Differential–algebraic equations in multibody system modeling

Numerical methods for the efficient integration of both stiff and nonstiff equations of motion of multibody systems having the form of differential-algebraic equations (DAE) of index 3 are discussed. Linear multi-step ABM and BDF methods are considered for the non-iterational integration of nonstiff DAE. The Park method is proposed for integration of stiff equations. This revised version was published online in June 2006 with corrections to the Cover Date.     

Weierstrass Points and Regular Maps

It was shown by G. A. Jones and the first author in [8] that underlying any map on a compact orientable surface S there is a natural complex structure making S into a Riemann surface. In this paper we consider regular maps and enquire about the Weierstrass points on the underlying Riemann surface. We are particularly interested to know when these are geometric, i.e. whether they lie at vertices, face-centres or edge-centres of the map.     

Distribution of melamine in polyester–melamine surface coatings cured under nonisothermal conditions

The influence of experimental cure parameters on the diffusion of reactive species in polyester–melamine thermoset coatings during curing has been investigated with X‐ray photoelectron spectroscopy and attenuated total reflectance Fourier transform infrared. The diffusion of melamine plays a vital role in the curing process and, therefore, in the ultimate properties of coatings. At a low (<20%) hexamethoxymethylmelamine (HMMM) crosslinker concentration, the matrix composition is uniform, but at high HMMM concentrations, excess HMMM rapidly segregates to the air–coating interface. The rate of migration is governed by the difference in the surface free energies of polyester and HMMM and the concentration gradient of HMMM between the bulk and the surface. An increased rate of energy absorption also increases the rate of migration of HMMM to the surface. A physical model has been proposed to explain this surface segregation phenomenon in terms of cocondensation and self‐condensation reactions. It suggests that an appropriate amount of melamine can be segregated on the surface and allowed to self‐condense to form a desired thickness of a melamine topcoat through the control of the binder composition and cure conditions. This technique can be implemented to apply a melamine topcoat during cure. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 83–91, 2004     

Influence of Particle Morphology and Flow Conditions on the Dispersion Behavior of Fumed Silica in Silicone Polymers

The dispersion behavior of agglomerates of several grades of fumed silica in poly(dimethyl siloxane) liquids has been studied as a function of particle morphology and applied flow conditions. The effects of primary particle size and aggregate density and structure on cohesivity were probed through tensile and shear strength tests on particle compacts. These cohesivity tests indicated that the shear strength of particle compacts was two orders of magnitude higher than the tensile strength at the same overall packing density. Experiments carried out in both steady and time‐varying simple‐shear flows indicate that dispersion occurs through tensile failure. In the steady‐shear experiments,enhanced dispersion was obtained at higher levels of applied stress and, at comparable levels of applied stress, dispersion was found to proceed faster at higher shear rates. Experiments conducted in time‐varying flows further corroborated the results obtained in tensile cohesivity tests. Experiments in which the mean and maximum stresses in the time‐varying flows were matched to the stresses produced in steady shear flows highlight the influence of flow dynamics on dispersion behavior.