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Abstract Neutrinos are one of the most promising messengers for signals of new physics Beyond the Standard Model (BSM). On the theoretical side, their elusive nature, combined with their unknown mass mechanism, seems to indicate that the neutrino sector is indeed opening a window to new physics. On the experimental side, several long-standing anomalies have been reported in the past decades, providing a strong motivation to thoroughly test the standard three-neutrino oscillation paradigm. In this Snowmass21 white paper, we explore the potential of current and future neutrino experiments to explore BSM effects on neutrino flavor during the next decade. 

Abstract Magnetic fields have an important role in the evolution of interstellar medium and star formation 1,2 . As the only direct probe of interstellar field strength, credible Zeeman measurements remain sparse owing to the lack of suitable Zeeman probes, particularly for cold, molecular gas 3 . Here we report the detection of a magnetic field of +3.8 ± 0.3 microgauss through the H  I narrow self-absorption (HINSA) 4,5 towards L1544 6,7 —a well-studied prototypical prestellar core in an early transition between starless and protostellar phases 8–10 characterized by a high central number density 11 and a low central temperature 12 . A combined analysis of the Zeeman measurements of quasar H  I absorption, H  I emission, OH emission and HINSA reveals a coherent magnetic field from the atomic cold neutral medium (CNM) to the molecular envelope. The molecular envelope traced by the HINSA is found to be magnetically supercritical, with a field strength comparable to that of the surrounding diffuse, magnetically subcritical CNM despite a large increase in density. The reduction of the magnetic flux relative to the mass, which is necessary for star formation, thus seems to have already happened during the transition from the diffuse CNM to the molecular gas traced by the HINSA. This is earlier than envisioned in the classical picture where magnetically supercritical cores capable of collapsing into stars form out of magnetically subcritical envelopes 13,14 . 

Abstract Mode shape information plays the essential role in deciding the spatial pattern of vibratory response of a structure. The uncertainty quantification of mode shape, i.e., predicting mode shape variation when the structure is subjected to uncertainty, can provide guidance for robust design and control. Nevertheless, computational efficiency is a challenging issue. Direct Monte Carlo simulation is unlikely to be feasible especially for a complex structure with a large number of degrees-of-freedom. In this research, we develop a new probabilistic framework built upon the Gaussian process meta-modeling architecture to analyze mode shape variation. To expedite the generation of input data set for meta-model establishment, a multi-level strategy is adopted which can blend a large amount of low-fidelity data acquired from order-reduced analysis with a small amount of high-fidelity data produced by high-dimensional full finite element analysis. To take advantage of the intrinsic relation of spatial distribution of mode shape, a multi-response strategy is incorporated to predict mode shape variation at different locations simultaneously. These yield a multi-level, multi-response Gaussian process that can efficiently and accurately quantify the effect of structural uncertainty to mode shape variation. Comprehensive case studies are carried out for demonstration and validation.