关于傅科摆相对运动轨迹的讨论

根据傅科摆确定的起始条件,正确导出其轨迹方程,并用计算机画出其相对运动轨迹曲线。同时推证得摆锤在最大幅角位置时,其相对速度为零这一重要特征。     

结晶PET驻极体的分子运动与陷阱性质

半晶性的聚对苯二甲酸乙二醇酯(PET)存在不同尺寸运动单元的多重形式的分子运动,而且PET等高聚物前结构欠序、晶界和杂质等缺陷还使电子价带与导带间的禁带中出现局域能级(陷阱),并成为捕获载流子的中心,从而影响载流子的输运性质。分子运动和陷阱     

聚偏氟乙烯共混体系的压电性及其分子运动——Ⅱ.PVDF与 P(VDF-HFE)以及PVDF与P(VDF-TFE)的共混体系

本文研究了 PVDF-P(VDF-HFE)以及 PVDF-P(VDF-TFE)共混体系的压电、介电、力学松弛谱。其松弛转变过程基本与 PVDF 的相似。α,β,γ压电松弛峰分别位于40～120℃,-40℃,-85℃附近。实验结果表明后一体系的压电性大于前一体系的。同时,PVDF-P(VDF-TFE)的压电性也大于PVDF-PMMA 共混体系的。选择第二组分时,以介电常数高,模量小而本身又具有压电性的,更有助于共混薄膜压电性的提高。在同样的极化条件下,经拉伸的 P(VDF-TFE)薄膜,其压电性大于未经拉伸的薄膜,这表明分子的取向对薄膜的压电性也有影响。TSC 表明,42℃的松弛峰与晶区表面捕获的空间电荷有关,对压电性也有一定的贡献。     

苯乙烯-异戊二烯嵌段共聚物分子运动的脉冲核磁共振研究

用西德Bruke,MSL-300核磁共振谱仪研究了三个不同系列的苯乙烯-异戊二烯嵌段共聚物的固体回波谱。用PASCAL语言在谱仪提供的计算机上、用线性最小二乘法回归分析把实验曲线分解成快速和慢速两个组分,它们分别对应于嵌段共聚物中刚性相和流动相,从而给出样品两相结构的定性定量信息。     

Computation of suboptimal randomized strategies for steering the random motion of a point under partial observation

Consider the random motion in the plane of a pointM, whose velocityv=(v ₁,v ₂) is perturbed by an ²-valued Gaussian white noise. Only noisy nonlinear observations taken on the point location (state) are available toM. The velocityv is of the formv(y)= _u (u ₁,u ₂) _y (du), wherey denotes the value of the observed signal,U is the range of the velocity, and, for eachy, _y is a probability measure on (U). Using the available observations, the pointM wishes to steer itself into a given target set by choosing a randomized strategy ={ _y :y ²}. Sufficient conditions on weak optimal randomized strategies are derived. An algorithm for computing weak suboptimal randomized strategies is suggested, and the strategies are computed for a variety of cases.This work was partially supported by a grant from Control Data.     

Spectral studies on VO ions in potassium thiourea bromide single crystals using EPR and optical absorption spectroscopy

Electron paramagnetic resonance (EPR) studies have been carried out on VO²⁺ ions doped in single crystals of ferroelectric material, potassium thiourea bromide (PTB) at room temperature and in the temperature range 103–343 K on X-band MW frequency. An isotropic octet spectrum characteristic of VO²⁺ ion was obtained due to the fast re-orientation of the VO²⁺ in PTB lattice, which exhibits glassy nature at certain range around room temperature. The temperature dependant EPR spectra of VO²⁺ ions in this host lattice has been attributed to the occurrence of multiple phase transitions due to the combined environment effects of KBr and thiourea materials in the single crystal. From the optical absorption spectrum, the crystal field splitting parameter Dq, tetragonal parameters Ds and Dt have been evaluated and discussed.     

Brownian motion of nonlinear oscillators: The projection operator method and its application to a double-well-potential oscillator

A projection operator method is presented, which provides the most efficient way for calculating the stationary behavior of nonlinear Brownian motion. A continued-fraction expansion of the Fourier-Laplace transform of the displacement correlation function or the spectral density is used. This method utilizes a successive optimization procedure on the nonlinear terms and includes the method of statistical linearization as the lowest order approximation. A systematic way to calculate the continued fraction numerically up to sufficient order for convergence is developed, which enables us to obtain the spectral density of a system previously uncomputable.Numerical computations of the spectral density of a nonlinear oscillator with a double-well potential are presented and compared with the results obtained by statistical linearization.This work was supported in part by the National Science Foundation under Grant CHE 75-20624.     

The Mathematical Theory of Ito Diffusions on Hypersurfaces, with Applications to NMR Relaxation Problems

A mathematical framework for translational Brownian motion on hypersurfaces is presented, using an imbedding of the surface and Ito diffusions in the ambient space. This includes a survey of Ito calculus and differential geometry. Computational methods for time correlation functions relevant to spin relaxation studies on curved interfaces are given, and explicit calculations of time correlation functions and order parameters for a Rippled surface are presented.     

Accurate values for the nonrelativistic energies of the lowest singlet and triplet S-states of the4He-Isotop

Accurate lower and upper bounds for the nonrelativistic lowest energies¹ E ₀ and³ E ₀ of the singlet and triplet-system of the⁴He-Isotop are calculated with the linearized method of variance minimization. The same was done for¹ E ₁ the energy of the first excitedS-state 2¹ S. The results especially for¹ E ₀ and³ E ₀ in a.u. are −2.9033076997₅ ≤¹ E ₀ ≤ −2.9033076921₈ −2.1749324263₇ ≤³ E ₀ ≤ −2.1749324245₉ i.e. the values are determined with an absolute error smaller than 0.00167 cm⁻¹ for¹ E ₀ and 0.00039 cm⁻¹ for³ E ₀.     

THE CORRELATION EFFECT ON THE CHAIN MOTION CONTRIBUTION TO IONIC TRANSPORT IN POLYMER ELECTROLYTES

The ionic transport process in polymer electrolytes (such as polyethylene oxide) wassimulated numerically on a two dimensional square lattice where charge carriers areaccommodated by the lattice sites connected randomly with available bonds to represent theamorphous chain configuration. Following the dynamic bond percolation theory(DBPT),the chainmotion contribution to the ionic conduction was incorporated via periodical renewal of the randombond configuration. To check and extend the prediction made by DBPT employing global abruptbond renewal,spatial correlation of the bond reassignment was introduced to the system by: 1)regional bond renewal and 2) organized bond motion. It is found that the difference between thediffusivities simulated involving regional bond renewal and those of DBPT becomes negligiblewhen the bond renewal rate approaches the carrier hopping rate.