Random Variable Generation Using Concavity Properties of Transformed Densities

Abstract

Algorithms are developed for constructing random variable generators for families of densities. The generators depend on the concavity structure of a transformation of the density. The resulting algorithms are rejection algorithms and the methods of this article are concerned with constructing good rejection algorithms for general densities.     

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.     

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     

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.     

Incorporating high-pressure electroosmotic pump and a nano-flow gradient generator into a miniaturized liquid chromatographic system for peptide analysis

We integrate a high-pressure electroosmotic pump (EOP), a nanoflow gradient generator, and a capillary column into a miniaturized liquid chromatographic system that can be directly coupled with a mass spectrometer for proteomic analysis. We have recently developed a low-cost high-pressure EOP capable of generating pressure of tens of thousands psi, ideal for uses in miniaturized HPLC. The pump worked smoothly when it was used for isocratic elutions. When it was used for gradient elutions, generating reproducible gradient profiles was challenging; because the pump rate fluctuated when the pump was used to pump high-content organic solvents. This presents an issue for separating proteins/peptides since high-content organic solvents are often utilized. In this work, we solve this problem by incorporating our high-pressure EOP with a nano-flow gradient generator so that the EOP needs only to pump an aqueous solution. With this combination, we develop a capillary-based nano-HPLC system capable of performing nano-flow gradient elution; the pump rate is stable, and the gradient profiles are reproducible and can be conveniently tuned. To demonstrate its utility, we couple it with either a UV absorbance detector or a mass spectrometer for peptide separations.     

螺旋线型微秒级高压长脉冲产生器数值模拟

 探索了采用CST软件和PSpice软件进行加速器场分布数值模拟的方法,利用该方法可方便地获取设备内部动态场分布图及动态电压变化规律。针对螺旋线型μs级高压长脉冲产生器系统建立了数值模拟模型,给出了详细的模拟步骤及结果。分析表明,利用场分布模拟方法获取的电压变化规律与电路模拟方法获取的结果是一致的。基于CST模拟方法,可以给出螺旋线及主开关等电气结构的瞬态电场分布,场强增强点主要出现在螺旋带的外沿及金属电极连接处,在介质支撑内部也有较高的场强分布。     

双喷嘴乳粒发生器的研制及初步应用

 叙述了双喷嘴乳粒发生器的工作原理、设计关键点及设计思路,利用该发生器开展了双层乳粒的制备实验研究工作。研制的双喷嘴乳粒发生器在喷嘴处的3层管的位置能够通过简单调节达到同心,使得双层乳粒包覆的可靠性得到提高。研究了制备的乳粒的分散性和稳定性,并分析了形成双层乳粒的油相和水相的流速比,结果证明：利用所研制的双喷嘴乳粒发生器可以容易地制备出单分散性双层乳粒,油相与水相的流速比为0.3~15.0时,可形成双层乳粒。     

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...     

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．