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1. Tropical Cyclone Intensification Simulated in the Ooyama-type Three-layer Model with a Multilevel Boundary Layer

   https://doi.org/10.1175/JAS-D-21-0127.1  

   Fei, Rong; Wang, Yuqing (September 2021, Journal of the Atmospheric Sciences)

   Abstract The first successful simulation of tropical cyclone (TC) intensification was achieved with a three-layer model, often named the Ooyama-type three-layer model, which consists of a slab boundary layer and two shallow water layers above. Later studies showed that the use of a slab boundary layer would produce unrealistic boundary layer wind structure and too strong eyewall updraft at the top of TC boundary layer and thus simulate unrealistically rapid intensification compared to the use of a height-parameterized boundary layer. To fully consider the highly height-dependent boundary layer dynamics in the Ooyama-type three-layer model, this study replaced the slab boundary layer with a multilevel boundary layer in the Ooyama-type model and used it to conduct simulations of TC intensification and also compared the simulation with that from the model version with a slab boundary layer. Results show that compared with the simulation with a slab boundary layer, the use of a multilevel boundary layer can greatly improve simulations of the boundary-layer wind structure and the strength and radial location of eyewall updraft, and thus more realistic intensification rate due to better treatments of the surface layer processes and the nonlinear advection terms in the boundary layer. Sensitivity of the simulated TCs to the model configuration and to both horizontal and vertical mixing lengths, sea surface temperature, the Coriolis parameter, and the initial TC vortex structure are also examined. The results demonstrate that this new model can reproduce various sensitivities comparable to those found in previous studies using fully physics models. 

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2. Cloud‐Surface Coupling Alters the Morning Transition From Stable to Unstable Boundary Layer

   https://doi.org/10.1029/2022GL102256  

   Su, Tianning; Li, Zhanqing; Zheng, Youtong (March 2023, Geophysical Research Letters)

   Abstract Due to surface heating, the morning boundary layer transits from stable to neutral or convective conditions, exerting critical influences on low tropospheric thermodynamics. Low clouds closely interact with the boundary layer development, yet their interactions bear considerable uncertainties. Our study reveals that cloud‐surface coupling alters the morning transition from stable to unstable boundary layer and thus notably affects the diurnal variation of the boundary layer. Specifically, due to the reduction in surface fluxes, decoupled clouds can delay the process of eroding nocturnal inversion by 0.8‐hr and even prevent the transition of the boundary layer from happening for 12% of decoupled cases, keeping the boundary layer in a stable state during the noontime. On the other hand, when clouds are coupled with the surface, cloud‐top radiative cooling can directly cool the upper boundary layer to facilitate sub‐cloud convection, leading to an unstable boundary layer in the earlier morning. 

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3. Holder estimates for kinetic Fokker-Planck equations up to the boundary

   Luis Silvestre (December 2022, Ars inveniendi analytica)

   We obtain local Holder continuity estimates up to the boundary for a kinetic Fokker-Planck equation with rough coefficients, with the prescribed influx boundary condition. Our result extends some recent developments that incorporate De Giorgi methods to kinetic Fokker-Planck equations. We also obtain higher order asymptotic estimates near the incoming part of the boundary. In particular, when the equation has a zero boundary conditions and no source term, we prove that the solution vanishes at infinite order on the incoming part of the boundary. 

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4. Computation of free boundary minimal surfaces via extremal Steklov eigenvalue problems

   https://doi.org/10.1051/cocv/2021033  

   Oudet, Édouard; Kao, Chiu-Yen; Osting, Braxton (January 2021, ESAIM: Control, Optimisation and Calculus of Variations)

   null (Ed.)

   Recently Fraser and Schoen showed that the solution of a certain extremal Steklov eigenvalue problem on a compact surface with boundary can be used to generate a free boundary minimal surface, i.e. , a surface contained in the ball that has (i) zero mean curvature and (ii) meets the boundary of the ball orthogonally (doi: 10.1007/s00222-015-0604-x ). In this paper, we develop numerical methods that use this connection to realize free boundary minimal surfaces. Namely, on a compact surface, Σ, with genus γ and b boundary components, we maximize σ j (Σ, g )  L ( ∂ Σ, g ) over a class of smooth metrics, g , where σ j (Σ, g ) is the j th nonzero Steklov eigenvalue and L ( ∂ Σ, g ) is the length of ∂ Σ. Our numerical method involves (i) using conformal uniformization of multiply connected domains to avoid explicit parameterization for the class of metrics, (ii) accurately solving a boundary-weighted Steklov eigenvalue problem in multi-connected domains, and (iii) developing gradient-based optimization methods for this non-smooth eigenvalue optimization problem. For genus γ = 0 and b = 2, …, 9, 12, 15, 20 boundary components, we numerically solve the extremal Steklov problem for the first eigenvalue. The corresponding eigenfunctions generate a free boundary minimal surface, which we display in striking images. For higher eigenvalues, numerical evidence suggests that the maximizers are degenerate, but we compute local maximizers for the second and third eigenvalues with b = 2 boundary components and for the third and fifth eigenvalues with b = 3 boundary components. 

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5. Systematics of boundary actions in gauge theory and gravity

   https://doi.org/10.1007/JHEP04(2023)121  

   Kim, Seolhwa; Kraus, Per; Myers, Richard M. (April 2023, Journal of High Energy Physics)

   A bstract We undertake a general study of the boundary (or edge) modes that arise in gauge and gravitational theories defined on a space with boundary, either asymptotic or at finite distance, focusing on efficient techniques for computing the corresponding boundary action. Such actions capture all the dynamics of the system that are implied by its asymptotic symmetry group, such as correlation functions of the corresponding conserved currents. Working in the covariant phase space formalism, we develop a collection of approaches for isolating the boundary modes and their dynamics, and illustrate with various examples, notably AdS 3 gravity (with and without a gravitational Chern-Simons terms) subject to assorted boundary conditions. 

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