Inverse Problems for Multidimensional Heat Equations by Measurements at a Single Point on the Boundary

In this article we recover a coefficient in a multidimensional inverse problem for a heat equation. We show that a sequence of measurements taken at the same point on the boundary but at different times is enough to determine the coefficient uniquely. We provide an identifiability algorithm for both Dirichlet and Neumann lateral boundary conditions and we examine the smoothness of the recovered coefficient.     

XPS study of silicon spheres as a density standard

As density is one of the basic physical properties of materials, an accurate density standard is absolutely essential. To determine density with high accuracy and precision, two 1-kg single-crystal silicon spheres (NMIJ-S4 and NMIJ-S5) are used as the primary standard at the National Metrology Institute of Japan. For the accurate measurement of the mass and volume of the silicon spheres, the effects of the surface layer must be carefully considered. In this work, a surface layer model of NMIJ-S4 and NMIJ-S5 was proposed and the thicknesses of each surface layer were determined using X-ray photoelectron spectroscopy. A detailed uncertainty budget is presented to aid use of the density standard.     

以时温等效方法研究尼龙1010应力松弛行为及使用寿命预测

以尼龙材料的应力松弛行为作为研究对象, 考察初始应变为1.0%, 2.8%和5.1%的尼龙1010样品在温度区间293353 K的松弛曲线, 采用时间-温度等效叠加方法得到了松弛模量主曲线, 计算出叠加过程中的表观活化能、 松弛过程中的活化体积和应力辅助功. 结果表明, 整个松弛过程中的表观活化能和应力辅助功表现出相同的变化趋势, 体现出松弛过程中克服运动单元位垒的过程. 当293323 K区间的松弛曲线叠加时, 随着初始应变的增加, 表观活化能和应力辅助功均逐渐降低, 有助于聚合物内部的运动单元越过能垒发生松弛, 与松弛过程中的应力辅助热活化理论相一致; 当333353 K区间的松弛曲线叠加时, 不同初始应变样品的表观活化能均为260 kJ/mol, 应力辅助功均为60 MPa·nm³, 说明松弛过程中克服运动单元的能垒与应力作用无关. 根据松弛主曲线, 计算出了尼龙1010在1.0%, 2.8%和5.1% 3种形变下, 长时间范围内应力衰减与时间的关系, 为预测实际使用过程中的应力松弛行为提供了依据.     

简谈普适气体常量R——贯穿普化教育的重要常量

The universal gas constant R is an important constant in physics, and one of the vital fundamental constant throughout the teaching of general chemistry. This article aims to present a general review about the universal gas constant to the science and engineering majored students, including its history, determination, physical meaning and applications in chemical education. The choice of R values under various conditions is also provided to help students better understand and master basic concepts.     

纳米孔道单分子电化学测量的低噪音控温系统研究

纳米孔道检测技术是一种利用单个分子测量界面实现在单分子水平上测量DNA、RNA、蛋白、多肽等生物分子的高灵敏的单分子检测技术. 由于单个分子与纳米孔道的相互作用受热力学控制,亟需精准控制纳米孔道单分子分析的实验温度. 因此,本文研制了一种低噪音控温系统用于具有皮安级电流分辨的纳米孔道单分子实验,以实现精确调控测量时的环境温度. 该系统利用半导体制冷片的热电效应对检测池环境加热/制冷,通过对高精度热敏电阻进行电磁屏蔽以实现在温度反馈的同时避免噪音的引入. 利用比例-积分-微分算法进行控制,达到高精度快速控温的要求. 该系统控温精度为±1 °C,无额外噪音引入至超灵敏纳米孔道单分子测量,获得了25 °C到5 °C下Poly(dA)5与单个气单胞菌溶素（Aerolysin）分子界面间作用产生信号的差异,应用于研究单分子与纳米孔道相互作用的热力学行为.     

Review of nonlinear oscillatory shear flow notations and presentations: polymeric liquids

We review notations for, along with ways of presenting, the shear stress responses to large-amplitude oscillatory shear flow (LAOS). We find that the Fourier loss and storage viscosities to be the simplest primal notations for interpreting LAOS. The relative intensities provide the best evidence for oscillatory shear entering the large-amplitude regime. Deviation from linear viscoelastic behaviors can be observed through the distortions of Lissajous loops. We explore these loops in their elastic and viscous projections. The centerpiece of this work is our review table, which summarizes experimental measurements for polymer melts and solutions, targeting 21st century publications. Our review also provides conversion formulae to go from any of many notations to the Fourier loss and storage viscosities. The review table also defines which part of the LAOS measurement field has yet to be ploughed and shines light on which notations have been used, and for which purposes, to interpret nonlinearities.     

Stokes Flows under Random Boundary Velocity Excitations

A viscous Stokes flow over a disc under random fluctuations of the velocity on the boundary is studied. We give exact Karhunen-Loève (K-L) expansions for the velocity components, pressure, stress, and vorticity, and the series representations for the corresponding correlation tensors. Both the white noise fluctuations, and general homogeneous random excitations of the velocities prescribed on the boundary are studied. We analyze the decay of correlation functions in angular and radial directions, both for exterior and interior Stokes problems. Numerical experiments show the fast convergence of the K-L expansions. The results indicate that ignoring the stochastic fluctuations in boundary conditions dramatically underestimates the variance of the velocity and pressure in the interior/exterior of the domain. The support of the RFBR Grant N 06-01-00498 is kindly acknowledged.     

A Representation of Quantum Measurement in Order-Unit Spaces

A certain generalization of the mathematical formalism of quantum mechanics beyond operator algebras is considered. The approach is based on the concept of conditional probability and the interpretation of the Lüders-von Neumann quantum measurement as a probability conditionalization rule. A major result shows that the operator algebras must be replaced by order-unit spaces with some specific properties in the generalized approach, and it is analyzed under which conditions these order-unit spaces become Jordan algebras. An application of this result provides a characterization of the projection lattices in operator algebras.