Estimating the complexity of a class of path-following methods for solving linear programs by curvature integrals

In this paper we study a particular class of primal-dual path-following methods which try to follow a trajectory of interior feasible solutions in primal-dual space toward an optimal solution to the primal and dual problem. The methods investigated are so-called first-order methods: each iteration consists of a long step along the tangent of the trajectory, followed by explicit recentering steps to get close to the trajectory again. It is shown that the complexity of these methods, which can be measured by the number of points close to the trajectory which have to be computed in order to achieve a desired gain in accuracy, is bounded by an integral along the trajectory. The integrand is a suitably weighted measure of the second derivative of the trajectory with respect to a distinguished path parameter, so the integral may be loosely called a curvature integral.     

Effect of temperature on the surface free energy of amorphous carbon films

Diamond-like carbon (DLC) and tetrahedral amorphous carbon (ta-C) have attracted much attention recently for biomedical and antifouling applications due to their excellent biocompatibility and inherent nonstick properties. It has been demonstrated that the solid surface free energy is a dominant factor in cellular or fouling adhesion. However, few data for the surface free energy of DLC and ta-C coatings at temperatures in the range 37-95 degrees C are available. In this study DLC and ta-C coatings on stainless steel 304 sheets were prepared using an unbalanced magnetron sputtering system and a filtered cathodic vacuum arc system, respectively. The contact angles of water, diiodomethane and ethylene glycol on the coated surfaces at temperatures in the range 20-95 degrees C were measured using a Dataphysics OCA-20 contact angle analyzer. The surface free energy of the coatings and their components (e.g., dispersion, polar or acid/base portions) were calculated using various methods. The experimental results showed that the total surface free energy and dispersive surface free energy of the ta-C coatings, DLC coatings, stainless steel 304 and titanium decreased with increasing surface temperature, while the acid-base SFE component increased with increasing temperature.