Comparing the orthogonal and homotopy functor calculi

Goodwillie’s homotopy functor calculus constructs a Taylor tower of approximations toF , often a functor from spaces to spaces. Weiss’s orthogonal calculus provides a Taylortower for functors from vector spaces to spaces. In particular, there is a Weiss towerassociated to the functor V ÞÑ FpSVq, where SVis the one-point compactification of V .In this paper, we give a comparison of these two towers and show that when F isanalytic the towers agree up to weak equivalence. We include two main applications, oneof which gives as a corollary the convergence of the Weiss Taylor tower of BO. We alsolift the homotopy level tower comparison to a commutative diagram of Quillen functors,relating model categories for Goodwillie calculus and model categories for the orthogonal calculus.

An energy based force prediction method for UD-CFRP orthogonal machining

The machining of carbon fiber reinforced polymer (CFRP) composite presents a significant challenge to the industry, and a better understanding of machining mechanism is the essential fundament to enhance the machining quality. In this study, a new energy based analytical method was developed to predict the cutting forces in orthogonal machining of unidirectional CFRP with fiber orientations ranging from 0° to 75°. The subsurface damage in cutting was also considered. Thus, the total specific energy for cutting has been estimated along with the energy consumed for forming new surfaces, friction, fracture in chip formation and subsurface debonding. Experiments were conducted to verify the validity of the proposed model.

Effect of heat treatment on reactivity-strength of alkali-activated natural pozzolans

Natural pozzolans can be activated and condensed with sodium silicate in an alkaline environment to synthesize high performance cementitious construction materials with low environmental impact. The nature of the starting materials including mineral composition, chemical composition and crystal structure groups affects the formation of the geopolymer gel phase. In this paper, the pozzolanic activities of five natural pozzolans are studied. From XRD and XRF results, most of the raw materials contain zeolite clay minerals and have a high loss on ignition. Therefore, before use, samples were calcined at 700, 800 and 900 °C, respectively. The improvement in pozzolanic properties was studied following heat treatment including calcinations and/or elevated curing temperature by using alkali solubility and compressive strength tests. The results show that pozzolan containing sodium zeolite clinoptilolite can be used to prepare a moderate to high strength binder by heat treatment and calcinations can impart disorder hornblende as a constituent of pozzolan with no amorphous phase to prepare a moderate strength binder.