A bifurcation study is made of laminar flow in curved ducts. The problem is formulated in a curvilinear coordinate system, and the governing equations, after orthogonal mapping is applied, are solved numerically by an iterative finite-difference method. Many computer runs were made with various duct cross-sections ranging from a circle to a square, to learn the transition of bifurcation structure with this change in cross-section and to reconcile the differences between them. In addition, a simpler technique is proposed to generate symmetric four-cell solutions in a circular pipe and a means is put forward to stabilize four-vortex structures in a complete cross-section.

Two approaches have been used to study the torsion effect on the fully developed laminar flow in a helical pipe of constant circular cross-section. The first approach is the series expansion method that perturbs the Poiseuille flow and is valid for low Dean numbers with both the dimensionless curvature and dimensionless torsion being much less than unity. The second is a numerical procedure that solves the complete Navier-Stokes equation and is applicable to intermediate values of the Dean number. The results obtained indicate that, as far as the secondary flow patterns are concerned, the presence of torsion can produce a large effect if the ratio of the curvature to the torsion is of order unity. In these cases the secondary flow, though still consisting of a pair of vortices, can be very much distorted. Under extreme conditions one vortex is so prevalent as to squeeze the second one into a narrow region. However, ordinarily the torsion effect is small and the secondary flow has the usual pattern of a pair of counter-rotating vortices of nearly equal strength. Concerning the flow resistance in the pipe the effect of torsion is always small in all the circumstances that have so far been considered.

A method for obtaining analytic solutions to the problem of blunt bodies in the supersonic stream of an ideal gas is presented. The solutions are written in terms of power series whose coefficients are elementary functions. These solutions are approximate, but the approximation is rational, i.e. any higher approximation can, in principle, be obtained. Some of these higher approximations have been calculated. Examples are presented for various free-stream conditions and prescribed body shapes. These are compared with results from standard numerical procedure and with available experimental measurements.

The atomic force microscopic technique is utilized to study the spatial distribution of silica nanoparticles embedded in poly(tetraethylene glycol diacrylate) matrix. The cast samples of these hybrid materials show distinct mechanical property change as the weight ratio (SiO2/polyacrylate) reaches 40%. The morphological observation from spin-coated films on silicon substrates shows pronounced nanoparticle network formation correlated to the elasticity transition. The percolating particles reduce the local strain field, i.e. inhibit the deformation of the stratum, and cause the dramatic increase in the Young's modulus. Our experimental result is consistent with recent theoretical prediction [1].