Uniform Approximation from Symbol Calculus on a Spherical Phase Space

We use symbol correspondence and quantum normal form theory to develop a more general method for finding uniform asymptotic approximations. We then apply this method to derive a result we announced in an earlier paper, namely, the uniform approximation of the $6j$-symbol in terms of the rotation matrices. The derivation is based on the Stratonovich-Weyl symbol correspondence between matrix operators and functions on a spherical phase space. The resulting approximation depends on a canonical, or area preserving, map between two pairs of intersecting level sets on the spherical phase space.Comment: 18 pages, 5 figure

Artificial Intelligence and the Disruption of Higher Education: Strategies for Integrations across Disciplines

Artificial intelligence (AI) and its impact on society have received a great deal of attention in the past five years since the first Stanford AI100 report. AI already globally impacts individuals in critical and personal ways, and many industries will continue to experience disruptions as the full algorithmic effects are understood. Higher education is one of the industries that will be greatly impacted; consequently, many institutions have begun accelerating its adoption across disciplines to address the fast-approaching market shift. Recent advances with the technology are especially promising for its potential to create and scale personalized learning for students, to optimize strategies for learning outcomes, and to increase access to a more diverse populations. In the US alone, colleges are predicted to witness a 48% growth in AI market between 2018-2022. Research has confirmed that the current use of AI in education (AIEd) leads to positive outcomes, including improved learning outcomes for students, along with increased access, increased retention, lower cost of education, and decreased time to completion. Future uses of AI will include the following: enabling engaging and interactive education anytime and anywhere; personalized AI mentors that will help students identify and reach their goals; and mass-personalization that will allow AI to be tailored to each student’s learning style, level, and needs. Yet with all the potential benefits that AI and machine learning (ML) may provide students, there remains a general reticence to adopt this technology because of misconceptions and perceptions that faculty will need to retool since their current teaching strategies will be outmoded. This study provides an overview for those in higher education of what AI is and is not, and how it may be used in various disciplines. Considerations of becoming an AI institution include the following: 1) curricular planning and oversight from academic affairs to identify appropriate use cases for AI in various disciplines, and 2) coordination with IT and technology infrastructure to develop ML to support student services in general

Physical mechanisms controlling self-aggregation of convection in idealized numerical modeling simulations

We elucidate the physics of self-aggregation by applying a new diagnostic technique to the output of a cloud resolving model. Specifically, the System for Atmospheric Modeling is used to perform 3- D cloud system resolving simulations of radiative-convective equilibrium in a nonrotating framework, with interactive radiation and surface fluxes and fixed sea surface temperature (SST). We note that self-aggregation begins as a dry patch that expands, eventually forcing all the convection into a single clump. Thus, when examining the initiation of self-aggregation, we focus on processes that can amplify this initial dry patch. We introduce a novel method to quantify the magnitudes of the various feedbacks that control self-aggregation within the framework of the budget for the spatial variance of column-integrated frozen moist static energy. The absorption of shortwave radiation by atmospheric water vapor is found to be a key positive feedback in the evolution of aggregation. In addition, we find a positive wind speed-surface flux feedback whose role is to counteract a negative feedback due to the effect of air-sea enthalpy disequilibrium on surface fluxes. The longwave radiation feedback can be either positive or negative in the early and intermediate stages of aggregation; however, it is the dominant positive feedback that maintains the aggregated state once it develops. Importantly, the mechanisms that maintain the aggregate state are distinct from those that instigate the evolution of self-aggregation.National Science Foundation (U.S.) (Grant 1032244)National Science Foundation (U.S.) (Grant 1136480)National Science Foundation (U.S.) (Grant 0850639)Massachusetts Institute of Technology. Joint Program on the Science & Policy of Global Chang

An object-based model for convective cold pool dynamics

A simple model of the organization of atmospheric moist convection by cold outflows is presented. The model consists of two layers: a lower layer where instability gradually builds up, and an upper layer where instability is rapidly released. Its formulation is inspired by Abelian sandpile models: instability and convection are both represented in terms of particles that are coupled to a lattice grid. An excess of particles in the lower layer triggers a particle release into the upper (cloud) layer. Particles in the upper layer also induce particle movement in the lower layer: this reverse coupling represents the effect of precipitation and the associated cold outflows. The model shows two behavioral regimes. Activity is scattered when the reverse coupling is weak, but when it is strong, convection forms cellular patterns. Though this model does not contain a detailed representation of physical processes in convection, it captures some key dynamical features of precipitating convection seen in satellite observations and LES studies. These include the formation of open cells, temporal oscillations in convective intensity, hysteresis, and the effect of precipitation on the scale of convection. We argue that an object-based representation of convection may be able to capture properties of convective organization that are missing in traditional parameterizations

Semiclassical Mechanics of the Wigner 6j-Symbol

The semiclassical mechanics of the Wigner 6j-symbol is examined from the standpoint of WKB theory for multidimensional, integrable systems, to explore the geometrical issues surrounding the Ponzano-Regge formula. The relations among the methods of Roberts and others for deriving the Ponzano-Regge formula are discussed, and a new approach, based on the recoupling of four angular momenta, is presented. A generalization of the Yutsis-type of spin network is developed for this purpose. Special attention is devoted to symplectic reduction, the reduced phase space of the 6j-symbol (the 2-sphere of Kapovich and Millson), and the reduction of Poisson bracket expressions for semiclassical amplitudes. General principles for the semiclassical study of arbitrary spin networks are laid down; some of these were used in our recent derivation of the asymptotic formula for the Wigner 9j-symbol.Comment: 64 pages, 50 figure