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The nuclear spin conversion of CH3D isolated in solid parahydrogen (pH2) was investigated by high-resolution Fourier transform infrared (FTIR) spectroscopy. From the analysis of the temporal changes in the CH3D/pH2 rovibrational absorption spectra, the nuclear spin conversion rates associated with rotational relaxation from the J = 1, K = 1 state to the J = 0, K = 0 state were determined over the 1.5−4.3 K temperature range. As-deposited CH3D/pH2 samples contain two different crystal structures allowing the CH3D nuclear spin conversion rates to be measured for two different trapping sites, which revealed that CH3D trapped in hexagonal closepacked (hcp) crystal sites relax more than twice as fast as CH3D isolated in face centered cubic (fcc) crystal sites. The nuclear spin conversion rates of CH3D trapped in single substitution hcp crystal sites increase rapidly above 2.5 K, but the rates were almost temperature independent below 2 K leading to a limiting nonzero conversion rate of k = 2.76(8) × 10−3 min−1 at 1.58(1) K. Comparison of the temperature dependence of the CH3D nuclear spin conversion rate measured here with analogous measurements for CH4 and CD4 trapped in solid pH2 shows that CH3D relaxes with a rate constant intermediate between CH4 and CD4, and the faster relaxation for species containing deuterium atoms can be qualitatively explained by the quadrupole interaction that is absent in all hydrogen containing CH4 isotopomers. 

Models of reaction networks within interacting compartments (RNIC) are a generalization of stochastic reaction networks. It is most natural to think of the interacting compartments as “cells” that can appear, degrade, split, and even merge, with each cell containing an evolving copy of the underlying stochastic reaction network. Such models have a number of parameters, including those associated with the internal chemical model and those associated with the compartment interactions, and it is natural to want efficient computational methods for the numerical estimation of sensitivities of model statistics with respect to these parameters. Motivated by the extensive work on computational methods for parametric sensitivity analysis in the context of stochastic reaction networks over the past few decades, we provide a number of methods in the basic RNIC setting. Provided methods include the (unbiased) Girsanov transformation method (also called the likelihood ratio method) and a number of coupling methods for the implementation of finite differences, each motivated by methods from previous work related to stochastic reaction networks. We provide several numerical examples comparing the various methods in the new setting. We find that the relative performance of each method is in line with its analog in the “standard” stochastic reaction network setting. We have made all the MATLAB codes used to implement the various methods freely available for download. 

Abstract We study Schubert polynomials using geometry of infinite-dimensional flag varieties and degeneracy loci. Applications include Graham-positivity of coefficients appearing in equivariant coproduct formulas and expansions of back-stable and enriched Schubert polynomials. We also construct an embedding of the type C flag variety and study the corresponding pullback map on (equivariant) cohomology rings. 

Virtual reality (VR) technologies are transforming educational paradigms by enabling highly immersive, interactive simulations that increase engagement and cognition. This paper presents KonnectVR (KVR), an innovative, open-source platform designed to mitigate common barriers in educational VR. Barriers such as high costs, limited content customization, and the absence of real-time assessments. The system, constructed by undergraduate students, facilitates experiential learning, real-time collaboration, and assessment delivery, empowering educators with an unprecedented degree of accessibility and customization. Employing a case study methodology, we provide unique insider perspectives into KVR's architectural design, underlying pedagogical framework, development processes, challenges encountered, and future directions. Findings reveal technical hurdles overcome by undergraduate student teams like VR-specific programming, user interface design, networking, and cybersecurity integration. The analysis uncovers key themes around project-based skill acquisition, problem-solving perseverance, cross-team knowledge gaps, and the benefits of an agile, user-centric approach. Ultimately, KVR demonstrates how emerging technologies and open-sourced solutions can converge to innovate learning, pushing boundaries while serving an egalitarian educational mission. The platform sets the foundation for a new generation of community-driven tools democratizing access to interactive, distributive, collaborative VR experiences that maximize knowledge construction. 

Abstract We give explicit presentations of the integral equivariant cohomology of the affine Grassmannians and flag varieties in type A, arising from their natural embeddings in the corresponding infinite (Sato) Grassmannian and flag variety. These presentations are compared with results obtained by Lam and Shimozono, for rational equivariant cohomology of the affine Grassmannian, and by Larson, for the integral cohomology of the moduli stack of vector bundles on. 

We prepare and analyze Rydberg states with orbital quantum numbers $\ell \le 6$using three-optical-photon electromagnetically induced transparency (EIT) and radio frequency (rf) dressing, and employ the high- $\ell$states in electric-field sensing. Rubidium-85 atoms in a room-temperature vapor cell are first promoted into the $25F_{5/2}$state via Rydberg-EIT with three infrared laser beams. Two rf dressing fields then (near-)resonantly couple the $25F, 25H(\ell =5)$, and $25I(\ell =6)$Rydberg states. The dependence of the rf-dressed Rydberg-state level structure on rf powers, rf and laser frequencies is characterized using EIT. Furthermore, we discuss the principles of dc-electric-field sensing using high- $\ell$Rydberg states and experimentally demonstrate the method using test electric fields of $\lesssim 50$V/m induced via photo-illumination of the vapor-cell wall. We measure the highly nonlinear dependence of the dc-electric-field strength on the power of the photo-illumination laser. Numerical calculations, which reproduce our experimental observations well, elucidate the underlying physics. Our paper is relevant to high-precision spectroscopy of high- $\ell$Rydberg states, Rydberg-atom-based electric-field sensing, and plasma electric-field diagnostics. Published by the American Physical Society2024 

The vibrational dynamics of diborane have been extensively studied both theoretically and experimentally ever since the bridge structure of diborane was established in the 1950s. Numerous infrared and several Raman spectroscopic studies have followed in the ensuing years at ever increasing levels of spectral resolution. In parallel, ab initio computations of the underlying potential energy surface have progressed as well as the methods to calculate the anharmonic vibration dynamics beyond the double harmonic approximation. Nevertheless, even 70 years after the bridge structure of diborane was established, there are still significant discrepancies between experiment and theory for the fundamental vibrational frequencies of diborane. In this work we use para-hydrogen (pH2) matrix isolation infrared spectroscopy to characterize six fundamental vibrations of B2H6 and B2D6 and compare them with results from configuration-selective vibrational configuration interaction theory. The calculated frequencies and intensities are in very good agreement with the pH2 matrix isolation spectra, even several combination bands are well reproduced. We believe that the reason discrepancies have existed for so long is related to the large amount of anharmonicity that is associated with the bridge BH stretching modes. However, the calculated frequencies and intensities reported here for the vibrational modes of all three boron isotopologues of B2H6 and B2D6 are within ± 2.00 cm− 1 and ± 1.44 cm− 1, respectively, of the experimental frequencies and therefore a refined vibrational assignment of diborane has been achieved.