Calcium‐containing poly(urethane‐urea)s: Synthesis,spectral, and thermal studies

A calcium salt of mono(hydroxypentyl)phthalate [Ca(HPP)₂] was synthesized by the reaction of 1,5‐pentanediol, phthalic anhydride, and calcium acetate. Four different bisureas such as hexamethylene bis(ω,N‐hydroxyethylurea), tolylene 2,4‐bis(ω,N‐hydroxyethylurea), hexamethylene bis(ω,N‐hydroxypropylurea), and tolylene 2,4‐bis(ω,N‐hydroxypropylurea) were prepared by reacting ethanolamine or propanolamine with hexamethylene diisocyanate (HMDI) or tolylene 2,4‐diisocyanate (TDI). Calcium‐containing poly(urethane‐urea)s (PUUs) were synthesized by reacting HMDI or TDI with 1:1 mixtures of Ca(HPP)₂ and each of the bisureas with di‐n‐butyltin dilaurate as a catalyst. The PUUs were well characterized by Fourier transform infrared spectroscopy, ¹H and ¹³C NMR, solid‐state ¹³C–cross‐polarization/magic‐angle spinning NMR, viscosity, solubility, elemental analysis, and X‐ray diffraction studies. Thermal properties of the polymers were also examined with thermogravimetric analyses and differential scanning calorimetry. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 1809–1819, 2004     

Analysis of a model for transport of charged particles in a random magnetic field

A model for the transport of charged particles in a random magnetic field is a Volterra integrodifferential equation with a long-range kernel. The integrodifferential equation is solved numerically with the method of Bellman, Kalaba, and Lockett (“Numerical Inversion of the Laplace Transform,” Elsevier, New York, 1966). The results are shown to be in excellent agreement with analytical asymptotic results.     

Moduli for principal bundles over algebraic curves: I

We classify principal bundles on a compact Riemann surface. A moduli space for semistable principal bundles with a reductive structure group is constructed using Mumford's geometric invarian theory.     

Magnetic behaviour of TbMnFe

Neutron diffraction and M?ssbauer measurements have been carried out on the cubic Laves phase intermetallic TbMnFe. The magnetic moment on the transition metal atom is found to be low, 0.2μ _B, at room temperature. This moment is temperature independent down to 10 K. Magnetic moment on the rare earth atom varies from 2.5μ _B at 296 K to 7.27μ _B at 10 K. M?ssbauer spectra recorded at 298 K and 78 K have magnetic character but there is a large distribution of hyperfine field values. Both these features arise due to magnetic frustration created in the sample due to the competing ferro and antiferromagnetic interactions between the transition metal atoms.     

Finite element study of free surface turbulent flow in rotating channels

Under certain conditions of liquid flow through rotating channels, the Coriolis force can induce a free surface to be formed. This problem is of practical importance in a Coriolis wear tester, which is used for determining the sliding wear coefficient of wear materials in slurry handling equipment. A deforming Galerkin finite element method is presented for predicting two‐dimensional turbulent free surface mean flow in rotating channels. Reynolds‐averaged Navier–Stokes (RANS) equations are cast into weak(algebraic) form using primitive variables (velocity and pressure). Eddy viscosity is determined via a mixing length model. Velocity is interpolated biquadratically, while pressure is interpolated bilinearly. The kinematic condition is used to form the Galerkin residual for the free surface. The free surface is represented by Hermite polynomials of zeroeth order for continuity of position and slope. Combined Newton's iteration is used to simultaneously solve for the free surface and the field variables. Results of velocity and pressure fields, as well as the free surface are shown to converge with mesh‐size refinement. There is excellent respect for mass conservation. Results are presented for various values of Rossby number (Ro) and height‐based Reynolds number (Re_H). Parameter continuation in Ro and Re_H space is used to compute solutions at higher values of flow rate and angular velocity. Copyright © 2002 John Wiley & Sons, Ltd.     

The applicability of an approximate expression for radiative heating

An analysis considering small departures from radiative equilibrium within a gas, for which radiative heating is approximately formulated in terms of a radiative response time, is compared with an exact solution. It is shown that the approximate formulation does not properly describe local departures from radiative equilibrium, although it is useful in a spatially averaged context.