Development and assessment of an intrusive polynomial chaos expansion-based continuous adjoint method for shape optimization under uncertainties

This article contributes to the development of methods for shape optimization under uncertainties, associated with the flow conditions, based on intrusive Polynomial Chaos Expansion (iPCE) and continuous adjoint. The iPCE to the Navier–Stokes equations for laminar flows of incompressible fluids is developed to compute statistical moments of the Quantity of Interest which are, then, compared with those obtained through the Monte Carlo method. The optimization is carried out using a continuous adjoint-enabled, gradient-based loop. Two different formulations for the continuous adjoint to the iPCE PDEs are derived, programmed, and verified. Intrusive PCE methods for the computation of the statistical moments require mathematical development, derivation of a new system of governing equations and their numerical solution. The development is presented for a chaos order of two and two uncertain variables and can be used as a guide to those willing to extend this development to a different set of uncertain variables or chaos order. The developed method and software, programmed in OpenFOAM, is applied to two optimization problems pertaining to the flow around isolated airfoils with uncertain farfield conditions.     

Asymptotic analysis of microscopic impenetrability constraints for atomistic systems

We analyze systems of atomistic interactions on a triangular lattice allowing for fracture under a geometric condition on the triangles corresponding to a microscopic impenetrability constraint. Such systems can be thought as a computational simulation of materials undergoing brittle fracture. We show that in the small-deformation regime such approximation can be validated analytically in the framework of variational models of fracture. Conversely, in a finite-deformation regime various pathologies show that the continuum approximation of such a system differs from the usual variational representations of fracture and either needs new types of formulations on the continuum, or a proper interpretation of the atomistic constraints limiting their range and adapting them to a dynamical framework.     

Binding energy of an off-center donor impurity in ellipsoidal quantum dot with parabolic confinement potential

The binding energy of an off-center hydrogenic donor impurity in weakly oblate Ellipsoidal Quantum Dot (EQD), using the expansion method within the framework of effective mass approximation in strong confinement, is investigated. In this regard, the binding energies of different states of GaAs structures, as functions of the donor position and ellipticity parameter, are calculated. The results show that variations of binding energies are proportional to the ellipticity constant, the dot dimension and the location of impurity.     

Accurate estimation of solvation free energy using polynomial fitting techniques

This report details an approach to improve the accuracy of free energy difference estimates using thermodynamic integration data (slope of the free energy with respect to the switching variable λ) and its application to calculating solvation free energy. The central idea is to utilize polynomial fitting schemes to approximate the thermodynamic integration data to improve the accuracy of the free energy difference estimates. Previously, we introduced the use of polynomial regression technique to fit thermodynamic integration data (Shyu and Ytreberg, J Comput Chem, 2009, 30, 2297). In this report we introduce polynomial and spline interpolation techniques. Two systems with analytically solvable relative free energies are used to test the accuracy of the interpolation approach. We also use both interpolation and regression methods to determine a small molecule solvation free energy. Our simulations show that, using such polynomial techniques and nonequidistant λ values, the solvation free energy can be estimated with high accuracy without using soft‐core scaling and separate simulations for Lennard‐Jones and partial charges. The results from our study suggest that these polynomial techniques, especially with use of nonequidistant λ values, improve the accuracy for ΔF estimates without demanding additional simulations. We also provide general guidelines for use of polynomial fitting to estimate free energy. To allow researchers to immediately utilize these methods, free software and documentation is provided via http://www.phys.uidaho.edu/ytreberg/software . © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

One-pot preparation of hydroxylated potassium organotrifluoroborates and subsequent Jones oxidation to potassium organocarbonyltrifluoroborates

Alcohol-containing potassium organotrifluoroborates as starting reagents were prepared from their corresponding dibromobenzenes through a sequential one-pot reaction. The oxidation reactions of these substrates, which were carried out using 3.0 equiv of 8 N Jones reagent in acetone at 0 °C, provided a high yield of the desired carbonyl-functionalized compounds. In addition, the cross-coupling reactions of these organocarbonyltrifluoroborates were successfully performed in the presence of 3 mol % of Pd(PPh₃)₄ catalyst at 100 °C.     

New q‐Hermite polynomials: characterization,operators algebra and associated coherent states

This paper addresses a construction of new q‐Hermite polynomials with a full characterization of their main properties and corresponding raising and lowering operator algebra. The three‐term recursive relation as well as the second‐order differential equation obeyed by these new polynomials are explicitly derived. Relevant operator actions, including the eigenvalue problem of the deformed oscillator and the self‐adjointness of the related position and momentum operators, are investigated and analyzed. The associated coherent states are constructed and discussed with an explicit resolution of the induced moment problem. The phase collapse in a q‐deformed boson system is studied.     

彩色打印机特性化多元回归模型的研究

多元回归法是彩色打印机特性化普遍采用的方法,实验对影响多元回归精度的阶数、色空间选择、以及训练样本选取进行了研究.研究结果表明:(1)二、三、四阶的特性化精度分别在10.9±0.3、6.6±0.2、6.0±0.2个CIELAB色差单位;(2)回归模型采用RGB到CIELAB或CIEXYZ的预测精度基本相同,大概相差1个...     

反射式Sagnac干涉光纤电流互感器的传感头误差研究

阐述了反射式Sagnac干涉型电流传感器的原理,对Sagnac型光纤电流传感器进行了深入的理论研究,建立了完整的系统理论模型。采用偏振系统的Jones矩阵对反射式Sagnac干涉型电流传感器的偏振误差进行了研究,并对光纤传感头中的线性双折射、圆双折射对测量准确度的影响进行了模拟分析,从理论上得到了反映影响规律的曲线。仿...     

一元多项式学习中易犯的几个错误

结合一元多项式中的一些重要概念,如多项式的最大公因式、多项式的重根及不可约多项式等,分析一元多项式学习中易犯的错误,并强调运用定理时要注意其适用的条件和前提．     

M(G,x)≤2的图匹配等价的充要条件

对一个图G,设μ(G,x)表示它的匹配多项式,M(G,x)表示μ(G,x)的最大实数根.令Г_1={G|M(G,x)<2}和Г2={G|M(G,x)≤2}.给出了Г_i(i=1,2)中的两个图G和H匹配等价的充要条件.