On the Motion of a Dynamic System with Minimal Dissipation

The motion of a holonomic scleronomic non-conservative mechanicalsystem with minimal dissipation is considered. As applicationsof the theory several problems are studied in detail.     

Generalized Derivatives for Solutions of Parametric Ordinary Differential Equations with Non-differentiable Right-Hand Sides

Sensitivity analysis provides useful information for equation-solving, optimization, and post-optimality analysis. However, obtaining useful sensitivity information for systems with nonsmooth dynamic systems embedded is a challenging task. In this article, for any locally Lipschitz continuous mapping between finite-dimensional Euclidean spaces, Nesterov’s lexicographic derivatives are shown to be elements of the plenary hull of the (Clarke) generalized Jacobian whenever they exist. It is argued that in applications, and in several established results in nonsmooth analysis, elements of the plenary hull of the generalized Jacobian of a locally Lipschitz continuous function are no less useful than elements of the generalized Jacobian itself. Directional derivatives and lexicographic derivatives of solutions of parametric ordinary differential equation (ODE) systems are expressed as the unique solutions of corresponding ODE systems, under Carathéodory-style assumptions. Hence, the scope of numerical methods for nonsmooth equation-solving and local optimization is extended to systems with nonsmooth parametric ODEs embedded.     

Gallium colloid formation during ion implantation of glass

Data are reported on the size and depth distribution of gallium colloids formed by gallium ion implantation at energies of 50 and 60 keV, and nominal doses up to 1.1 × 10¹⁷ ions/cm² into coverlip glass, float glass and white crown glass. Measurement techniques used to reveal colloid-induced changes include the wavelength dependence of optical reflectivity, transmission electron microscopy (TEM) and Rutherford backscattering (RBS). The reflectivity can be controlled by variations in ion dose, implant temperature and ion beam energy. The highest reflectivity is found after implants near 50°C and the level is extremely sensitive to the implant temperature. For controlled beam conditions, the reflectivity data are reproducible, despite there being variations in the colloid size and depth distributions as seen by TEM and RBS. The TEM data reveal that the depth distribution develops in two distinct regions, which at high concentration can precipitate into two layers of large colloids. Subsidiary experiments are reported to attempt to separate the effects of variations in the implant temperature and surface charging which influence the reflectivity, RBS and colloid formation.     

Pressure recovery in a radiused sudden expansion

Experiments on a steady flow through a nominally 2-D exit geometry with rounded edges are presented for the Reynolds number range 300<Re<25,000. The results indicate that the channel flow expands and decelerates upstream of the exit plane resulting in large pressure recovery, especially for turbulent channel flow. It is shown that pressure recovery is a function of the dimensionless edge radius and Re. Pressure recoveries of up to 20% are reported at large Re for dimensionless radii as small as r/h=0.625. It is also found that the rounded exit results in turbulence levels as much as 25% higher than sharp-edged exits.