A novel approach to the determination of the crosslink density in rubber materials with the dipolar correlation effect in low magnetic fields

We present a novel NMR approach to the determination of crosslink densities in rubber materials. The method is based on the dipolar correlation effect (DCE) on the stimulated echo examined in a series of rubber samples and linear polyisoprene. The parameter evaluated from the echo attenuation curves is the mean‐squared dipolar fluctuation associated with anisotropic reorientations of macromolecular backbones. The contributions to the DCE of the constraints due to excluded volume effects and chemical crosslinks are estimated. A strong dependence of the mean‐squared dipolar fluctuation on the crosslink density of rubber combined with the simplicity of performing the measurements with inexpensive low‐field instruments suggests that the DCE is a useful tool for routine applications. The potential and problems of performing DCE measurements in low‐magnetic‐field conditions are discussed in detail. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2207–2216, 2001     

Minimum Weight Design for Structural Eigenvalue Problems by Optimal Control Theory*, †

The application of optimal control theory to minimum weight design of continuous one-dimensional structural elements subject to eigenvalue constraints is discussed. If not only the value of an eigenvalue is prescribed but also its position in the sequence of the ordered eigenvalues—for example, the critical buckling load of a column—the corresponding optimal control problem is shown to include necessarily all eigenvalues. Considering the unspecified eigenvalues as free parameters, necessary conditions for minimum weight design are derived. These conditions are compared with those obtained by use of variational methods. Attention is focused on the special case of multimodal solutions.     

KRS and Powers of determinantal ideas

The goal of this paper is to determine Göbner bases of powers of determinantal ideals and to show that the Rees algebras of (products of) determinantal ideals are normal and Cohen–Macaulay if the characteristic of the base field is non-exceptional. Our main combinatorial result is a generalization of Schensted's Theorem on the Knuth–Robinson–Schensted correspondence.     

A Collocation Code for Singular Boundary Value Problems in Ordinary Differential Equations

We present a MATLAB package for boundary value problems in ordinary differential equations. Our aim is the efficient numerical solution of systems of ODEs with a singularity of the first kind, but the solver can also be used for regular problems. The basic solution is computed using collocation methods and a new, efficient estimate of the global error is used for adaptive mesh selection. Here, we analyze some of the numerical aspects relevant for the implementation, describe measures to increase the efficiency of the code and compare its performance with the performance of established standard codes for boundary value problems.     

Investigation of copolymers of styrene and ethyl methacrylate by size exclusion chromatography and gradient HPLC

Summary Copolymers of styrene and ethyl methacrylate have been separated according to composition by gradient HPLC on silica columns or CN bonded phase columns. This mode of separation according to composition was applied to fractions obtained by size exclusion chromatography (SEC). From viscosity and molecular mass data of copolymers with a styrene content ranging from 7.5 to 95.3 mass-% it can be concluded that SEC separates mainly by molecular mass even in this copolymer system. Thus, chromatographic cross-fractionation is possible by prefractionation by SEC and subsequent separation according to composition by gradient HPLC.

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Untersuchung von Copolymeren von Styrol und Ethylmethacrylat durch Ausschluß-Chromatographie und Gradienten-HPLC