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1. Tropical Cyclone Genesis Potential Using a Ventilated Potential Intensity

   https://doi.org/10.1175/JCLI-D-24-0186.1  

   Chavas, Daniel R; Camargo, Suzana J; Tippett, Michael K (April 2025, Journal of Climate)

   Abstract Genesis potential indices (GPIs) are widely used to understand the climatology of tropical cyclones (TCs). However, the sign of projected future changes depends on how they incorporate environmental moisture. Recent theory combines potential intensity and midtropospheric moisture into a single quantity called the ventilated potential intensity, which removes this ambiguity. This work proposes a new GPI (GPI_υ) that is proportional to the product of the ventilated potential intensity and the absolute vorticity raised to a power. This power is estimated to be approximately 5 by fitting observed tropical cyclone best track and ECMWF Reanalysis v5 (ERA5) data. Fitting the model with separate exponents yields nearly identical values, indicating that their product likely constitutes a single joint parameter. Likewise, results are nearly identical for a Poisson model as for the power law. GPI_υperforms comparably well to existing indices in reproducing the climatological distribution of tropical cyclone genesis and its covariability with El Niño–Southern Oscillation, while only requiring a single fitting exponent. When applied to phase 6 of the Coupled Model Intercomparison Project (CMIP6) projections, GPI_υpredicts that environments globally will become gradually more favorable for TC genesis with warming, consistent with prior work based on the normalized entropy deficit, though significant changes emerge only at higher latitudes under relatively strong warming. The GPI_υhelps resolve the debate over the treatment of the moisture term and its implication for changes in TC genesis favorability with warming, and its clearer physical interpretation may offer a step forward toward a theory for genesis across climate states. Significance StatementTropical cyclones cause significant human impacts globally, yet we currently do not understand what controls the number of storms that form each year. Tropical cyclone formation depends on fine-scale processes that our climate models cannot capture. Thus, it is common to use parameters from the background environment to represent regions favorable for cyclone formation. However, there are a variety of formulations because the link between environment and cyclone formation is complicated. This work proposes a new method that unifies a few common formulations, which helps resolve a divergence in current explanations of how tropical cyclone formation may change under climate change. 

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2. Geometric Contact Potential

   https://doi.org/10.1145/3731142  

   Huang, Zizhou; Paik, Maxwell; Ferguson, Zachary; Panozzo, Daniele; Zorin, Denis (August 2025, ACM Transactions on Graphics)

   Barrier potentials gained popularity as a means for robust contact handling in physical modeling and for modeling self-avoiding shapes. The key to the success of these approaches is adherence to geometric constraints, i.e., avoiding intersections, which are the cause of most robustness problems in complex deformation simulation with contact. However, existing barrier-potential methods may lead to spurious forces and imperfect satisfaction of the geometric constraints. They may have strong resolution dependence, requiring careful adaptation of the potential parameters to the object discretizations. We present a systematic derivation of a continuum potential defined for smooth and piecewise smooth surfaces, starting from identifying a set of natural requirements for contact potentials, including the barrier property, locality, differentiable dependence on shape, and absence of forces in rest configurations. Our potential is formulated independently of surface discretization and addresses the shortcomings of existing potential-based methods while retaining their advantages. We present a discretization of our potential that is a drop-in replacement for the potential used in the incremental potential contact formulation [Li et al. 2020], and compare its behavior to other potential formulations, demonstrating that it has the expected behavior. The presented formulation connects existing barrier approaches, as all recent existing methods can be viewed as a variation of the presented potential, and lays a foundation for developing alternative (e.g., higher-order) versions. 

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3. Potential automorphy for $$GL_n$$

   https://doi.org/10.1007/s00222-022-01161-6  

   Qian, Lie (September 2022, Inventiones mathematicae)

   We prove potential automorphy results for a single Galois representation 𝐺𝐹→𝐺𝐿𝑛(ℚ⎯⎯⎯⎯⎯𝑙) where F is a CM number field. The strategy is to use the p, q switch trick to go between the p-adic and q-adic realisation of a certain variant of the Dwork motive. We choose this variant to break self-duality shape of the motives, but not the Hodge-Tate weights. Another key result to prove is that certain p-adic representations we choose that come from the Dwork motives is ordinarily automorphic. One input is the automorphy lifting theorem in Allen et al.: (Potential automorphy over CM fields, Cornell University, New York 2018) . 

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4. Codimensional incremental potential contact

   https://doi.org/10.1145/3450626.3459767  

   Li, Minchen; Kaufman, Danny M.; Jiang, Chenfanfu (August 2021, ACM Transactions on Graphics)

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5. Tropical Cyclone Potential Size

   https://doi.org/10.1175/JAS-D-21-0325.1  

   Wang, Danyang; Lin, Yanluan; Chavas, Daniel R. (November 2022, Journal of the Atmospheric Sciences)

   Abstract A model for tropical cyclone (TC) potential size (PS), which is capable of predicting the equilibrium outer radius of a TC solely from environmental parameters, is proposed. The model combines an updated Carnot cycle model with a physical model for the wind profile, which serve as energetic and dynamic constraints, respectively, on the minimum pressure. Physically, the Carnot cycle model defines how much the surface pressure can be dropped energetically, and the wind profile model defines how large the steady-state storm needs to be to yield that pressure drop for a given maximum wind speed. The model yields an intrinsic length scale V Carnot / f , with f the Coriolis parameter, V Carnot similar to the potential intensity V p , but without a dependence on the surface exchange coefficients of enthalpy C k and momentum C d . Analytic tests with the theory varying outflow temperature, sea surface temperature (SST), and f demonstrate that the model predictions are qualitatively consistent with the V p / f scaling for outer size found in past work. The model also predicts a weak dependence of outer size on C d , C k , and horizontal mixing length l h of turbulence, consistent with numerical simulation results. Idealized numerical simulation experiments with varied tropopause temperature, SST, f , C d , C k , and l h show that the model performs well in predicting the simulated outer radius. The V Carnot / f scaling also better captures the dependence of simulated TC size on SST than V p / f . Overall, the model appears to capture the essential physics that determine equilibrium TC size on the f plane. 

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