Optimal bounds and extremal trajectories for time averages in nonlinear dynamical systems

For any quantity of interest in a system governed by ordinary differential equations, it is natural to seek the largest (or smallest) long-time average among solution trajectories, as well as the extremal trajectories themselves. Upper bounds on time averages can be proved a priori using auxiliary functions, the optimal choice of which is a convex optimization problem. We prove that the problems of finding maximal trajectories and minimal auxiliary functions are strongly dual. Thus, auxiliary functions provide arbitrarily sharp upper bounds on time averages. Moreover, any nearly minimal auxiliary function provides phase space volumes in which all nearly maximal trajectories are guaranteed to lie. For polynomial equations, auxiliary functions can be constructed by semidefinite programming, which we illustrate using the Lorenz system.     

制造企业成品出入库两级排队协同服务模型

优化企业成品出入库协同服务水平、平衡工作负荷,从而提高企业仓储服务效率、降低物流成本,是现代制造企业亟待解决的一个重要的管理细节问题。针对这个问题,本研究以仓储入库和出库两个排队过程为研究对象,建立出入库等待时间溢出情景下的两级排队协同服务模型,分析了在排队等待时间控制目标下,出入库员工优化配置方案。该模型引入溢出和串联两个协同服务机制,分三种情景即前方与后方服务台都有空闲,前方繁忙与后方空闲,前方空闲(或繁忙)与后方繁忙,建立了各情景下的系统状态转移方程,求解系统状态的概率,并进而推算出反映系统表现的各项指标,如员工使用率,队列长度,等待时间,以及等待时间超过溢出界值的概率。用制造企业成品出入库管理案例进行验证分析,对企业目前采用的M/M/S出入库排队系统与两级排队协同服务系统进行了数值计算对比。结果表明后者能有效提升出入库服务效率,减少出入库排队系统平均等待时间,降低由于入库和出库两个服务过程效率不均衡而产生的企业内部物流成本,是提升企业内部物流协同管理水平的一个重要方法。其应用可以服务于仓储出入库协同管理的信息化与自动化水平的提高。     

Three linear probe polarization method in Mueller polarimetry with a source of arbitrary ellipticity

This is a study of the effect of the ellipticity of the polarization of radiation at the inlet of the shaping polarizer in the probe channel of a Mueller polarimeter operating with three linear probe polarizations on the accuracy with which the incomplete Mueller matrix is determined (without a fourth beam). It is shown that the appearance of and variations in the ellipticity cause a change in the conditions for optimization of the set of polarizations of the probe radiation from the standpoint of minimizing the measurement error. In the case of linear polarization (zero ellipticity), the measurement error is the same as the error when four probe polarizations are used. This allows measurement of the complete Mueller matrix and makes this version of the polarimeter especially promising, because in the input channel of the polarimeter, a single polarizing element, i.e., a linear polarizer with a controllable azimuthal orientation, can be used as the polarization transducer. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 6, pp. 875–880, November–December, 2008.     

Benchmarking of adjoint sensitivity-based optimization techniques using a vehicle ride case study

Several studies on multibody dynamics optimization have been conducted. One important limitation of these studies is their computational e?ciency, especially when optimizing a complex system’s performance. The co-authors developed a very e?cient optimization technique based on an adjoint sensitivity analysis methodology. The scope of this article is to validate this technique by conducting a benchmark analysis against some of the most popular optimization methods, including gradient-based optimization using finite differences, design of experiment using optimal Latin hypercube, and design of experiment using full factorial design matrix. A vehicle system is used as a case study for optimizing its ride comfort.     

Temperature field design,process analysis and control of SAPMAC method for the growth of large size sapphire crystals

In this paper, the relationship between quality of sapphire crystal and growing parameters of SAPMAC (Sapphire growth technique with micro‐pulling and shoulder‐expanding at cooled center) method was discussed. Optimized temperature distribution and technique control were proposed by theoretical analysis, numerical simulation computation and experimental validation to obtain large size sapphire crystals. For a‐axis crystallized direction, with 1.0‐5.0mm/h growth velocity and 10‐30K/h temperature decreasing speed, large sapphire single crystal (∅︁240mm×210mm, 27.5kg) having high optical quality was successfully grown. The absorption spectrum of standard samples was measured as well. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A High-Efficiency Spectral Method for Two-Dimensional Ocean Acoustic Propagation Calculations

The accuracy and efficiency of sound field calculations highly concern issues of hydroacoustics. Recently, one-dimensional spectral methods have shown high-precision characteristics when solving the sound field but can solve only simplified models of underwater acoustic propagation, thus their application range is small. Therefore, it is necessary to directly calculate the two-dimensional Helmholtz equation of ocean acoustic propagation. Here, we use the Chebyshev–Galerkin and Chebyshev collocation methods to solve the two-dimensional Helmholtz model equation. Then, the Chebyshev collocation method is used to model ocean acoustic propagation because, unlike the Galerkin method, the collocation method does not need stringent boundary conditions. Compared with the mature Kraken program, the Chebyshev collocation method exhibits a higher numerical accuracy. However, the shortcoming of the collocation method is that the computational efficiency cannot satisfy the requirements of real-time applications due to the large number of calculations. Then, we implemented the parallel code of the collocation method, which could effectively improve calculation effectiveness.     

Selection of Catalyst for the Esterification Step of the PPT Polymerization Process

Summary: TBOT is a proven catalyst for the esterification step of the PPT polymerization process. Previous studies have shown that the performance of TBOT is superior in terms of the enhanced degree of polymerization and shorter processing time. However, one interesting aspect which has not yet been investigated is whether with different process objectives, like by‐product minimization and controlled growth of desired functional groups, any other catalyst offers any increase in process performance. The present study gives a detailed process analysis through different sets of optimized operations, which consists basically of searching for other catalytic options for process improvements. A well validated kinetic model for the esterification step of the PPT polymerization process and the advanced Real‐Coded NSGA‐II optimization routine have been used in this study. It can be seen that with all the process considerations, such as maximization of the degree of polymerization, minimization of processing time and the enhanced controlled growth of desired functional groups and minimization of by‐products, the Zn‐based catalyst can replace the conventional Ti‐based catalyst. An Sn‐based catalyst was also found to be able to compete with these two catalysts in some cases.

Optimized Pareto plot for a study on the 4 objectives case for various catalysts. The Zn‐based catalyst outperforms the others.     

Phase shift of the population oscillation and population trapping

Using our recently developed time-dependent multilevel approach, we have calculated the phase shift of the population oscillation of the excited potassium atom in frequency-modulated fields when the modulation amplitude is suddenly changed. The numerical results are in good agreement with the measurements. A new way of realizing population trapping is suggested.     

Conjugate gradient algorithms for best rank-1 approximation of tensors

Motivated by considerations of pure state entanglement in quantum information, we consider the problem of finding the best rank-1 approximation to an arbitrary r -th order tensor. Reformulating the problem as an optimization problem on the Lie group SU (n₁) ⊗ … ⊗ SU (n_r) of so-called local unitary transformations and exploiting its intrinsic geometry yields a new approach, which finally leads to Riemannian variant of the conjugate gradient algorithm. Numerical simulations support that our method offers an alternative to the higher-order power method for computing the best rank-1 approximation to a tensor. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

传统合金型热电材料研究进展

随着热电材料制备方法的多样化和性能表征手段的具体化,合金型热电材料以其优异性能在众多热电材料中脱颖而出,成为拥有高热电性能和高转换率的热电材料.主要介绍了根据适用温度划分的三类传统合金型热电材料:低温热电材料Bi2 Te3、中温热电材料PbTe和高温热电材料SiGe,重点归纳总结了金属合金热电性能优化方法,最后概述了其实际应用领域并展望其未来的发展前景.