Effect of disorder on relaxation in the one-dimensional Glauber model

We study the long-time relaxation of magnetization in a disordered linear chain of Ising spins from an initially aligned state. The coupling constants are ferromagnetic and nearest-neighbor only, taking valuesJ ₀ andJ ₁ with probabilitiesp and 1–p, respectively. The time evolution of the system is governed by the Glauber master equation. It is shown that for large timest, the magnetizationM(t) varies as [exp(–₀ t](t), where ₀ is a function of the stronger bond strengthJ ₀ only, and (t) decreases slower than an exponential. For very long times, we find that ln (t) varies as –t ^1/3. For low enough temperatures, there is an intermediate time regime when ln (t) varies as –t ^1/2. The results can be extended to more general probability distributions of ferromagnetic coupling constants, assuming thatM(t) can only increase if any bond in the chain is strengthened. If the coupling constants have a continuous distribution in which the probability density varies as a power law near some maximum valueJ ₀, we find that ln (t) varies as –t ^1/3(lnt)^2/3 for large times.     

单向应力条件下松弛时间率相关的非线性粘弹性本构模型

基于单向拉伸实验研究和内变量理论 ,提出了一种新的简单的一维非线性粘弹性本构关系 .对两种粘弹性材料 ,即高密度聚乙烯和聚丙烯进行了不同加载速率作用下的拉伸实验研究 ,实验结果表明 ,两种材料的应力应变关系与加载速率相关 ;对材料的应力应变实验数据进行拟合发现 ,材料的松弛时间具有很强的应变率相关性 ,当应变率发生数量级变化时 ,材料的松弛时间也发生数量级的变化 .采用内变量理论 ,导出了在单轴应力条件下松弛时间率相关的非线性粘弹性本构关系的迭代形式 ,并给出其收敛条件 .当采取一次迭代形式时 ,本构关系退化为松弛时间率相关的Maxwell模型 .数值拟合的结果表明 ,一次迭代形式的本构关系就可以很好地拟合和预测实验结果 .     

Temperature Dependent Dielectric Relaxation in Solvent Mixtures at Microwave Frequencies

By the use of time domain reflectometry method, dielectric measurements were carried out on dimethylformamide‐2‐nitrotoluene solvent mixtures in the frequency range 10 MHz‐20 GHz, at various temperatures from 15 °C to 45 °C. These solvent mixtures as well as pure solvents display a Debye type dispersion. Their frequency dependent dielectric properties can be summarized by the three parameters in the Debye equation: a static permittivity, permittivity at high frequency and a dielectric relaxation time constant. The free energy of activation for dipolar relaxation process and the Kirkwood correlation factor were determined using these fitting parameters for these solvent mixtures at various concentrations and temperatures. By using these dielectric parameters, the excess permittivity and excess inverse relaxation time is obtained. The excess permittivity is found to be positive for all concentrations and temperatures whereas the excess inverse relaxation time is negative.     

用~(13)C NMR弛豫研究星形聚苯乙烯在溶液中的分子运动(Ⅱ)

对不同支化度和不同支链链长的20％(W/V)星形聚苯乙烯溶液测定了~(13)C NMR弛豫参数,用1g-x~2分布、Cole-Cole分布和构象跳跃模型对主链的分子运动进行了分析讨论,并对芳环侧基的内旋转运动也进行了分析,求出了活化能和跳跃速率。结果表明,轻度化学交联对相关时间分布有一定影响,对链段运动的势垒没有明显影响。支链链长对~(13)C NMR弛豫的影响和对线形聚合物的影响是类似的。     

The relaxation field for the general case of electrolyte mixtures

The relaxation field for solutions of mixed electrolytes of any type is calculated. the calculation is based on the well-known treatment due to Fuoss-Onsager with the same distance parameter for all the ions in solution. A general conductance-continuity equation has been established and an improved iterative method of calculation, using Laplace transforms, is proposed. The relaxation-field results are derived to the second iteration in the perturbation method of integration.     

Dipolar relaxations in an epoxy-amine system

Dipolar relaxations in a reactive epoxy-amine system based on diglycidyl ether of bisphenol A with 4,4^′-diaminodiphenylsulfone were studied with the Havriliak-Negami function. The system was cured isothermally at 140 °C using simultaneous kinetic and microdielectric studies.The relaxation time was calculated from the frequency f_max of the peak of the loss factor ε^′′ versus frequency f. A linear relation exists between the logarithm of the relaxation time τ and the glass transition temperature T_g. Then, logτ follows the Di Benedetto equation revisited by Pascault and Williams allowing the prediction of the relaxation time τ during cure.The unrelaxed permittivity at high frequency ε_u, the relaxed or static permittivity ε_s and the skewness parameter β were found independent on the conversion or the curing time. The distribution parameter α decreases as curing time t increases. The difficulty of orientation of dipoles in the electric field due to vitrification is responsible of these behaviours.     

Precise and accurate quantitative C NMR with reduced experimental time

In order to detect small variations in ¹³C isotopomers concentrations, high sensitivity, accuracy and precision have to be achieved. To assess such criteria, when using ¹³C NMR, ¹³C bi-labelled ethanol has been proposed as a molecular probe. Advantage has been taken of the pre-established structural relationship between the peak areas of the ¹³C NMR spectrum of this molecule, i.e. the ratio of signal areas is set to a fixed value. It is shown that the quality performance, required by quantitative ¹³C NMR spectroscopy, is not affected by a large reduction of the repetition delay using relaxation reagents.     

H and H NMR studies of cyclohexane nanocrystals in controlled pore glasses

The formation and behaviour of cyclohexane and cyclohexane-d₁₂ nanocrystals in mesoporous solids of well-defined dimensional constraints are studied by ¹H and ²H NMR. The NMR line widths, spin–spin relaxation times (T₂), spin–lattice relaxation times (T₁) and diffusivities (D) were measured as a function of temperature, and the results are discussed with reference to the values obtained for the bulk materials. The confined solids exhibit substantial changes in the phase behaviour and molecular dynamics. Thus, the line-shape measurements reveal a two-phase system consisting of a highly mobile component at the surface of the pore and a plastically crystalline phase in the centre of the pore. The liquid-like surface layer in the mesopores is observable well below the reduced transition temperature of the confined cyclohexane. However, the T₂ and diffusion measurements show that the mobile phase also embraces a minor component attributed to non-frozen liquid in pockets or offshoots.     

Thermal analysis study of Bi<Subscript>2</Subscript>Sr<Subscript>2</Subscript>Ca<Subscript>2</Subscript>Cu<Subscript>3-x</Subscript>Er<Subscript>x</Subscript>O<Subscript>10+δ</Subscript> glass-ceramic system

Summary We have fabricated glasses in the Bi-2223 HT_c superconductor system with Bi₂Sr₂Ca₂Cu_3-xEr_xO_{10+ δ} nominal composition, where x=0.5 and 1.0, by the glass-ceramic technique. Using an analysis developed for non-isothermal crystallization studies, information on some aspects of crystallization temperature and thermal properties has been obtained. The crystallization studies were made using DTA with several uniform rates. The calculations of crystallization activation energies, E_a, and the Avrami parameters, n, were made based on the non-isothermal kinetic theory of Kissinger and the Ozawa’s equations. The DTA data of the samples showed that the first crystallization temperature, T_x1, increases and the second crystallization temperature, T_x2, decreases by increasing the Er concentration. This suggests that the Er substitution had significant effect on the glassification of the BSCCO material due to change on the surface nucleation and increased ionic activities at high temperature region. The activation energy for crystallization, E_a, of the samples was also showed an increase at high Er concentration case. However, the Avrami parameter, n, decreased from 2.5 to 1.7 for x=0.5 and 1.0 samples, respectively. This suggests that the growth mechanism is diffusion-controlled and three-dimensional parabolic growth takes place near the first crystallization temperature. The oxidization rates and the activation barrier for oxygen out-diffusion process, E, was calculated using the TG data. It was found that the total mass gain in the x=0.5 sample is comparably smaller than that of the x=1.0 sample. This shows that the oxygen absorption of the x=1.0 sample is faster than the x=0.5 sample, leading to increase in the oxidization rate in the x=1.0 material.     

A class of random field memory models for mortality forecasting

This article proposes a parsimonious alternative approach for modeling the stochastic dynamics of mortality rates. Instead of the commonly used factor-based decomposition framework, we consider modeling mortality improvements using a random field specification with a given causal structure. Such a class of models introduces dependencies among adjacent cohorts aiming at capturing, among others, the cohort effects and cross generations correlations. It also describes the conditional heteroskedasticity of mortality. The proposed model is a generalization of the now widely used AR-ARCH models for random processes. For such a class of models, we propose an estimation procedure for the parameters. Formally, we use the quasi-maximum likelihood estimator (QMLE) and show its statistical consistency and the asymptotic normality of the estimated parameters. The framework being general, we investigate and illustrate a simple variant, called the three-level memory model, in order to fully understand and assess the effectiveness of the approach for modeling mortality dynamics.