自由曲面光学虚拟制造与检测系统的探讨

自由曲面光学产品设计、制造与检测的工艺流程，通常采取试凑法逐次逼近。由于加工 检测 再加工，循环往复，既费时，成本又高，产生了瓶颈问题。为了解决此弊端，本文运用虚拟制造技术，提出光学虚拟制造的基本构想，即虚拟制造系统结构模型，给出光学系统虚拟原型的构成和光学系统成像质量虚拟检测系统的构成，讨论光学成像质量的仿真检测以及敏度分析方法。研究结果表明：运用虚拟制造与检测技术，可缩短研发周期，降低成本，优化工艺并提高产品质量。     

Take back costs and product durability

Extended Producer Responsibility (EPR) initiatives may require a manufacturer to be responsible in the future for taking back the products it produces today. A ramification of EPR is that take back costs may influence firms’ decisions regarding product durability. In the absence of EPR, prior literature has shown that a firm may intentionally lower durability, yielding planned obsolescence. We use a two period model to examine the impact of take back costs on a manufacturer’s product durability and pricing decisions, under both selling and leasing scenarios. We show that compared to selling, leasing provides a greater incentive to raise durability, thus extending a classic insight to a setting with product take backs. Interestingly, we also show that it is possible for the optimal product durability to decrease if the stipulated take back fraction increases. In such situations, were the take back fraction tied to durability rather than a fixed fraction, we demonstrate durability can increase. We explore the impact of take backs on profits and surplus by alternatively considering products for which take back costs are either increasing or decreasing functions of durability. When increasing durability implies higher take back costs, our results demonstrate that leasing can increase durability, profits, and surplus significantly compared to selling. In contrast, when increasing durability implies a lower take back cost, there is a built-in incentive for the firm to increase durability, which can make selling more efficient (i.e., surplus enhancing) than leasing.     

Capacity decisions for high-tech products with obsolescence

Modern high-tech products experience rapid obsolescence. Capacity investments must be recouped during the brief product lifecycle, during which prices fall continuously. We employ a multiplicative demand model that incorporates price declines due to both market heterogeneity and product obsolescence, and study a monopolistic firm’s capacity decision. We investigate profit concavity, and characterize the structure of the optimal capacity solution. Moreover, for products with negligible variable costs, we identify two distinct strategies for capacity choice demarcated by an obsolescence rate threshold that relates both to market factors and capacity costs. Finally, we empirically test the demand model by analyzing shipping and pricing data from the PC microprocessor market.     

Anomalous potentials from inverse analyses of interfacial polydisperse attractive colloidal fluids

This paper investigates effects of using monodisperse inverse analyses to extract particle-particle and particle-surface potentials from simulated interfacial colloidal fluids of polydisperse attractive particles. Effects of polydispersity are investigated as functions of particle concentration and attractive well depth and range for van der Waals and depletion potentials. Forward Monte Carlo simulations are used to generate particle distribution functions for polydisperse interfacial colloidal fluids from which inverted potentials are obtained using an inverse Ornstein-Zernike analysis and an inverse Monte Carlo simulation method. Attractive potentials are successfully recovered for monodisperse colloidal fluids, but polydispersity that is unaccounted for in inverse analyses produces (1) apparent softening of strong forces, (2) anomalous repulsive and attractive interactions, and (3) aphysical particle overlaps. This investigation provides insights into the role of polydispersity in altering the equilibrium structure and corresponding inverted potentials of attractive colloidal fluids near surfaces. These findings should assist the design and interpretation of optical microscopy experiments involving interfacial colloidal fluids similar to the simulated experiments reported here.     

Role of polydispersity in anomalous interactions in electrostatically levitated colloidal systems

In this paper, we investigate the effects of using inverse analyses developed for monodisperse particles to extract particle-particle and particle-surface potentials from simulated interfacial colloidal configurations having finite-size polydispersity. Forward Monte Carlo simulations are used to generate three-dimensional equilibrium configurations of log normal-distributed polydisperse particles confined by gravity near an underlying surface. Particles remain levitated above the substrate and stabilized against aggregation by repulsive electrostatic Derjaguin-Landau-Verwey-Overbeek pair potentials. An inverse Ornstein-Zernike analysis and an inverse Monte Carlo simulation method are used to obtain interactions from simulated distribution functions as a function of polydispersity (sigma), relative range of repulsion (kappa a), and projected interfacial concentration (rho). Both inverse analyses successfully recover input potentials for all monodisperse cases, but fail for polydispersities often encountered in experiments. For different conditions (sigma, kappa a, and rho), our results indicate softened short-range repulsion, anomalous long-range attraction, and apparent particle overlaps, which are similar to commonly reported observations in optical microscopy measurements of quasi-two-dimensional interfacial colloidal ensembles. By demonstrating signatures of, and limitations due to, polydispersity when extracting pair potentials from measured distribution functions, our specific goal is to provide a basis to objectively interpret and resolve the effects of polydispersity in optical microscopy experiments.     

自由曲面光学透镜注射成型误差因素研究

自由曲面光学透镜注射成型误差对其光学性能将产生直接影响。注射成型过程中，注射工艺参数组合的优劣，直接影响成型误差的大小。为了获得高精密度的光学元件，就热塑性塑料的注射温度、模具温度、注射压力、保压压力及保压时间等主要工艺参数，对注射成型误差的影响进行综合研究,并且进行了实验验证。研究结果表明：适当提高注射温度与模具温度，同时采用高压注射、高压保压以及快速保压工艺，可显著降低注塑工件的体积收缩率，显著提高面形精密度，其光学表面面形误差小于0.1μm。可为注射工艺设计提供合理的依据。     

Rotational Dynamics of Adamantanecarboxylic Acid in Complex with β-cyclodextrin

The reorientation of 1-adamantanecarboxylic acid (AdCA) within the β-cyclodextrin (β-CD) cavity is investigated by means of multiple-field ¹³C NMR relaxation. The dissociation constant describing the complexation equilibrium is determined using translational diffusion measurements for the guest during a titration by the host in D₂O/DMSO solvent mixture. The changes in apparent diffusion properties of AdCA during the titration are at 25 °C well described assuming the formation of a 1:1 complex, whereas at 0 °C the data indicate the presence of a 2:1 (guest:host) complex. The ¹³C NMR relaxation parameters for the AdCA molecule bound inside the β-CD cavity are extracted. Despite the high association constant, indicating a strong interaction between the two molecules, the guest molecule is quite mobile. The reorientation of the bound AdCA at 25 °C can be described by either the Lipari–Szabo or the axially symmetric rotational diffusion model. The motion is extremely anisotropic: the adamantyl group rotates fast around the β-CD symmetry axis, inside its cylindrical cavity. At lower temperature, the relaxation properties are no longer possible to explain using these models. Instead, the data are analyzed using extended, three-step spectral density of Clore et al. [J. Am. Chem. Soc. 112, 4989 (1990)].     

Eventual Positivity of Hermitian Algebraic Functions and Associated Integral Operators∗

Quillen proved that repeated multiplication of the standard sesquilinear form to a positive Hermitian bihomogeneous polynomial eventually results in a sum of Hermitian squares, which was the first Hermitian analogue of Hilbert’s seventeenth problem in the nondegenerate case. Later Catlin-D’Angelo generalized this positivstellensatz of Quillen to the case of Hermitian algebraic functions on holomorphic line bundles over compact complex manifolds by proving the eventual positivity of an associated integral operator. The arguments of Catlin-D’Angelo involve subtle asymptotic estimates of the Bergman kernel. In this article, the authors give an elementary and geometric proof of the eventual positivity of this integral operator, thereby yielding another proof of the corresponding positivstellensatz.     

SELECTION OF TRAINING SAMPLES FOR MODEL UPDATING USING NEURAL NETWORKS

One unique feature of neural networks is that they have to be trained to function. In developing an iterative neural network technique for model updating of structures, it has been shown that the number of training samples required increases exponentially as the number of parameters to be updated increases. Training the neural network using these samples becomes a time-consuming task. In this study, we investigate the use of orthogonal arrays for the sample selection. A comparison between this orthogonal arrays method and four other methods is illustrated by two numerical examples. One is the update of the felxural rigidities of a simply supported beam and the other is the update of the material properties and the boundary conditions of a circular plate. The results indicate that the orthogonal arrays method can significantly reduce the number of training samples without affecting too much the accuracy of the neural network prediction.