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.

What is the Point of Copyright History?

Copyright history has long been a subject of intense and contested enquiry, and has once again become the subject of critical scrutiny with the publication of "Copyright at Common Law in 1774" by Prof Tomas Gomez-Arostegui in the Connecticut Law Review ((2014) 47 Conn. L. Rev. 1).
This online resource documents two events organised to explore the impact of "Copyright at Common Law in 1774". It incorporates a public lecture by Prof Gomez-Arostegui, and the full record of a one-day symposium of international experts debating the implications of Gomez-Arostegui's scholarship in this domain.

High resolution numerical simulation of triple point collision and origin of unburned gas pockets in turbulent detonations

A key issue in pulse detonation engine development is better understanding of the detonation structure and its propagation mechanism. Thus, in the present work the turbulent structure of an irregular detonation is studied through very high resolution numerical simulations of 600 points per half reaction length. The aim is to explore the nature of the transverse waves during the collision and reflection processes of the triple point with the channel walls. Consequently the formation and consumption mechanism of unreacted gas pockets is studied. Results show that the triple point and the transverse wave collide simultaneously with the wall. The strong transverse wave switches from a primary triple point before collision to a new one after reflection. Due to simultaneous interaction of the triple point and the transverse wave with the wall in the second half of the detonation cell, a larger high-pressurised region appears on the wall. During the reflection the reaction zone detaches from the shock front and produces a pocket of unburned gas. Three mechanisms found to be of significance in the re-initiation mechanism of detonation at the end of the detonation cell; i: energy resealed via consumption of unburned pockets by turbulent mixing ii: compression waves arise due to collision of the triple point on the wall which helps the shock to jump abruptly to an overdriven detonation iii: drastic growth of the Richtmyer–Meshkov instability causing a part of the front to accelerate with respect to the neighbouring portions.