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This paper presents four years (2021-2024) of data from a study that aims to understand engineering students' environmental awareness and pro-environmental behavior at different levels in a prominent HBCU. Through extensive surveys developed as part of this project, students' ecological knowledge and higher-level environmental behavior were explored. In this context, the study also investigated their willingness and preparedness to pursue careers in the industries developing sustainable resources. With a focus on imparting these qualities, a pedagogical system with a comprehensive pool of interventions has been designed and implemented in a senior-level mechanical engineering course. The paper summarizes the survey development process and the data that explores the impact of the intervention on students' ecological knowledge, behavior, attitudes, and job decisions. The study indicates that early academic interventions can shape students' environmental attitudes and behavior and help prepare a diverse renewable energy workforce for the future. 

Abstract Differential operators are widely used in geometry processing for problem domains like spectral shape analysis, data interpolation, parametrization and mapping, and meshing. In addition to the ubiquitous cotangent Laplacian, anisotropic second‐order operators, as well as higher‐order operators such as the Bilaplacian, have been discretized for specialized applications. In this paper, we study a class of operators that generalizes the fourth‐order Bilaplacian to support anisotropic behavior. The anisotropy is parametrized by asymmetric frame field, first studied in connection with quadrilateral and hexahedral meshing, which allows for fine‐grained control of local directions of variation. We discretize these operators using a mixed finite element scheme, verify convergence of the discretization, study the behavior of the operator under pullback, and present potential applications. 

Abstract Recently proposed as a stable means of evaluating geometric compactness, theisoperimetric profileof a planar domain measures the minimum perimeter needed to inscribe a shape with prescribed area varying from 0 to the area of the domain. While this profile has proven valuable for evaluating properties of geographic partitions, existing algorithms for its computation rely on aggressive approximations and are still computationally expensive. In this paper, we propose a practical means of approximating the isoperimetric profile and show that for domains satisfying a“thick neck”condition, our approximation is exact. For more general domains, we show that our bound is still exact within a conservative regime and is otherwise an upper bound. Our method is based on a traversal of the medial axis which produces efficient and robust results. We compare our technique with the state‐of‐the‐art approximation to the isoperimetric profile on a variety of domains and show significantly tighter bounds than were previously achievable. 

Abstract We consider the tasks of representing, analysing and manipulating maps between shapes. We model maps as densities over the product manifold of the input shapes; these densities can be treated as scalar functions and therefore are manipulable using the language of signal processing on manifolds. Being a manifold itself, the product space endows the set of maps with a geometry of its own, which we exploit to define map operations in the spectral domain; we also derive relationships with other existing representations (soft maps and functional maps). To apply these ideas in practice, we discretize product manifolds and their Laplace–Beltrami operators, and we introduce localized spectral analysis of the product manifold as a novel tool for map processing. Our framework applies to maps defined between and across 2D and 3D shapes without requiring special adjustment, and it can be implemented efficiently with simple operations on sparse matrices.