Studies on solution cast perfluorocarbonsulfonic acid ionomers

The thermal properties of perfluorocarbonsulfonic acid ionomer films cast from solution and their temperature-dependent far infrared spectra have been investigated. In addition to the endotherms and spectral changes associated with the loss of solvent as the films were heated, a significant exotherm has been observed and assigned to the relaxation associated with rearrangements resulting in partially crystallized phases in insoluble thermally treated membranes. © 1993 John Wiley & Sons, Inc.     

气密性碳涂覆光纤筛选强度与电阻关系研究

通过实验分析确立了把光纤电阻作为衡量气密性碳涂覆光纤通过２％应变筛选的过渡标准。要拉制２％应变筛选的碳涂覆光纤，其电阻值应小于３０ｋΩ／ｃｍ。     

Interval parameter perturbation method for evaluating the bounds on natural frequencies of structures with interval parameters

For structural parameters with uncertainties, interval mathematics can, in the case where the probabilistic distribution density of uncertain variables is unavailable, deal with the influence of uncertainties in structural parameters on the response of structures. In order to evaluate the region containing natural frequencies of structures with interval parameters, the interval parameter perturbation method is presented in this paper. The advantage of the present method is its computational efficiency in evaluating the region containing natural frequencies. A numerical example is used to illustrate the efficiency of the method proposed. The project is supported by National Youth Natural Science Foundation of China and National Outstanding Youth Science Foundation of China.     

Nuclear spin-lattice relaxation mechanisms in kaolinite confirmed by magic-angle spinning

Spin-lattice relaxation mechanisms in kaolinite have been reinvestigated by magic-angle spinning (MAS) of the sample. MAS is useful to distinguish between relaxation mechanisms: the direct relaxation rate caused by the dipole-dipole interaction with electron spins is not affected by spinning while the spin diffusion-assisted relaxation rate is. Spin diffusion plays a dominant role in ¹H relaxation. MAS causes only a slight change in the relaxation behavior, because the dipolar coupling between ¹H spins is strong. ²⁹Si relaxes directly through the dipole-dipole interaction with electron spins under spinning conditions higher than 2 kHz. A spin diffusion effect has been clearly observed in the ²⁹Si relaxation of relatively pure samples under static and slow-spinning conditions. ²⁷Al relaxes through three mechanisms: phonon-coupled quadrupole interaction, spin diffusion and dipole-dipole interaction with electron spins. The first mechanism is dominant, while the last is negligibly small. Spin diffusion between ²⁷Al spins is suppressed completely at a spinning rate of 2.5 kHz. We have analyzed the relaxation behavior theoretically and discussed quantitatively. Concentrations of paramagnetic impurities, electron spin-lattice relaxation times and spin diffusion rates have been estimated.     

On the relationship betweenT 1 andT 2 for stochastic relaxation models

We consider the relaxation dynamics of two quantum levels coupled to a stochastic bath. We emphasize that even if the matrix elements of the fluctuating Hamiltonian are Gaussian, a second-order cumulant truncation is not exact. For various stochastic models, including the case of a spin-1/2 particle in a fluctuating magnetic field, we calculate 1/T ₁, the population relaxation rate, and 1/T ₂, the phase relaxation rate, up to fourth order in perturbation theory. We show that unlike the commonly accepted second-order result that 1/T ₂1/2T ₁, when fourth-order terms are included, in some instances 1/T ₂<1/2T ₁.     

Dynamical systems with relaxation time

We define mathematically a class of dynamical systems that exhibit relaxation corresponding to that observed in physical systems, and then show that this class is identical with the class ofK-mixing dynamical systems.     

Time-resolved fluorescence relaxation of 3-methyllumiflavin in polar solution

We have studied the fluorescent properties of a well-defined model flavin compound (3-methyllumiflavin) in a relatively polar solvent like propylene glycol or ethanol. Inhomogeneous spectral broadening effects were directly time-resolved by detection at the extreme blue and red edges of the fluorescence band of 3-methyllumiflavin using excitation in the main absorption band. At the high-energy side of the emission band a rapid decay component (tens of picoseconds) was resolved indicative for the disappearance of the initially prepared, nonequilibrium state with a characteristic dipolar relaxation time. At the low-energy side the rise of a solvent relaxed fluorescent species could be time-resolved. The wavelength-dependent effects on the dipolar relaxation were abolished when excitation was at the low-energy side of the absorption band. The experimental decays of the flavin solvate at different energies of fluorescence and excitation are presented as they represent an easy diagnosis for energy dependent solvation dynamics. Wavelength dependent rotation of 3-methyllumiflavin, examined by fluorescence anisotropy decay, turned out to be absent for 3-methyllumiflavin in propylene glycol between 263 and 293 K, probably because of the small change in dipole moment upon flavin excitation.     

Parameter choice by discrepancy principles for ill-posed problems leading to optimal convergence rates

Schock (Ref. 1) considered a general a posteriori parameter choice strategy for the Tikhonov regularization of the ill-posed operator equationTx=y which provides nearly the optimal rate of convergence if the minimal-norm least-squares solution belongs to the range of the operator (T ^* T) ^v , o<v1. Recently, Nair (Ref. 2) improved the result of Schock and also provided the optimal rate ifv=1. In this note, we further improve the result and show in particular that the optimal rate can be achieved for 1/2v1.The final version of this work was written while M. T. Nair was a Visiting Fellow at the Centre for Mathematics and Its Applications, Australian National University, Canberra, Australia. The work of S. George was supported by a Senior Research Fellowship from CSIR, India.     

The Newton modified barrier method for QP problems

The Modified Barrier Functions (MBF) have elements of both Classical Lagrangians (CL) and Classical Barrier Functions (CBF). The MBF methods find an unconstrained minimizer of some smooth barrier function in primal space and then update the Lagrange multipliers, while the barrier parameter either remains fixed or can be updated at each step. The numerical realization of the MBF method leads to the Newton MBF method, where the primal minimizer is found by using Newton's method. This minimizer is then used to update the Lagrange multipliers. In this paper, we examine the Newton MBF method for the Quadratic Programming (QP) problem. It will be shown that under standard second-order optimality conditions, there is a ball around the primal solution and a cut cone in the dual space such that for a set of Lagrange multipliers in this cut cone, the method converges quadratically to the primal minimizer from any point in the aforementioned ball, and continues, to do so after each Lagrange multiplier update. The Lagrange multipliers remain within the cut cone and converge linearly to their optimal values. Any point in this ball will be called a hot start. Starting at such a hot start, at mostO(In In ^-1) Newton steps are sufficient to perform the primal minimization which is necessary for the Lagrange multiplier update. Here, >0 is the desired accuracy. Because of the linear convergence of the Lagrange multipliers, this means that onlyO(In ^-1)O(In In ^-1) Newton steps are required to reach an -approximation to the solution from any hot start. In order to reach the hot start, one has to perform Newton steps, wherem characterizes the size of the problem andC>0 is the condition number of the QP problem. This condition number will be characterized explicitly in terms of key parameters of the QP problem, which in turn depend on the input data and the size of the problem.Partially supported by NASA Grant NAG3-1397 and National Science Foundation Grant DMS-9403218.     

Langevin dynamic simulation of hysteresis in a field-swept Landau potential

Numerical simulations are done of Langevin dynamics for a uniform-orderparameter, field-swept Landau model,= –|a/2|m ²+|b/4|m ⁴–mh(t) , to study hysteresis effects. The field is swept at a constant rateh(t)=h(0)+ht. The stochastic jump values of the field {h_J from an initially prepared metastable minimumm(0) are recorded, on passage to a global minimum m(). The results are: (a) The mean jump¯h _J(h) increases (hysteresis loop widens) with h, confirming a previous theoretical criterion based on rate competition between field-sweep and inverse mean first-passage time (FPT); (b) The broad jump distribution(h _J,h) is related to intrinsically large FPT fluctuations ( ²–²)/ ² O(1), and can be quantitatively understood. Possible experimental tests of the ideas are indicated.