery electrode material

Journal of Solid State Electrochemistry - In this work, three-dimensional ZnS/reduced graphene oxide/polypyrrole ternary composites were synthesized. The as-prepared composites are investigated as...     

Vibrational analysis of a rate-slowing conformational kinetic isotope effect

An enthalpy-entropy approach to analyzing a rate-slowing conformational kinetic isotope effect (CKIE) in a deuterated doubly-bridged biaryl system is described. The computed isotope effect (k_H/k_D?=?1.075, 368?K) agrees well with the measured value (k_H/k_D?=?1.06, 368?K). The rate-slowing (normal isotope effect) nature of the computed CKIE is shown to originate from a vibrational entropy contribution defined by the twenty lowest frequency normal modes in the ground state and transition state structures. This normal entropy contribution is offset by an inverse vibrational enthalpy contribution, which also arises from the twenty lowest frequency normal modes. Zero point vibrational energy contributions are found to be relatively small when all normal modes are considered. Analysis of the H_ZPE, H_vib, and S_vib energy terms arising from the low frequency vibrational modes reveals their signs and magnitudes are determined by larger vibrational energy differences in the labeled and unlabeled ground state structures.     

TRANSIENT THERMAL RESPONSE IN THICK ORTHOTROPIC HOLLOW CYLINDERS WITH FINITE LENGTH： HIGH ORDER SHELL THEORY

The transient thermal response of a thick orthotropic hollow cylinder with finite length is studied by a high order shell theory. The radial and axial displacements are assumed to have quadratic and cubic variations through the thickness, respectively. It is important that the radial stress is approximated by a cubic expansion satisfying the boundary conditions at the inner and outer surfaces, and the corresponding strain should be least-squares compatible with the strain derived from the strain-displacement relation. The equations of motion are derived from the integration of the equilibrium equations of stresses, which are solved by precise integration method （PIM）. Numerical results are.obtained, and compared with FE simulations and dynamic thermo-elasticity solutions, which indicates that the high order shell theory is capable of predicting the transient thermal response of an orthotropic （or isotropic） thick hollow cylinder efficiently, and for the detonation tube of actual pulse detonation engines （PDE） heated continuously, the thermal stresses will become too large to be neglected, which are not like those in the one time experiments with very short time.     

考虑材料设计变量的热-固耦合结构的优化设计

从材料-结构协同设计的角度研究了热-固耦合结构的优化设计问题,将决定结构材料性质的细观参数与结构宏观几何参数作为设计变量,利用均匀化方法推导了细观设计变量灵敏度显式计算式,并结合耦合场有限元方程构造了耦合场设计变量灵敏度计算式;提出了材料-结构协同设计的三种优化设计模型.利用结构响应最小优化模型对算例进行了计算,比较了宏观设计变量优化和材料-结构协同设计优化的效果.计算结果显示,材料-结构协同优化设计可以取得较单一宏观设计变量更好的优化效果.     

Multi-resonator coupled metamaterials for broadband vibration suppression

In this study,multi-resonator coupled metamaterials(MRCMs)with local resonators are proposed to obtain the multiple and wide band gaps.Kinetic models of the MRCMs are established,and the boundary conditions of the unit cell are obtained with Bloch's theorem.The effects of structural parameters,including the mass of the resonator and the spring stiffness,on the distributions of the band gaps are studied.Furthermore,the frequency domain responses and the time domain responses are calculated for analyzing the structural vibration characteristics and the effects of damping on structural vibration.The results show that the frequency domain response can accurately express the distributions of the band gaps of the MRCMs,and we can increase the number and the width of the band gaps by using the MRCMs for the superior vibration suppression capability.