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The relevance of upper division mathematics courses for future secondary teachers is a longstanding thorny issue. Suggested improvements include capstone courses and revised upper division content courses to explicitly address future teachers’ relevant secondary mathematics content knowledge, beliefs about teaching and learning, and experience with learning mathematics while engaging in authentic mathematical practices. In this report, we investigate prospective teachers’ reflections on their opportunities in an upper division Inquiry-Oriented Dynamical Systems course to engage in the eight Common Core State Standards for Mathematical Practice. Analysis of students’ self-reported engagement in the eight Practices revealed five practices that strongly resonated with them and the various ways that their experiences in an inquiry-oriented classroom supported meaningful and powerful engagement in these Mathematical Practices. We conclude with implications for practice. 

Magnetically trapped antihydrogen atoms can be cooled by expanding the volume of the trap in which they are confined. We report a proof-of-principle experiment in which antiatoms are deliberately released from expanded and static traps. Antiatoms escape at an average trap depth of $0.08\pm 0.01\mathrm{K}$(statistical errors only) from the expanded trap while they escape at average depths of $0.22\pm 0.01$and $0.17\pm 0.01\mathrm{K}$from two different static traps. (We employ temperature-equivalent energy units.) Detailed simulations qualitatively agree with the escape times measured in the experiment and show a decrease of $38\%$(statistical $\text{error}<0.2\%$) in the mean energy of the population after the trap expansion without significantly increasing antiatom loss compared to typical static confinement protocols. This change is bracketed by the predictions of one-dimensional and three-dimensional semianalytic adiabatic expansion models. These experimental, simulational, and model results are consistent with obtaining an adiabatically cooled population of antihydrogen atoms that partially exchanged energy between axial and transverse degrees of freedom during the trap expansion. This result is important for future antihydrogen gravitational experiments which rely on adiabatic cooling, and it will enable antihydrogen cooling beyond the fundamental limits of laser cooling. Published by the American Physical Society2024 

Abstract Variation in soil organic C (%OC) concentration has been associated with the concentration of reactive Fe- and Al-oxyhydroxide phases and exchangeable Ca, with the relative importance of these two stabilizing components shifting as soil pH moves from acid to alkaline. However, it is currently unknown if this pattern is similar or different with regard to measures of soil C persistence. We sampled soils from 3 horizons (uppermost A, uppermost B, C or lowest B horizons) across a pH gradient of 11 grass-dominated and 13 deciduous/mixed forest-dominated NEON sites to examine similarities and differences in the drivers of C concentration and persistence. Variation in C concentrations in all soils could be linked to abundances of Fe, Al and Ca, but were not significantly linked to variation in soil C persistence. Though pH was related to variation in Δ 14 OC, higher persistence was associated with more alkaline pH values. In forested soils, depth explained 75% of the variation in Δ 14 OC ( p  < 0.0001), with no significant additional correlations with extractable metal phases. In grasslands, soil organic C persistence was not associated with exchangeable Ca concentrations, but instead was explained by depth and inorganic C concentrations (R 2  = 0.76, p  < 0.0001), implying stabilization of organic C through association with carbonate precipitation. In grasslands, measures of substrate quality suggested greater persistence is also associated with a more advanced degree of decomposition. Results suggest that explanatory variables associated with C concentrations differ from those associated with persistence, and that reactive Fe- and Al-oxyhydroxide phases may not be present in high enough concentrations in most soils to offer any significant protective capacity. These results have significant implications for our understanding of how to model the soil C cycle and may suggest previously unrecognized stabilization mechanisms associated with carbonates and forms of extractable Si. 

Abstract Einstein’s general theory of relativity from 1915¹remains the most successful description of gravitation. From the 1919 solar eclipse²to the observation of gravitational waves³, the theory has passed many crucial experimental tests. However, the evolving concepts of dark matter and dark energy illustrate that there is much to be learned about the gravitating content of the universe. Singularities in the general theory of relativity and the lack of a quantum theory of gravity suggest that our picture is incomplete. It is thus prudent to explore gravity in exotic physical systems. Antimatter was unknown to Einstein in 1915. Dirac’s theory⁴appeared in 1928; the positron was observed⁵in 1932. There has since been much speculation about gravity and antimatter. The theoretical consensus is that any laboratory mass must be attracted⁶by the Earth, although some authors have considered the cosmological consequences if antimatter should be repelled by matter^7–10. In the general theory of relativity, the weak equivalence principle (WEP) requires that all masses react identically to gravity, independent of their internal structure. Here we show that antihydrogen atoms, released from magnetic confinement in the ALPHA-g apparatus, behave in a way consistent with gravitational attraction to the Earth. Repulsive ‘antigravity’ is ruled out in this case. This experiment paves the way for precision studies of the magnitude of the gravitational acceleration between anti-atoms and the Earth to test the WEP. 

Abstract The positron, the antiparticle of the electron, predicted by Dirac in 1931 and discovered by Anderson in 1933, plays a key role in many scientific and everyday endeavours. Notably, the positron is a constituent of antihydrogen, the only long-lived neutral antimatter bound state that can currently be synthesized at low energy, presenting a prominent system for testing fundamental symmetries with high precision. Here, we report on the use of laser cooled Be + ions to sympathetically cool a large and dense plasma of positrons to directly measured temperatures below 7 K in a Penning trap for antihydrogen synthesis. This will likely herald a significant increase in the amount of antihydrogen available for experimentation, thus facilitating further improvements in studies of fundamental symmetries. 

Abstract This paper is a write-up of the ideas that were presented, developed and discussed at the third International Workshop on QCD Challenges from pp to A–A, which took place in August 2019 in Lund, Sweden (Workshop link: https://indico.lucas.lu.se/event/1214/ ). The goal of the workshop was to focus on some of the open questions in the field and try to come up with concrete suggestions for how to make progress on both the experimental and theoretical sides. The paper gives a brief introduction to each topic and then summarizes the primary results. 

Abstract The photon—the quantum excitation of the electromagnetic field—is massless but carries momentum. A photon can therefore exert a force on an object upon collision 1 . Slowing the translational motion of atoms and ions by application of such a force 2,3 , known as laser cooling, was first demonstrated 40 years ago 4,5 . It revolutionized atomic physics over the following decades 6–8 , and it is now a workhorse in many fields, including studies on quantum degenerate gases, quantum information, atomic clocks and tests of fundamental physics. However, this technique has not yet been applied to antimatter. Here we demonstrate laser cooling of antihydrogen 9 , the antimatter atom consisting of an antiproton and a positron. By exciting the 1S–2P transition in antihydrogen with pulsed, narrow-linewidth, Lyman-α laser radiation 10,11 , we Doppler-cool a sample of magnetically trapped antihydrogen. Although we apply laser cooling in only one dimension, the trap couples the longitudinal and transverse motions of the anti-atoms, leading to cooling in all three dimensions. We observe a reduction in the median transverse energy by more than an order of magnitude—with a substantial fraction of the anti-atoms attaining submicroelectronvolt transverse kinetic energies. We also report the observation of the laser-driven 1S–2S transition in samples of laser-cooled antihydrogen atoms. The observed spectral line is approximately four times narrower than that obtained without laser cooling. The demonstration of laser cooling and its immediate application has far-reaching implications for antimatter studies. A more localized, denser and colder sample of antihydrogen will drastically improve spectroscopic 11–13 and gravitational 14 studies of antihydrogen in ongoing experiments. Furthermore, the demonstrated ability to manipulate the motion of antimatter atoms by laser light will potentially provide ground-breaking opportunities for future experiments, such as anti-atomic fountains, anti-atom interferometry and the creation of antimatter molecules.