A door to model reduction in high-dimensional parameter space

Model reduction techniques such as Proper Generalized Decomposition (PGD) are decision-making tools that are about to revolutionize many domains. Unfortunately, their computation is still problematic for problems involving many parameters, for which one has to face the “curse of dimensionality”. An answer to this challenge is given in solid mechanics by the so-called “parameter-multiscale PGD”, which is based on Saint-Venant's principle. In this article, a model problem composed of up to a thousand parameters is presented, showing that the method is able to overcome the “curse of dimensionality”.     

On the basic laws of anisotropic viscoelasticity

The main aim of this work is to develop a consistent formulation of the rheological behavior for different anisotropic polymer systems. The unified theory of anisotropic viscoelasticity is developed based on the symmetry principles. The Maxwell rheological equation is extended to nonsymmetric anisotropic liquids. Transitions from the most general anisotropy to particular cases of anisotropy are established. It appears that the coupled relaxation of symmetric and antisymmetric stresses is a natural phenomenon in nonsymmetric viscoelasticity. Within the concept of an internal state variable, a stress–order relation is derived for a fully nonlinear case. The order tensor dynamics is also considered. A simple method of deriving the equation of the internal rotational motion is developed for the general macroscopic anisotropy. This paper was presented at the 3rd Annual Rheology Conference, AERC 2006, April 27–29, 2006, Crete, Greece     

Order of Reactivity of OH/NH Groups of Glucosamine Hydrochloride and N-Acetyl Glucosamine Toward Benzylation Using NaH/BnBr in DMF

The order of reactivity of OH and NH groups of glucosamine hydrochloride (GlcNH₂^.HCl) and N-acetyl glucosamine (GlcNAc) toward benzylation with NaH/BnBr in DMF was investigated. For GlcNH₂^.HCl, benzyl groups were introduced in the order of N-Bn > N-Bn₂ > 1-O-Bn > 6-O-Bn > 4-O-Bn > 3-O-Bn; for GlcNAc, benzyl groups were introduced in the order of 1-O-Bn > 6-O-Bn > 4-O-Bn > 3-O-Bn > N-Bn. A range of partially benzylated 2-N,N′-dibenzyl glucopyranosides and GlcNAc derivatives were obtained in a single step.     

Bessel functions of third order and the distribution of cyclic planar motions with three directions

The exact distribution of a cyclic planar motion with three directions is explicitly derived in terms of Bessel functions of order three (suitably combined). The absolutely continuous part of the distribution is proved to satisfy suitable boundary conditions and some of its properties are analyzed. The transformations converting the governing equations of order three is presented and its solutions (used here) derived by applying the Frobenius method.     

Profitability of online order fulfillment in multi-channel retailing

Store-based retailers have been concerned about the high fulfillment costs and low gross margins of their online sales. This paper incorporates such issues in a non-linear mixed-integer profit maximization model of the online order fulfillment process for multi-channel retailers. A solution approach based on an iterative outer-approximation technique is developed. Using empirical data from a large U.S. retailer, the profitability of different options used by multi-channel retailers to fill online orders is evaluated. Managerial insights are developed through a factorial research design that highlights the effect of relevant logistics processes and fulfillment methods on the profitability of online sales for retailers.     

Order acceptance and scheduling with machine availability constraints

We consider an order acceptance and scheduling model with machine availability constraints. The manufacturer (machine) is assumed to be available to process orders only within a number of discontinuous time intervals. To capture the real-life behavior of a typical manufacturer who has restrictions of time availability to process orders, our model allows the manufacturer to reject or outsource some of the orders. When an order is rejected or outsourced, an order-dependent cost of penalty will occur. The objective is to minimize the makespan of all accepted orders plus the total penalty of all rejected/outsourced orders. We study the approximability of the model and some of its important special cases.     

On Estimation of Temperature Uncertainty Using the Second Order Adjoint Problem

The uncertainty of temperature prediction from the heat flux error is estimated using first and second order adjoint equations. The adjoint codes developed for the inverse heat transfer problems provide the uncertainty estimation for the corresponding forward problems. Numerical tests corroborate the feasibility of fast uncertainty estimation using Hessian maximum eigenvalue obtained via second order adjoint equations.     

Inside the Solvency 2 Black Box: Net Asset Values and Solvency Capital Requirements with a least-squares Monte-Carlo approach

The calculation of Net Asset Values and Solvency Capital Requirements in a Solvency 2 context–and the derivation of sensitivity analyses with respect to the main financial and actuarial risk drivers–is a complex procedure at the level of a real company, where it is illusory to be able to rely on closed-form formulas. The most general approach to performing these computations is that of nested simulations. However, this method is also hardly realistic because of its huge computation resources demand. The least-squares Monte Carlo method has recently been suggested as a way to overcome these difficulties. The present paper confirms that using this method is indeed relevant for Solvency 2 computations at the level of a company.     

Analytical models for supplier selection and order quantity allocation

In the literature, decision models and techniques for supplier selection do not often consider inventory management of the items being purchased as part of the analysis. In this article, two mixed integer nonlinear programming models are proposed to select the best set of suppliers and determine the proper allocation of order quantities while minimizing the annual ordering, inventory holding, and purchasing costs under suppliers’ capacity and quality constraints. The first model allows independent order quantities for each supplier while the second model restricts all order quantities to be of equal size, as it would be required in a multi-stage (supply chain) inventory model. Illustrative examples are used to highlight the advantages of the proposed models over a previous model introduced in the literature.     

熵驱大分子胶体粒子的柱状受限结晶

熵是物理化学的基本状态参量,在统计力学和热力学中处于核心位置.按照玻尔兹曼的微观解释,熵可以由孤立系统微观状态的数目(W)给出,即S=kBlnW,这里kB为玻尔兹曼常数[1,2].根据此公式,微观状态数越多,系统越混乱,熵越大,所以熵常被视作体系无序程度的度量.但熵增仅对应体系微观状态数的增加,与可观测的结构有序程度无关[3~5].在一些典型的软物质体系中,结构越有序熵反而越大,如胶体硬球在随机密堆积点的有序结晶[6]及描述各向异性棒状分子从各向同性相到向列相转变的Onsager原理[7].