Relationship between Fujikawa's Method and the Background Field Method for the Scale Anomaly

We show the equivalence between Fujikawa's method for calculating the scale anomaly and the diagrammatic approach to calculating the effective potential via the background field method, for an $O(N)$ symmetric scalar field theory. Fujikawa's method leads to a sum of terms, each one superficially in one-to-one correspondence with a vacuum diagram of the 1-loop expansion. From the viewpoint of the classical action, the anomaly results in a breakdown of the Ward identities due to a scale-dependence of the couplings, whereas in terms of the effective action, the anomaly is the result of the breakdown of Noether's theorem due to explicit symmetry breaking terms of the effective potential.Comment: 9 pages (this version is the published version

Time-reversal symmetric resolution of unity without background integrals in open quantum systems

We present a new complete set of states for a class of open quantum systems, to be used in expansion of the Green's function and the time-evolution operator. A remarkable feature of the complete set is that it observes time-reversal symmetry in the sense that it contains decaying states (resonant states) and growing states (anti-resonant states) parallelly. We can thereby pinpoint the occurrence of the breaking of time-reversal symmetry at the choice of whether we solve Schroedinger equation as an initial-condition problem or a terminal-condition problem. Another feature of the complete set is that in the subspace of the central scattering area of the system, it consists of contributions of all states with point spectra but does not contain any background integrals. In computing the time evolution, we can clearly see contribution of which point spectrum produces which time dependence. In the whole infinite state space, the complete set does contain an integral but it is over unperturbed eigenstates of the environmental area of the system and hence can be calculated analytically. We demonstrate the usefulness of the complete set by computing explicitly the survival probability and the escaping probability as well as the dynamics of wave packets. The origin of each term of matrix elements is clear in our formulation, particularly the exponential decays due to the resonance poles.Comment: 62 pages, 13 figure

Waste Gasification

This document summarizes the work the IGT Team has conducted on the topic of waste to energy gasification over the Cal Poly Winter, Spring, and Fall quarters of 2019. The project is being carried out by four Cal Poly Mechanical Engineering students: Nash Taylor, Glyn Lewis, David McCallum, and Nicholas Ordonez and the sponsor of this project is Tod duBois. The team’s original goal was to successfully create a system that compiles residential solid waste on a small scale, gasifies it, and measures the typical syngas outputs, so that the team may assess the viability of gasification of household waste on a small scale. The project has drastically changed multiple times and the changes have been documented throughout this paper. Due to safety concerns and uncertainty regarding the prototype vessel, the team’s final goal is to prove successful gasification using their keg based system. The team has spent most of the quarters conducting researching and narrowing the scope of work to something they believe they can successfully and manageably complete over the next year. The purpose of this document is to summarize the research, present and justify some design choices, and present the design solution as resolved to the current date

Mitigation of EMU Cut Glove Hazard from Micrometeoroid and Orbital Debris Impacts on ISS Handrails

Recent cut damages sustained on crewmember gloves during extravehicular activity (ISS) onboard the International Space Station (ISS) have been caused by contact with sharp edges or a pinch point according to analysis of the damages. One potential source are protruding sharp edged crater lips from micrometeoroid and orbital debris (MMOD) impacts on metallic handrails along EVA translation paths. A number of hypervelocity impact tests were performed on ISS handrails, and found that mm-sized projectiles were capable of inducing crater lip heights two orders of magnitude above the minimum value for glove abrasion concerns. Two techniques were evaluated for mitigating the cut glove hazard of MMOD impacts on ISS handrails: flexible overwraps which act to limit contact between crewmember gloves and impact sites, and; alternate materials which form less hazardous impact crater profiles. In parallel with redesign efforts to increase the cut resilience of EMU gloves, the modifications to ISS handrails evaluated in this study provide the means to significantly reduce cut glove risk from MMOD impact crater