Relaxation dynamics of stretched polymer chains traced by shear induced Shish‐Kebab structure

We have developed a morphologic method to investigate the relaxation processing of the stretched polymer chains in melts, in which an atomic force microscope probe was used to shear the surface of an isotactic polypropylene melt to obtain the isolated shish‐kebab structure. We present the results of the time dependence of length of the isolated shish‐kebab structure and the stress dependence of the kebab density along the direction of shish in this paper. Our results demonstrate that the shear‐oriented polymer melts show the relaxation dynamics of worm‐like chain where the length deficit of the isolated shish‐kebab structure is scaled with the relaxation time as a power of 1/3. The melting behavior of shish‐kebab structure was also investigated. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2013, 51, 907–914     

Frequency‐dependent NMR relaxation of liquids confined inside porous media containing an increased amount of magnetic impurities

Frequency‐dependent NMR relaxation studies have been carried out on water (polar) and cyclohexane (nonpolar) molecules confined inside porous ceramics containing variable amounts of iron oxide (III). The porous ceramics were prepared by compression of powders mixed with iron oxide followed by thermal treatment. The pore size distribution was estimated using a technique based on diffusion in internal fields that exposed a narrow distribution of macropore sizes with an average pore dimension independent of iron oxide content. The relaxation dispersion curves were obtained at room temperature using a fast field cycling NMR instrument. They display an increase of the relaxation rate proportional to the iron oxide concentration. This behavior is more prominent at low Larmor frequencies and is independent of the polar character of the confined molecules. The results reported here can be fitted well with a relaxation model considering exchange between molecules in the close vicinity of the paramagnetic centers located in the surface and bulk‐like molecules inside the pores. This model allows the extraction of the transverse diffusional correlation time that can be related to the polar character of the confined molecules. Copyright © 2013 John Wiley & Sons, Ltd.     

Increased Rigidity in Complexes Formed from Negatively Charged Lariat Ethers and Alkali Metal Cations

Abstract

C-13 NMR longitudinal relaxation times have been measured for lariat ether complexes in which a negative charge is present in the ligand but the system is diamagnetic. A -CH₂COO^? group connected to the nitrogen of aza-15-crown-5 results in drastically increased T₁'s in the presence of Li⁺ compared to the values for the free carboxylic acid and for the acid in the presence of LiClO₄. Longer relaxation times upon complexation show the ‘cryptand-like’ behavior of the complexes, resulting from overall molecular reorientation rates due to compression. These conclusions are supported by molecular mechanics calculations described herein.     

Frequency domain measurements on Na2B4O7−V2O5 semiconducting glass

Summary Dielectric measurements on Na₂B₄O₇(99.5%)−V₂O₅(0.5%) glass system, in the frequency range 10⁻³ to 10⁴ Hz and temperature range 300 to 500 K, have been carried out. The normalized plots of complex capacitance have shown a single mechanism responsible for conduction for both volume and surface measurements with their close values of activation energies (0.67±0.03) eV and (0.64±0.03) eV, respectively. The low-frequency dispersion (LFD) behaviour has been observed to be perturbed by the presence of more than one competing process. The impedance plots have shown a parallel combination of a capacitor (C) and a resistor (R), with some contribution of a dispersive element due to charge accumulation in the vicinity of the electrodes. The values ofR andC were found to be of the same order of magnitude, for both surface and volume measurements. The observedR has shown a decrease with an increase in temperature due to an increase in mobility of Na⁺ ions, whereasC remains practicaly constant. The complex capacitance surface behaviour is dominated by volume, due to hygroscopy of this glass system.     

过渡金属羰基化合物Mn(CO)5Br和Re(CO)5Br结构与动力学的超快光谱

利用超快泵浦探测红外光谱、稳态线性红外光谱和计算化学方法,对过渡金属羰基化合物Mn(CO)₅Br和Re(CO)₅Br的振动和结构动力学进行了研究. 借助羰基的两个伸缩振动峰(处于低频的A₁模式和处于高频的简并E模式)进行了观测. 结果表明,在两个配合物中,A₁和E模式振动峰的振动频率位置及频率差都与中心金属原子对羰基的键级和振动力常数的影响相关. 而A₁模式比E模式的线宽宽一些,部分由于振动寿命的影响. 此外,从瞬态光谱中获得了振动模式依赖的对角非谐性常数,发现在两个羰基化合物中E模式的非谐性总是较小.     

The smallest point of a polytope

This note suggests new ways for calculating the point of smallest Euclidean norm in the convex hull of a given set of points inR ⁿ . It is shown that the problem can be formulated as a linear least-square problem with nonnegative variables or as a least-distance problem. Numerical experiments illustrate that the least-square problem is solved efficiently by the active set method. The advantage of the new approach lies in the solution of large sparse problems. In this case, the new formulation permits the use of row relaxation methods. In particular, the least-distance problem can be solved by Hildreth's method.     

Some Properties for the Euclidean Distance Matrix and Positive Semidefinite Matrix Completion Problems

The Euclidean distance matrix (EDM) completion problem and the positive semidefinite (PSD) matrix completion problem are considered in this paper. Approaches to determine the location of a point in a linear manifold are studied, which are based on a referential coordinate set and a distance vector whose components indicate the distances from the point to other points in the set. For a given referential coordinate set and a corresponding distance vector, sufficient and necessary conditions are presented for the existence of such a point that the distance vector can be realized. The location of the point (if it exists) given by the approaches in a linear manifold is independent of the coordinate system, and is only related to the referential coordinate set and the corresponding distance vector. An interesting phenomenon about the complexity of the EDM completion problem is described. Some properties about the uniqueness and the rigidity of the conformation for solutions to the EDM and PSD completion problems are presented.     

An Open Question on Cyclic Relaxation

The problem discussed in this note is highly interesting. It is related to several dual iterative methods, such as the methods proposed by Kaczmarz, Hildreth, Agmon, Cryer, Mangasarian, Herman, Lent, Censor, and others. Cast as row-action methods these algorithms have been proved as useful tools for solving large convex feasibility problems that arise in medical image reconstruction from projections, in inverse problems in radiation therapy, and in linear programming.The question that we want to answer is how these algorithms behave when the feasible region is empty. It is shown that under certain conditions the primal sequence still converges while the dual sequence {y _k } obeys the rule y _k =u _k +k v, where {u _k } is a converging sequence and v is a fixed vector that satisfies A ^T v=0,v0,and,b ^T v>0. It is conjectured that these properties hold whenever the feasible region is empty. However, the validity of this claim remains an open question.This revised version was published online in October 2005 with corrections to the Cover Date.     

On the Global Stability of Solutions of Moment Systems in Nonequilibrium Thermodynamics

In this paper, we study the linearization of the Cauchy problem and the mixed problem for the system of Grad--Hermite moments in nonequilibrium thermodynamics in the neighborhood of the equilibrium state. Stability conditions for solutions of the Cauchy problem are proved as a generalization of the classical Hermite--Biller theorem on stable polynomials. For the mixed problem, we prove an analog of the Vishik--Lyusternik theorem on small singular perturbations of general elliptic problems. The last observation allows us to introduce the Shapiro--Lopatinskii condition, which implies the well-posedness of the mixed problem.     

Two exact algorithms for the capacitated p-median problem

The p-median problem has been widely studied in combinatorial optimisation, but its generalisation to the capacitated case has not. We propose a branch and price algorithm, comparing it with a standard MIP solver and a branch and bound algorithm based on Lagrangean relaxation. We present computational experience, using test instances drawn from the literature and new instances with higher ratio between the number of medians p and the number of nodes N. The branch and price algorithm shows very good performances and computational time robustness in solving problems for any ratio.Received: December 2002, Revised: August 2003AMS classification: 90C10, 90C27