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1. Shape Analysis of Functional Data with Elastic Partial Matching

   https://doi.org/10.1109/TPAMI.2021.3130535  

   Bryner, Darshan ; Srivastava, Anuj ( November 2021 , IEEE Transactions on Pattern Analysis and Machine Intelligence)

   Elastic Riemannian metrics have been used successfully for statistical treatments of functional and curve shape data. However, this usage suffers from a significant restriction: the function boundaries are assumed to be fixed and matched. Functional data often comes with unmatched boundaries, {\it e.g.}, in dynamical systems with variable evolution rates, such as COVID-19 infection rate curves associated with different geographical regions. Here, we develop a Riemannian framework that allows for partial matching, comparing, and clustering functions under phase variability {\it and} uncertain boundaries. We extend past work by (1) Defining a new diffeomorphism group G over the positive reals that is the semidirect product of a time-warping group and a time-scaling group; (2) Introducing a metric that is invariant to the action of G; (3) Imposing a Riemannian Lie group structure on G to allow for an efficient gradient-based optimization for elastic partial matching; and (4) Presenting a modification that, while losing the metric property, allows one to control the amount of boundary disparity in the registration. We illustrate this framework by registering and clustering shapes of COVID-19 rate curves, identifying basic patterns, minimizing mismatch errors, and reducing variability within clusters compared to previous methods. 

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2. “Lagrangian disks” in M-theory

   https://doi.org/10.1007/JHEP11(2020)033  

   Franco, Sebastían ; Gukov, Sergei ; Lee, Sangmin ; Seong, Rak-Kyeong ; Sparks, James ( November 2020 , Journal of High Energy Physics)

   null (Ed.)

   A bstract While the study of bordered (pseudo-)holomorphic curves with boundary on Lagrangian submanifolds has a long history, a similar problem that involves (special) Lagrangian submanifolds with boundary on complex surfaces appears to be largely overlooked in both physics and math literature. We relate this problem to geometry of coassociative submanifolds in G 2 holonomy spaces and to Spin(7) metrics on 8-manifolds with T 2 fibrations. As an application to physics, we propose a large class of brane models in type IIA string theory that generalize brane brick models on the one hand and 2d theories T [ M 4 ] on the other. 

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3. Incorporating Full Elastodynamic Effects and Dipping Fault Geometries in Community Code Verification Exercises for Simulations of Earthquake Sequences and Aseismic Slip (SEAS)

   https://doi.org/10.1785/0120220066  

   Erickson, Brittany A. ; Jiang, Junle ; Lambert, Valère ; Barbot, Sylvain D. ; Abdelmeguid, Mohamed ; Almquist, Martin ; Ampuero, Jean-Paul ; Ando, Ryosuke ; Cattania, Camilla ; Chen, Alexandre ; et al ( January 2023 , Bulletin of the Seismological Society of America)

   ABSTRACT Numerical modeling of earthquake dynamics and derived insight for seismic hazard relies on credible, reproducible model results. The sequences of earthquakes and aseismic slip (SEAS) initiative has set out to facilitate community code comparisons, and verify and advance the next generation of physics-based earthquake models that reproduce all phases of the seismic cycle. With the goal of advancing SEAS models to robustly incorporate physical and geometrical complexities, here we present code comparison results from two new benchmark problems: BP1-FD considers full elastodynamic effects, and BP3-QD considers dipping fault geometries. Seven and eight modeling groups participated in BP1-FD and BP3-QD, respectively, allowing us to explore these physical ingredients across multiple codes and better understand associated numerical considerations. With new comparison metrics, we find that numerical resolution and computational domain size are critical parameters to obtain matching results. Codes for BP1-FD implement different criteria for switching between quasi-static and dynamic solvers, which require tuning to obtain matching results. In BP3-QD, proper remote boundary conditions consistent with specified rigid body translation are required to obtain matching surface displacements. With these numerical and mathematical issues resolved, we obtain excellent quantitative agreements among codes in earthquake interevent times, event moments, and coseismic slip, with reasonable agreements made in peak slip rates and rupture arrival time. We find that including full inertial effects generates events with larger slip rates and rupture speeds compared to the quasi-dynamic counterpart. For BP3-QD, both dip angle and sense of motion (thrust versus normal faulting) alter ground motion on the hanging and foot walls, and influence event patterns, with some sequences exhibiting similar-size characteristic earthquakes, and others exhibiting different-size events. These findings underscore the importance of considering full elastodynamics and nonvertical dip angles in SEAS models, as both influence short- and long-term earthquake behavior and are relevant to seismic hazard. 

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4. Deformations and moduli of irregular canonical covers with $$K^2=4p_g-8$$

   https://doi.org/10.1007/s13163-023-00462-5  

   Bangere, Purnaprajna ; Gallego, Francisco Javier ; Mukherjee, Jayan ; Raychaudhury, Debaditya ( March 2023 , Revista Matemática Complutense)

   In this article, we study the moduli of irregular surfaces of general type with at worst canonical singularities satisfying$$K^2 = 4p_g-8$$$K^2=4p_g-8$, for any even integer$$p_g\ge 4$$$p_g\ge 4$. These surfaces also have unbounded irregularityq. We carry out our study by investigating the deformations of the canonical morphism$$\varphi :X\rightarrow {\mathbb {P}}^N$$$\phi :X\to P^N$, where$$\varphi $$$\phi$is a quadruple Galois cover of a smooth surface of minimal degree. These canonical covers are classified in Gallego and Purnaprajna (Trans Am Math Soc 360(10):5489-5507, 2008) into four distinct families, one of which is the easy case of a product of curves. The main objective of this article is to study the deformations of the other three, non trivial, unbounded families. We show that any deformation of$$\varphi $$$\phi$factors through a double cover of a ruled surface and, hence, is never birational. More interestingly, we prove that, with two exceptions, a general deformation of$$\varphi $$$\phi$is two-to-one onto its image, whose normalization is a ruled surface of appropriate irregularity. We also show that, with the exception of one family, the deformations ofXare unobstructed even though$$H^2(T_X)$$$H^2\left(T_X\right)$does not vanish. Consequently,Xbelongs to a unique irreducible component of the Gieseker moduli space. These irreducible components are uniruled. As a result of all this, we show the existence of infinitely many moduli spaces, satisfying the strict Beauville inequality$$p_g > 2q-4$$$p_g>2q-4$, with an irreducible component that has a proper quadruple sublocus where the degree of the canonical morphism jumps up. These components are above the Castelnuovo line, but nonetheless parametrize surfaces with non birational canonical morphisms. The existence of jumping subloci is a contrast with the moduli of surfaces with$$K^2 = 2p_g- 4$$$K^2=2p_g-4$, studied by Horikawa. Irreducible moduli components with a jumping sublocus also present a similarity and a difference to the moduli of curves of genus$$g\ge 3$$$g\ge 3$, for, like in the case of curves, the degree of the canonical morphism goes down outside a closed sublocus but, unlike in the case of curves, it is never birational. Finally, our study shows that there are infinitely many moduli spaces with an irreducible component whose general elements have non birational canonical morphism and another irreducible component whose general elements have birational canonical map.

    

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5. Evidence of Mixed Scaling for Mean Profile Similarity in the Stable Atmospheric Surface Layer

   https://doi.org/10.1175/JAS-D-22-0260.1  

   Heisel, Michael ; Chamecki, Marcelo ( August 2023 , Journal of the Atmospheric Sciences)

   A new mixed scaling parameterZ=z/(Lh)^1/2is proposed for similarity in the stable atmospheric surface layer, wherezis the height,Lis the Obukhov length, andhis the boundary layer depth. In comparison with the parameterζ=z/Lfrom Monin–Obukhov similarity theory (MOST), the new parameterZleads to improved mean profile similarity for wind speed and air temperature in large-eddy simulations. It also yields the same linear similarity relation for CASES-99 field measurements, including in the strongly stable (but still turbulent) regime where large deviations from MOST are observed. Results further suggest that similarity for turbulent energy dissipation rate depends on bothZandζ. The proposed mixed scaling ofZand relevance ofhcan be explained by physical arguments related to the limit ofz-less stratification that is reached asymptotically above the surface layer. The presented evidence and fitted similarity relations are promising, but the results and arguments are limited to a small sample of idealized stationary stable boundary layers. Corroboration is needed from independent datasets and analyses, including for complex and transient conditions not tested here.

    

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