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1. Stability and Large-Time Behavior on 3D Incompressible MHD Equations with Partial Dissipation Near a Background Magnetic Field

   https://doi.org/10.1007/s00205-025-02100-4  

   Lin, Hongxia; Wu, Jiahong; Zhu, Yi (April 2025, Archive for Rational Mechanics and Analysis)

   Abstract Physical experiments and numerical simulations have observed a remarkable stabilizing phenomenon: a background magnetic field stabilizes and dampens electrically conducting fluids. This paper intends to establish this phenomenon as a mathematically rigorous fact on a magnetohydrodynamic (MHD) system with anisotropic dissipation in$$\mathbb R^3$$ $R^3$. The velocity equation in this system is the 3D Navier–Stokes equation with dissipation only in the$$x_1$$ $x_1$-direction, while the magnetic field obeys the induction equation with magnetic diffusion in two horizontal directions. We establish that any perturbation near the background magnetic field (0, 1, 0) is globally stable in the Sobolev setting$$H^3({\mathbb {R}}^3)$$ $H^3\left(R^3\right)$. In addition, explicit decay rates in$$H^2({\mathbb {R}}^3)$$ $H^2\left(R^3\right)$are also obtained. For when there is no presence of a magnetic field, the 3D anisotropic Navier–Stokes equation is not well understood and the small data global well-posedness in$$\mathbb R^3$$ $R^3$remains an intriguing open problem. This paper reveals the mechanism of how the magnetic field generates enhanced dissipation and helps to stabilize the fluid. 

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2. PANDORA Project for the study of photonuclear reactions below $$A=60$$

   https://doi.org/10.1140/epja/s10050-023-01081-w  

   Tamii, A; Pellegri, L; Söderström, P-A; Allard, D; Goriely, S; Inakura, T; Khan, E; Kido, E; Kimura, M; Litvinova, E; et al (September 2023, The European Physical Journal A)

   Borge, Maria (Ed.)

   Abstract Photonuclear reactions of light nuclei below a mass of$$A=60$$ $A=60$are planned to be studied experimentally and theoretically with the PANDORA (Photo-Absorption of Nuclei and Decay Observation for Reactions in Astrophysics) project. Two experimental methods, virtual photon excitation by proton scattering and real photo absorption by a high-brilliance$$\gamma $$ $\gamma$-ray beam produced by laser Compton scattering, will be applied to measure the photoabsorption cross sections and decay branching ratio of each decay channel as a function of the photon energy. Several nuclear models, e.g. anti-symmetrized molecular dynamics, mean-field and beyond-mean-field models, a large-scale shell model, and ab initio models, will be employed to predict the photonuclear reactions. The uncertainty in the model predictions will be evaluated based on the discrepancies between the model predictions and experimental data. The data and predictions will be implemented in the general reaction calculation code, . The results will be applied to the simulation of the photo-disintegration process of ultra-high-energy cosmic rays in inter-galactic propagation. 

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3. Twisted-bilayer FeSe and the Fe-based superlattices

   https://doi.org/10.21468/SciPostPhys.15.3.081  

   Eugenio, Paul Myles; Vafek, Oskar (January 2023, SciPost Physics)

   We derive BM-like continuum models for the bands of superlattice heterostructures formed out of Fe-chalcogenide monolayers: (I) a single monolayer experiencing an external periodic potential, and (II) twisted bilayers with long-range moire tunneling. A symmetry derivation for the inter-layer moire tunnelling is provided for both the\Gamma $\Gamma$andM $M$high-symmetry points. In this paper, we focus on moire bands formed from hole-band maxima centered on\Gamma $\Gamma$, and show the possibility of moire bands withC=0 $C=0$or±1 $\pm 1$topological quantum numbers without breaking time-reversal symmetry. In theC=0 $C=0$region for\theta→0 $\theta \to 0$(and similarly in the limit of large superlattice period for I), the system becomes a square lattice of 2D harmonic oscillators. We fit our model to FeSe and argue that it is a viable platform for the simulation of the square Hubbard model with tunable interaction strength. 

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4. Mean curvature flow with generic initial data

   https://doi.org/10.1007/s00222-024-01258-0  

   Chodosh, Otis; Choi, Kyeongsu; Mantoulidis, Christos; Schulze, Felix (April 2024, Inventiones mathematicae)

   Abstract We show that the mean curvature flow of generic closed surfaces in$$\mathbb{R}^{3}$$ $R^3$avoids asymptotically conical and non-spherical compact singularities. We also show that the mean curvature flow of generic closed low-entropy hypersurfaces in$$\mathbb{R}^{4}$$ $R^4$is smooth until it disappears in a round point. The main technical ingredient is a long-time existence and uniqueness result for ancient mean curvature flows that lie on one side of asymptotically conical or compact shrinking solitons. 

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5. The anisotropic Bernstein problem

   https://doi.org/10.1007/s00222-023-01222-4  

   Mooney, Connor; Yang, Yang (January 2024, Inventiones mathematicae)

   Abstract We construct nonlinear entire anisotropic minimal graphs over$$\mathbb{R}^{4}$$ $R^4$, completing the solution to the anisotropic Bernstein problem. The examples we construct have a variety of growth rates, and our approach both generalizes to higher dimensions and recovers and elucidates known examples of nonlinear entire minimal graphs over$$\mathbb{R}^{n},\, n \geq 8$$ $R^n,n\ge 8$. 

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