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1. Accretion and ablation in deformable solids with an Eulerian description: examples using the method of characteristics

   https://doi.org/10.1177/10812865211054573  

   Naghibzadeh, S Kiana; Walkington, Noel; Dayal, Kaushik (January 2021, Mathematics and Mechanics of Solids)

   null (Ed.)

   Accretion and ablation, i.e., the addition and removal of mass at the surface, are important in a wide range of physical processes, including solidification, growth of biological tissues, environmental processes, and additive manufacturing. The description of accretion requires the addition of new continuum particles to the body, and is therefore challenging for standard continuum formulations for solids that require a reference configuration. Recent work has proposed an Eulerian approach to this problem, enabling side-stepping of the issue of constructing the reference configuration. However, this raises the complementary challenge of determining the stress response of the solid, which typically requires the deformation gradient that is not immediately available in the Eulerian formulation. To resolve this, the approach introduced the elastic deformation as an additional kinematic descriptor of the added material, and its evolution has been shown to be governed by a transport equation. In this work, the method of characteristics is applied to solve concrete simplified problems motivated by biomechanics and manufacturing. Specifically, (1) for a problem with both ablation and accretion in a fixed domain and (2) for a problem with a time-varying domain, the closed-form solution is obtained in the Eulerian framework using the method of characteristics without explicit construction of the reference configuration. 

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2. Stable reconstruction of simple Riemannian manifolds from unknown interior sources

   https://doi.org/10.1088/1361-6420/ace6c9  

   de_Hoop, Maarten V; Ilmavirta, Joonas; Lassas, Matti; Saksala, Teemu (July 2023, Inverse Problems)

   Abstract Consider the geometric inverse problem: there is a set of delta-sources in spacetime that emit waves travelling at unit speed. If we know all the arrival times at the boundary cylinder of the spacetime, can we reconstruct the space, a Riemannian manifold with boundary? With a finite set of sources we can only hope to get an approximate reconstruction, and we indeed provide a discrete metric approximation to the manifold with explicit data-driven error bounds when the manifold is simple. This is the geometrization of a seismological inverse problem where we measure the arrival times on the surface of waves from an unknown number of unknown interior microseismic events at unknown times. The closeness of two metric spaces with a marked boundary is measured by a labeled Gromov–Hausdorff distance. If measurements are done for infinite time and spatially dense sources, our construction produces the true Riemannian manifold and the finite-time approximations converge to it in the metric sense 

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3. Schubert line defects in 3d GLSMs. Part II. Partial flag manifolds and parabolic quantum polynomials

   https://doi.org/10.1007/JHEP04(2026)075  

   Closset, Cyril; Gu, Wei; Khlaif, Osama; Sharpe, Eric; Zhang, Hao; Zou, Hao (April 2026, Journal of High Energy Physics)

   A<sc>bstract</sc> We construct Schubert line defects in the 3d$$ \mathcal{N}=2 $$ $N=2$supersymmetric gauged linear sigma model (GLSM) with target space a partial flag manifoldX= Fl(k;n), generalizing our construction for complete flag manifolds given in a companion paper (part I) [1]. In the context of the 3d GLSM/quantum K-theory correspondence, the Schubert line defects are constructed as 1d$$ \mathcal{N}=2 $$ $N=2$supersymmetric gauge theories coupled to the 3d field theory, and they flow to objects supported on Schubert varietiesX_w⊆Xin the quantum K-theory. The flavored Witten index of the 1d defect is expected to compute the Chern character of [𝒪_w] — more precisely, it gives us a polynomial representative of the Schubert class in the quantum K-theory ring. We give strong evidence for this claim by showing in examples that the Witten indices of Schubert defects indeed reproduce a recently-defined set of polynomials that represent the Schubert classes in the Whitney presentation, which we call the parabolic Whitney polynomials. Moreover, upon using the quantum ring relations, we can convert these polynomials into seemingly new polynomials in the Toda presentation, which we call the parabolic quantum Grothendieck polynomials. These new polynomials specialize to known polynomials in various limits, including to the quantum Grothendieck polynomials in the case of the complete flag. In the 2d limit, our construction also realizes the Schubert classes [X_w] in the quantum cohomology ring of the partial flag manifold, and the parabolic quantum Grothendieck polynomials then reduce to previously known parabolic quantum Schubert polynomials. 

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4. An Inverse Boundary Value Problem for a Semilinear Wave Equation on Lorentzian Manifolds

   https://doi.org/10.1093/imrn/rnab088  

   Hintz, Peter; Uhlmann, Gunther; Zhai, Jian (May 2021, International Mathematics Research Notices)

   null (Ed.)

   Abstract We consider an inverse boundary value problem for a semilinear wave equation on a time-dependent Lorentzian manifold with time-like boundary. The time-dependent coefficients of the nonlinear terms can be recovered in the interior from the knowledge of the Neumann-to-Dirichlet map. Either distorted plane waves or Gaussian beams can be used to derive uniqueness. 

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5. Spectroscopic Properties and Reactivity of a Mn ^III ‐Hydroperoxo Complex that is Stable at Room Temperature

   https://doi.org/10.1002/chem.202403051  

   Grotemeyer, Elizabeth N; Aghaei, Zahra; Jackson, Timothy A (December 2024, Chemistry – A European Journal)

   Abstract Manganese catalysts that activate hydrogen peroxide have seen increased use in organic transformations, such as olefin epoxidation and alkane C−H bond oxidation. Proposed mechanisms for these catalysts involve the formation and activation of Mn^III‐hydroperoxo intermediates. Examples of well‐defined Mn^III‐hydroperoxo complexes are rare, and the properties of these species are often inferred from Mn^III‐alkylperoxo analogues. In this study, we show that the reaction of the Mn^III‐hydroxo complex [Mn^III(OH)(^6Medpaq)]⁺(1) with hydrogen peroxide and acid results in the formation of a dark‐green Mn^III‐hydroperoxo species [Mn^III(OOH)(^6Medpaq)]⁺(2). The formulation of2is based on electronic absorption,¹H NMR, IR, and ESI‐MS data. The thermal decay of2follows a first order process, and variable‐temperature kinetic studies of the decay of2yielded activation parameters that could be compared with those of a Mn^III‐alkylperoxo analogue. Complex2reacts with the hydrogen‐atom donor TEMPOH two‐fold faster than the Mn^III‐hydroxo complex1. Complex2also oxidizes PPh₃, and this Mn^III‐hydroperoxo species is 600‐fold more reactive with this substrate than its Mn^III‐alkylperoxo analogue [Mn^III(OO^tBu)(^6Medpaq)]⁺. DFT and time‐dependent (TD) DFT computations are used to compare the electronic structure of2with similar Mn^III‐hydroperoxo and Mn^III‐alkylperoxo complexes. 

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