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SUMMARY Evidence of seismic anisotropy is widespread within the Earth, including from individual crystals, rocks, borehole measurements, active-source seismic data, and global seismic data. The seismic anisotropy of a material determines how wave speeds vary as a function of propagation direction and polarization, and it is characterized by density and the elastic map, which relates strain and stress in the material. Associated with the elastic map is a symmetric $$6 \times 6$$ matrix, which therefore has 21 parameters. The 21-D space of elastic maps is vast and poses challenges for both theoretical analysis and typical inverse problems. Most estimation approaches using a given set of directional wave speed measurements assume a high-symmetry approximation, typically either in the form of isotropy (2 parameters), vertical transverse isotropy (radial anisotropy: 5 parameters), or horizontal transverse isotropy (azimuthal anisotropy: 6 parameters). We offer a general approach to explore the space of elastic maps by starting with a given elastic map $$\mathbf {T}$$. Using a combined minimization and projection procedure, we calculate the closest $$\Sigma$$-maps to $$\mathbf {T}$$, where $$\Sigma$$ is one of the eight elastic symmetry classes: isotropic, cubic, transverse isotropic, trigonal, tetragonal, orthorhombic, monoclinic and trivial. We apply this approach to 21-parameter elastic maps derived from laboratory measurements of minerals; the measurements include dependencies on pressure, temperature, and composition. We also examine global elasticity models derived from subduction flow modelling. Our approach offers a different perspective on seismic anisotropy and motivates new interpretations, such as for why elasticity varies as a function of pressure, temperature, and composition. The two primary advances of this study are (1) to provide visualization of elastic maps, including along specific pathways through the space of model parameters, and (2) to offer distinct options for reducing the complexity of a given elastic map by providing a higher-symmetry approximation or a lower-anisotropic version. This could contribute to improved imaging and interpretation of Earth structure and dynamics from seismic anisotropy. 

Abstract Oceanographic observations have revealed that basin‐scale Rossby waves can travel at speeds systematically exceeding values predicted by linear theory based on the flat‐bottom approximation. Using the recently developed parametric “sandpaper” theory of seafloor roughness, we construct a set of analytical solutions for the vertical structure and dispersion relationship of Rossby waves. We then use simulations to confirm these results and show that baroclinic Rossby waves can be accelerated by irregular small‐scale rough topography by up to a factor of 1.6 relative to their flat‐bottom counterparts. This acceleration is most extreme at high latitudes and wavelengths of approximately 600 km. Our investigation demonstrates the importance of relatively small‐scale processes for the large‐scale flow dynamics in general and baroclinic Rossby waves in particular. 

There is growing recognition that mathematical modeling can be a lever for equity in elementary mathematics classrooms. This study focuses on the impact of a professional development program focused on culturally responsive mathematical modeling on 8 kindergarten through 2nd grade teachers’ practices in modeling lessons. We use a project developed observation tool to evaluate two video recorded modeling lessons from each teacher (16 total). Findings focus on patterns in the strengths and challenges in primary grade teachers’ practices for teaching modeling, including how teachers’ practices align with culturally responsive teaching. We discuss implications of our findings for the design and refinement of professional development. 

We present a numerical framework for modeling extended hyperelastic bodies based on a Lagrangian formulation of general relativistic elasticity theory. We use finite element methods to discretize the body, then use the semidiscrete action to derive ordinary differential equations of motion for the discrete nodes. The nodes are evolved in time using fourth-order Runge-Kutta. We validate our code against the normal modes of oscillation of a hyperelastic sphere, which are known analytically in the limit of small (linear), slow (Newtonian) oscillations. The algorithm displays second order convergence. This numerical framework can be used to obtain the orbital motion and internal dynamics of a hyperelastic body of any shape, for any spacetime metric, and for varying hyperelastic energy models 

The purpose of this work was to test the inter-rater reliability (IRR) of a rubric used to grade technical reports in a senior-level chemical engineering laboratory course that has multiple instructors that grade deliverables. The rubric consisted of fifteen constructs that provided students detailed guidance on instructor expectations with respect to the report sections, formatting and technical writing aspects such as audience, context and purpose. Four student reports from previous years were scored using the rubric, and IRR was assessed using a two-way mixed, consistency, average-measures intraclass correlation (ICC) for each construct. Then, the instructors met as a group to discuss their scoring and reasoning. Multiple revisions were made to the rubric based on instructor feedback and constructs rated by ICC as poor. When fair or poor constructs were combined, the ICCs improved. In addition, the overall score construct continued to be rated as excellent, indicating that while different instructors may have variation at the individual construct level, they evaluate the overall quality of the report consistently. A key learning from this process was the importance of the instructor discussion around their reasoning for the scores and the importance of an ‘instructor orientation’ involving discussion and practice using the rubrics in the case of multiple instructors or a change in instructors. The developed rubric has the potential for broad applicability to engineering laboratory courses with technical writing components and could be adapted for alternative styles of technical writing genre. 

Realistically improving upper-limb prostheses is only possible if we listen to users’ actual technological needs. 

Laboratory experimentation is a key component of the development of professional engineers. However, experiments conducted in chemical engineering laboratory classes are commonly more prescriptive than the problems faced by practicing engineers, who have agency to make consequential decisions across the experiment and communication of results. Thus, understanding how experiments in laboratory courses vary in offering students opportunities to make such decisions, and how students navigate higher agency learning experiences is important for preparing graduates ready to direct these practices. In this study, we sought to answer the following research questions: How do students perceive their agency in course-based undergraduate research experiences? What factors are measured by the Consequential Agency in Laboratory Experiments survey? To better understand student perceptions of their agency in relation to laboratory experiments, we first conducted a case study of a course-based research experience (CURE) in a senior-level chemical engineering laboratory course. We then surveyed six upper-division laboratory courses across two universities using an initial version of the Consequential Agency in Laboratory Experiments survey. We used exploratory factor analysis to investigate the validity of the data from the survey for measuring relevant constructs of authenticity, agency in specific domains, responsibility, and opportunity to make decisions. We found that with instructional support, students in the CURE recognized that failure could itself provide opportunities for learning. They valued having the agency to make consequential decisions, even when they also found the experience challenging. We also found strong support for items measuring agency as responsibility, authenticity, agency in the communication domain, agency in the experimental design domain, and opportunity to make decisions. These findings give us insight into the value of higher agency laboratory experiments, and they provide a foundation for developing a more precise survey capable of measuring agency across various laboratory experiment practices. Such a survey will enable future studies that investigate the impacts of increasing agency in just one domain versus in several. In turn, this can aid faculty in developing higher agency learning experiences that are more feasible to implement, compared to CUREs. 

Laboratory experimentation is a key component of the development of professional engineers. However, experiments conducted in chemical engineering laboratory classes are commonly more prescriptive than the problems faced by practicing engineers, who have agency to make consequential decisions across the experiment and communication of results. Thus, understanding how experiments in laboratory courses vary in offering students opportunities to make such decisions, and how students navigate higher agency learning experiences is important for preparing graduates ready to direct these practices. In this study, we sought to answer the following research question: What factors are measured by the Consequential Agency in Laboratory Experiments survey? To better understand student perceptions of their agency in relation to laboratory experiments, developed an initial version of the Consequential Agency in Laboratory Experiments survey, following research-based survey development guidelines. We implemented it in six upper-division laboratory courses across two universities. We used exploratory factor analysis to investigate the validity of the data from the survey for measuring relevant constructs of authenticity, agency in specific domains, responsibility, and opportunity to make decisions. We found strong support for items measuring agency as responsibility, authenticity, agency in the communication domain, agency in the experimental design domain, and opportunity to make decisions. These findings provide a foundation for developing a more precise survey capable of measuring agency across various laboratory experiment practices. Such a survey will enable future studies that investigate the impacts of increasing agency in just one domain versus in several. In turn, this can aid faculty in developing higher agency learning experiences that are more feasible to implement, compared to authentic research experiences.