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1. Approximation of fractional harmonic maps

   https://doi.org/10.1093/imanum/drac029  

   Antil, Harbir; Bartels, Sören; Schikorra, Armin (July 2022, IMA Journal of Numerical Analysis)

   Abstract This paper addresses the approximation of fractional harmonic maps. Besides a unit-length constraint, one has to tackle the difficulty of nonlocality. We establish weak compactness results for critical points of the fractional Dirichlet energy on unit-length vector fields. We devise and analyze numerical methods for the approximation of various partial differential equations related to fractional harmonic maps. The compactness results imply the convergence of numerical approximations. Numerical examples on spin chain dynamics and point defects are presented to demonstrate the effectiveness of the proposed methods. 

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2. The Structural Compactness of a Tropical Cyclone Seed Affects Its Persistence

   https://doi.org/10.1175/JAS-D-23-0149.1  

   Lu, Kuan-Yu; Chavas, Daniel R; Wang, Danyang (May 2025, Journal of the Atmospheric Sciences)

   Abstract Tropical cyclones (TCs) are often generated from preexisting “seed” vortices. Seeds with higher persistence might have a higher chance to undergo TC genesis. What controls seed persistence remains unclear. This study proposes that planetary Rossby wave drag is a key factor that affects seed persistence. Using recently developed theory for the response of a vortex to the planetary vorticity gradient, a new parameter given by the ratio of the maximum wind speed (V_max) to the Rhines speed at the radius of maximum wind (R_max), here termed “vortex structural compactness” (C_υ), is introduced to characterize the vortex weakening by planetary Rossby wave drag. The relationship between vortex compactness and weakening rate is tested via barotropicβ-plane experiments. The vortex’s initialC_υis varied by systematically varying their initialV_maxandR_maxin idealized wind profile models. Experiments are also conducted with real-world seed vortices from reanalysis data, which possess natural compactness variability. The weakening rate depends strongly on the vortex’s initialC_υacross both idealized and real-world experiments, and the initial axis-asymmetry introduces minor differences. Experiments doubling the size of seed vortices cause them to weaken more rapidly, in line with other experiment sets. The dependence of the weakening rate on initial compactness can be predicted from a simple theory, which is more robust for more compact vortices. Our results suggest that a seed’s structure strongly modulates how long it can persist in the presence of a planetary vorticity gradient. Connections to real seeds on Earth are discussed. Significance StatementThis study explores the evolution of tropical cyclone (TC) seeds, which are preexisting weakly rotating rainstorms, in a simple setting that isolates the dynamical effects of the rotating sphere. It is not clear why some seeds can persist for a longer duration and might have a higher chance to eventually undergo genesis. We proposed that a factor called “planetary Rossby wave drag” plays a crucial role in this process. To investigate this, we introduce a new parameter called “compactness” to describe how the size and intensity of a seed vortex determines how quickly it will weaken due to this drag. We conducted experiments with numerical simulations and real-world TC seeds to test our ideas. Our findings show that the initial compactness of seeds strongly influences how quickly they weaken. We have developed a formula to predict how quickly these seeds weaken based on their compactness, which is especially accurate for more compact seeds. This research helps us understand how planetary Rossby wave drag affects the persistence of a TC seed and, ultimately, how it might impact the frequency of TCs. 

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3. Radiative Majorana neutrino masses in a parity solution to the strong CP problem

   https://doi.org/10.1007/JHEP03(2024)047  

   Hall, Lawrence J; Harigaya, Keisuke; Shpilman, Yogev (March 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> The strong CP problem is solved in Parity symmetric theories, with the electroweak gauge group containing SU(2)_L× SU(2)_Rbroken by the minimal set of Higgs fields. Neutrino masses may be explained by adding the same number of gauge singlet fermions as the number of generations. The neutrino masses vanish at tree-level and are only radiatively generated, leading to larger couplings of right-handed neutrinos to Standard Model particles than with the tree-level seesaw mechanism. We compute these radiative corrections and the mixing angles between left- and right-handed neutrinos. We discuss sensitivities to these right-handed neutrinos from a variety of future experiments that search for heavy neutral leptons with masses from tens of MeV to the multi-TeV scale. 

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4. Earth System Model Analysis of How Astronomical Forcing Is Imprinted Onto the Marine Geological Record: The Role of the Inorganic (Carbonate) Carbon Cycle and Feedbacks

   https://doi.org/10.1029/2020PA004090  

   Vervoort, Pam; Kirtland Turner, Sandra; Rochholz, Fiona; Ridgwell, Andy (September 2021, Paleoceanography and Paleoclimatology)

   Abstract Astronomical cycles are strongly expressed in marine geological records, providing important insights into Earth system dynamics and an invaluable means of constructing age models. However, how various astronomical periods are filtered by the Earth system and the mechanisms by which carbon reservoirs and climate components respond, particularly in absence of dynamic ice sheets, is unclear. Using an Earth system model that includes feedbacks between climate, ocean circulation, and inorganic (carbonate) carbon cycling relevant to geological timescales, we systematically explore the impact of astronomically modulated insolation forcing and its expression in model variables most comparable to key paleoceanographic proxies (temperature, the δ¹³C of inorganic carbon, and sedimentary carbonate content). Temperature predominately responds to short and long eccentricity and is little influenced by the modeled carbon cycle feedbacks. In contrast, the cycling of nutrients and carbon in the ocean generates significant precession power in atmospheric CO₂, benthic ocean δ¹³C, and sedimentary wt% CaCO₃, while inclusion of marine sedimentary and weathering processes shifts power to the long eccentricity period. Our simulations produce reducedpCO₂and dissolved inorganic carbon (DIC) δ¹³C at long eccentricity maxima and, contrary to early Cenozoic marine records, CaCO₃preservation in the model is enhanced during eccentricity‐modulated warmth. Additionally, the magnitude of δ¹³C variability simulated in our model underestimates marine proxy records. These model‐data discrepancies hint at the possibility that the Paleogene silicate weathering feedback was weaker than modeled here and that additional organic carbon cycle feedbacks are necessary to explain the full response of the Earth system to astronomical forcing. 

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5. Earth System Model Analysis of How Astronomical Forcing Is Imprinted Onto the Marine Geological Record: The Role of the Inorganic (Carbonate) Carbon Cycle and Feedbacks

   https://doi.org/10.1029/2023PA004826  

   Vervoort, P.; Kirtland Turner, S.; Rochholz, F.; Ridgwell, A. (March 2024, Paleoceanography and Paleoclimatology)

   Abstract Astronomical cycles are strongly expressed in marine geological records, providing important insights into Earth system dynamics and an invaluable means of constructing age models. However, how various astronomical periods are filtered by the Earth system and the mechanisms by which carbon reservoirs and climate components respond, particularly in absence of dynamic ice sheets, is unclear. Using an Earth system model that includes feedbacks between climate, ocean circulation, and inorganic (carbonate) carbon cycling relevant to geological timescales, we systematically explore the impact of astronomically‐modulated insolation forcing and its expression in model variables most comparable to key paleoceanographic proxies (temperature, the δ¹³C of inorganic carbon, and sedimentary carbonate content). Temperature predominately responds to obliquity and is little influenced by the modeled carbon cycle feedbacks. In contrast, the cycling of nutrients and carbon in the ocean generates significant precession power in atmospheric CO₂, benthic ocean δ¹³C, and sedimentary wt% CaCO₃, while inclusion of marine sedimentary and weathering processes shifts power to the long eccentricity period. Our simulations produce reducedpCO₂and dissolved inorganic carbon δ¹³C at long eccentricity maxima and, contrary to early Cenozoic marine records, CaCO₃preservation in the model is enhanced during eccentricity modulated warmth. Additionally, the magnitude of δ¹³C variability simulated in our model underestimates marine proxy records. These model‐data discrepancies hint at the possibility that the Paleogene silicate weathering feedback was weaker than modeled here and that additional organic carbon cycle feedbacks are necessary to explain the full response of the Earth system to astronomical forcing. 

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