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In geometrically frustrated assemblies local intersubunit misfits propagate to intra-assembly strain gradients, giving rise to anomalous self-limiting assembly thermodynamics. Here we use theory and coarse-grained simulation to study a recently developed class of “curvamer” particles, flexible shell-like particles that exhibit self-limiting assembly due to the build up of curvature deformation in cohesive stacks. To address a generic, yet poorly understood aspect of frustrated assembly, we introduce a model of curvamer assembly that incorporates both intraparticle shape deformation as well as compliance of interparticle cohesive gaps, an effect we can attribute to a finite range of attraction between particles. We show that the ratio of intraparticle (bending elasticity) to interparticle stiffness not only controls the regimes of self-limitation but also the nature of frustration propagation through curvamer stacks. We find a transition from uniformly bound, curvature-focusing stacks at small size to gap opened, uniformly curved stacks at large size is controlled by a dimensionless measure of inter- versus intracurvamer stiffness. The finite range of interparticle attraction determines the range of cohesion in stacks that are self-limiting, a prediction which is in strong agreement with numerical studies of our coarse-grained colloidal model. These predictions provide critical guidance for experimental realizations of frustrated particle systems designed to exhibit self-limitation at especially large multiparticle scales. 

Abstract We find ourselves at a time when the need for transformation in science education is aligning with opportunity. Significant science education resources, namely the Next Generation Science Standards (NGSS) and the Ambitious Science Teaching (AST) framework, need an intentional aim of centering social justice for minoritized communities and youth as well as practices to enact it. While NGSS and AST provide concrete guidelines to support deep learning, revisions are needed to explicitly promote social justice. In this study, we sought to understand how a commitment to social justice, operationalized through culturally sustaining pedagogy (Paris, Culturally sustaining pedagogies and our futures.The Educational Forum, 2021; 85, pp. 364–376), might shape the AST framework to promote more critical versions of teaching science for equity. Through a qualitative multi‐case study, we observed three preservice teacher teams engaged in planning, teaching, and debriefing a 6‐day summer camp in a rural community. Findings showed that teachers shaped the AST sets of practices in ways that sustained local culture and addressed equity aims: anchoring scientific study in phenomena important to community stakeholders; using legitimizing students' stories by both using them to plan the following lessons and as data for scientific argumentation; introducing local community members as scientific experts, ultimately supporting a new sense of pride and advocacy for their community; and supporting students in publicly communicating their developing scientific expertise to community stakeholders. In shaping the AST framework through culturally sustaining pedagogy, teachers made notable investments: developing local networks; learning about local geography, history, and culture; building relationships with students; adapting lessons to incorporate students' ideas; connecting with community stakeholders to build scientific collaborations; and preparing to share their work publicly with the community. Using these findings, we offer a justice‐centered ambitious science teaching (JuST) framework that can deliver the benefits of a framework of practices while also engaging in the necessarily more critical elements of equity work. 

Collective movement and organization of cell monolayers are important for wound healing and tissue development. Recent experiments highlighted the importance of liquid crystal order within these layers, suggesting that +1 topological defects have a role in organizing tissue morphogenesis. We study fibroblast organization, motion, and proliferation on a substrate with micron-sized ridges that induce +1 and −1 topological defects using simulation and experiment. We model cells as self-propelled deformable ellipses that interact via a Gay–Berne potential. Unlike earlier work on other cell types, we see that density variation near defects is not explained by collective migration. We propose instead that fibroblasts have different division rates depending on their area and aspect ratio. This model captures key features of our previous experiments: the alignment quality worsens at high cell density and, at the center of the +1 defects, cells can adopt either highly anisotropic or primarily isotropic morphologies. Experiments performed with different ridge heights confirm a prediction of this model: Suppressing migration across ridges promotes higher cell density at the +1 defect. Our work enables a mechanism for tissue patterning using topological defects without relying on cell migration.