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Let $$\B_3$$ be the Artin braid group on $$3$$ strands and $$\PB_3$$ be the corresponding pure braid group. In this paper, we construct the groupoid $$\GTSh$$ of $$\GT$$-shadows for a (possibly more tractable) version $$\GTh_0$$ of the Grothendieck-Teichmueller group $$\GTh$$ introduced in paper \cite{HS-fund-groups} by D. Harbater and L. Schneps. We call this group the gentle version of $$\GTh$$ and denote it by $$\GTh_{gen}$$. The objects of $$\GTSh$$ are finite index normal subgroups $$\N$$ of $$\B_3$$ satisfying the condition $$\N \le \PB_3$$. Morphisms of $$\GTSh$$ are called $$\GT$$-shadows and they may be thought of as approximations to elements of $$\GTh_{gen}$$. We show how $$\GT$$-shadows can be obtained from elements of $$\GTh_{gen}$$ and prove that $$\GTh_{gen}$$ is isomorphic to the limit of a certain functor defined in terms of the groupoid $$\GTSh$$. Using this result, we get a criterion for identifying genuine $$\GT$$-shadows. 

A major challenge in synthesizing strong and tough protein fibers based on spider silk motifs is understanding the coupling between protein sequence and the postspin drawing process. We clarify how drawing-induced elongational force affects ordering, chain extension, interchain contacts, and molecular mobility through mesoscale simulations of silk-based fibers. We show that these emergent features can be used to predict mechanical property enhancements arising from postspin drawing. Simulations recapitulate a purely process-dependent mechanical property envelope in which order enhances fiber strength while preserving toughness. The relationship between chain extension and crystalline domain alignment observed in simulations is validated by Raman spectroscopy of wet-spun fibers. Property enhancements attributed to the progression of anisotropic extension are verified by mechanical tests of drawn silk fibers and justified by theory. These findings elucidate how drawing enhances properties of protein-based fibers and shed light on how to incorporate this effect into predictive models. 

Wind turbine blade leading edge erosion (LEE) reduces energy production and increases wind energy operation and maintenance costs. Degradation of the blade coating and ultimately damage to the underlying blade structure are caused by collisions of falling hydrometeors with rotating blades. The selection of optimal methods to mitigate/reduce LEE are critically dependent on the rates of coating fatigue accumulation at a given location and the time variance in the accumulation of material stresses. However, no such assessment currently exists for the United States of America (USA). To address this research gap, blade coating lifetimes at 883 sites across the USA are generated based on high-frequency (5-min) estimates of material fatigue derived using a mechanistic model and robust meteorological measurements. Results indicate blade coating failure at some sites in as few as 4 years, and that the frequency and intensity of material stresses are both highly episodic and spatially varying. Time series analyses indicate that up to one-third of blade coating lifetime is exhausted in just 360 5-min periods in the Southern Great Plains (SGP). Conversely, sites in the Pacific Northwest (PNW) exhibit the same level of coating lifetime depletion in over three times as many time periods. Thus, it may be more cost-effective to use wind turbine deregulation (erosion-safe mode) for damage reduction and blade lifetime extension in the SGP, while the application of blade leading edge protective measures may be more appropriate in the PNW. Annual total precipitation and mean wind speed are shown to be poor predictors of blade coating lifetime, re-emphasizing the need for detailed modeling studies such as that presented herein. 

An original concept for catalytic electrochemical dehydration has enabled a suite of acid substitutions, including amidation, esterification, and thioesterification, through a linchpin anhydride formed in situ. By avoiding stoichiometric dehydrating agents, this method addresses a leading challenge in organic synthesis and green chemistry. It also proceeds without acid additives at room temperature, accesses a diverse range of product structures, is easily scaled, and enabled the first example of catalytic peptide coupling at room temperature. 

Abstract Consequential STEM experiences in informal settings can address issues of equity by fully engaging historically marginalized high school students in complex socio-scientific issues. However, inclusive and effective programs are in high demand, and there is little research on what specific aspects, context, and timeframes are most important when scaling these experiences. Using a mixed method approach, this study demonstrates that students make significant gains, in the short and long term, through in-person and remote informal programs ranging between 22-h and 320-h. Progress across STEM learning constructs is attributed to authentic research experiences, students’ connections to STEM professionals, direct hands-on participation in projects, and group work. Relative to formal education settings, research-based informal STEM programs can be implemented with minimal resources, can maintain effectiveness while scaling, and work towards addressing the societal challenge of improving STEM learning and outcomes for high school students from historically marginalized communities. 

Abstract Subaerial biofilms (SAB) are intricate microbial communities living on terrestrial surfaces, of interest in a variety of contexts including cultural heritage preservation, microbial ecology, biogeochemical cycling, and biotechnology. Here we propose a mathematical model aimed at better understanding the interplay between cyanobacteria and heterotrophic bacteria, common microbial SAB constituents, and their mutual dependence on local environmental conditions. SABs are modeled as thin mixed biofilm-liquid water layers sitting on stone. A system of ordinary differential equations regulates the dynamics of key SAB components: cyanobacteria, heterotrophs, polysaccharides and decayed biomass, as well as cellular levels of organic carbon, nitrogen and energy. These components are interconnected through a network of energetically dominant metabolic pathways, modeled with limitation terms reflecting the impact of biotic and abiotic factors. Daily cylces of temperature, humidity, and light intensity are considered as input model variables that regulate microbial activity by influencing water availability and metabolic kinetics. Relevant physico-chemical processes, including pH regulation, further contribute to a description of the SAB ecology. Numerical simulations explore the dynamics of SABs in a real-world context, revealing distinct daily activity periods shaped by water activity and light availability, as well as longer time scale survivability conditions. Results also suggest that heterotrophs could play a substantial role in decomposing non-volatile carbon compounds and regulating pH, thus influencing the overall composition and stability of the biofilm. 

An electrochemical coupling between carboxylic acids and penta uorophenol (PFP–OH) to access synthetically versatile penta uorophenyl (PFP) esters has been developed. Novel reactivity of PFP–OH was turned on by modulating its oxidation state, leveraging both its native O-nucleophilicity and its latent, oxidation-induced C-electrophilicity to promote a unique cascade of nucleophilic aromatic and acyl substitutions. Its esteri cation with acids was thus achieved for the rst time without exogenous dehydrating agents. The acidity of PFP–OH and the oxidizability of its conjugate base enabled its mild and selective activation via deprotonation–oxidation, readily affording PFP esters that are useful in many applications (peptide synthesis, chemical biology, etc.) and that contain redox-sensitive functional groups. Finally, we verified in a unified forum that an amino-acid-derived PFP ester can be converted into a range of acyl-substitution products while retaining key stereochemical information, and we demonstrated that PFP esters have excellent stability to hydrolysis, comparing favorably even to N-hydroxysuccinimidyl (NHS) esters.