Quantum fields on curved spacetimes and a new look at the Unruh effect

We describe a new viewpoint on canonical quantization of linear fields on a general curved background that encompasses and generalizes the standard treatment of canonical QFT given in textbooks. Our method permits the construction of pure states and mixed stated with the same technique. We apply our scheme to the study of Rindler QFT and we present a new derivation of the Unruh effect based on invariance arguments

Quantum Theory on Lobatchevski Spaces

In this paper we set up a general formalism to deal with quantum theories on a Lobatchevski space, i.e. a spatial manifold that is homogeneous, isotropic and has negative curvature. The heart of our approach is the construction of a suitable basis of plane waves which are eigenfunctions of the Laplace-Beltrami operator relative to the geometry of the curved space. These functions were previously introduced in the mathematical literature in the context of group theory; here we revisit and adapt the formalism in a way specific for quantum mechanics. Our developments render dealing with Lobatchevski spaces, which used to be quite difficult and source of controversies, easily tractable. Applications to the Milne and de Sitter universes are discussed as examples

Constraining the strength of Dark Matter Interactions from Structure Formation

We discuss the damping of primordial dark matter fluctuations, taking into account explicitly the interactions of dark matter - whatever their intensity - both with itself and with other particle species. Relying on a general classification of dark matter particle candidates, our analysis provides, from structure formation, a new set of constraints on the dark matter particle mass and interaction rates (in particular with photons and neutrinos). This determines up to which cross sections the dark matter interactions may effectively be disregarded, and when they start playing an essential role, either through collisional damping or through an enhancement of the free-streaming scale. It leads us to extend the notions of Cold, Warm and Hot Dark Matter scenarios when dark matter interactions are no longer taken to be negligible. It also suggests the possibility of new scenarios of Collisional Warm Dark Matter, with moderate damping induced by dark matter interactions.Comment: 12 pages. Invited talk at DARK 2002, 4th Int. Conf. on Dark Matter in Astro and Particle Physics, Cape Town, Feb. 200

Latent Variable Method Demonstrator -- Software for Understanding Multivariate Data Analytics Algorithms

The ever-increasing quantity of multivariate process data is driving a need for skilled engineers to analyze, interpret, and build models from such data. Multivariate data analytics relies heavily on linear algebra, optimization, and statistics and can be challenging for students to understand given that most curricula do not have strong coverage in the latter three topics. This article describes interactive software - the Latent Variable Demonstrator (LAVADE) - for teaching, learning, and understanding latent variable methods. In this software, users can interactively compare latent variable methods such as Partial Least Squares (PLS), and Principal Component Regression (PCR) with other regression methods such as Least Absolute Shrinkage and Selection Operator (lasso), Ridge Regression (RR), and Elastic Net (EN). LAVADE helps to build intuition on choosing appropriate methods, hyperparameter tuning, and model coefficient interpretation, fostering a conceptual understanding of the algorithms' differences. The software contains a data generation method and three chemical process datasets, allowing for comparing results of datasets with different levels of complexity. LAVADE is released as open-source software so that others can apply and advance the tool for use in teaching or research.Comment: 18 pages, 14 figures, code available: https://github.com/JoachimSchaeffer/LAVADE, preprint submitted to Computers & Chemical Engineerin

Varying effects of subgoal labeled expository text in programming, chemistry, and statistics

Originally intended as a replication study, this study discusses differences in problem solving performance among different domains caused by the same instructional intervention. The learning sciences acknowledges similarities in the learners’ cognitive architecture that allow interventions to apply across domains, but it also argues that each domain has characteristics that might affect how interventions impact learning. The present study uses an instructional design technique that had previously improved learners’ problem solving performance in programming: subgoal labeled expository text and subgoal labeled worked examples. It intended to replicate this effect for solving problems in statistics and chemistry. However, each of the experiments in the three domains had a different pattern of results for problem solving performance. While the subgoal labeled worked example consistently improved performance, the subgoal labeled expository text, which interacted with subgoal labeled worked examples in programming, had an additive effect with subgoal labeled worked examples in chemistry and no effect in statistics. Differences in patterns of results are believed to be due to complexity of the content to be learned, especially in terms of mapping problem solving procedures to solving problems, and the familiarity of tools used to solve problems in the domain. Subgoal labeled expository text was effective only when students learned more complex content and used unfamiliar problem solving tools

Interaction of Instructional Material Order and Subgoal Labels on Learning in Programming

Subgoal labeled expository instructions and worked examples have been shown to positively impact student learning and performance in computer science education. This study examined whether problem solving performance differed based on the order of expository instructions and worked examples and the presence of subgoal labels within the instructions. Participants were 132 undergraduate college students. A significant interaction showed that when learners were presented with the worked example followed by the expository instructions containing subgoal labels, the learner was better at outlining the procedure for creating an application. However, the manipulations did not affect novel problem solving performance or explanations of solutions,. These results suggest that the order instructional materials are presented have has little impact on problem solving, although some benefit can be gained from presenting the worked example before the expository instructions when subgoal labels are included

Correspondence between Minkowski and de Sitter Quantum Field Theory

In this letter we show that the ``preferred'' Klein-Gordon Quantum Field Theories (QFT's) on a d-dimensional de Sitter spacetime can be obtained from a Klein-Gordon QFT on a (d+1)-dimensional ``ambient'' Minkowski spacetime satisfying the spectral condition and, conversely, that a Klein-Gordon QFT on a (d+1)-dimensional ``ambient'' Minkowski spacetime satisfying the spectral condition can be obtained as superposition of d-dimensional de Sitter Klein-Gordon fields in the preferred vacuum. These results establish a correspondence between QFT's living on manifolds having different dimensions. The method exposed here can be applied to study other situations and notably QFT on Anti de Sitter spacetime.Comment: 7 pages, no figures, typos corrected, added one referenc

Conceptual design of a manned orbital transfer vehicle

With the advent of the manned space station, man now requires a spacecraft based on the space station with the ability to deploy, recover, and repair satellites quickly and economically. Such a craft would prolong and enhance the life and performance of many satellites. A basic design was developed for an orbital tansfer vehicle (OTV). The basic design criteria are discussed. The design of the OTV and systems were researched in the following areas: avionics, crew systems, electrical power systems, environmental control/life support systems, navigation and orbital maneuvers, propulsion systems, reaction control systems (RCS), servicing systems, and structures. The basic concepts in each of the areas are summarized

Two designs for an orbital transfer vehicle

The Orbital Transfer Vehicle (OTV) and systems were researched in the following areas: avionics, crew systems, electrical power systems, environmental control/life support systems, navigation and orbital maneuvers, propulsion systems, reaction control systems (RCS), servicing systems, and structures