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INTERTWINING OPERATORS BEYOND THE STARK EFFECT

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arXiv 2024年

作者： Fanelli, Luca Su, Xiaoyan Wang, Ying Zhang, Junyong Zheng, Jiqiang Ikerbasque Basque Foundation for Science Departamento de Matemáticas Universidad del País Vasco Euskal Herriko Unibertsitatea PV/EHU Leioa48940 Spain BCAM - Basque Center for Applied Mathematics Bilbao48009 Spain Loughborough University Loughborough United Kingdom Basque Center for Applied Mathematics Bilbao Spain Department of Mathematics Beijing Institute of Technology Beijing100081 China Institute of Applied Physics and Computational Mathematics National Key Laboratory of Computational Physics Beijing100088 China

The main mathematical manifestation of the Stark effect in quantum mechanics is the shift and the formation of clusters of eigenvalues when a spherical Hamiltonian is perturbed by lower order terms. Understanding this mechanism turned out to be fundamental in the description of the large-time asymptotics of the associated Schrödinger groups and can be responsible for the lack of dispersion [14, 16, 17]. Recently, Miao, Su, and Zheng introduced in [31] a family of spectrally projected intertwining operators, reminiscent of the Kato’s wave operators, in the case of constant perturbations on the sphere (inverse-square potential), and also proved their boundedness in Lp. Our aim is to establish a general framework in which some suitable intertwining operators can be defined also for non constant spherical perturbations in space dimensions 2 and higher. In addition, we investigate the mapping properties between Lp-spaces of these operators. In 2D, we prove a complete result, for the Schrödinger Hamiltonian with a (fixed) magnetic potential an electric potential, both scaling critical, allowing us to prove dispersive estimates, uniform resolvent estimates, and Lp-bounds of Bochner–Riesz means. In higher dimensions, apart from recovering the example of inverse-square potential, we can conjecture a complete result in presence of some symmetries (zonal potentials), and open some interesting spectral problems concerning the asymptotics of eigenfunctions. © 2024, CC BY.

关键词： Eigenvalues and eigenfunctions

Formation Mechanism of Laser-Driven Magnetized "Pillars of Creation"

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arXiv 2024年

作者： Lei, Zhu Wang, Lifeng Li, Jiwei Zou, Shiyang Wu, Junfeng Zhao, Zhonghai Sun, Wei Yuan, Wenqiang Li, Longxing Yan, Zheng Li, Jun Ye, Wenhua He, Xiantu Qiao, Bin Institute of Applied Physics and Computational Mathematics Beijing100094 China Center for Applied Physics and Technology HEDPS State Key Laboratory of Nuclear Physics and Technology School of Physics Peking University Beijing100871 China Beijing102413 China Frontiers Science Center for Nano-optoelectronic Peking University Beijing100094 China

Pillars of Creation, one of the most recognized objects in the sky, are believed to be associated with the formation of young stars. However, so far, the formation and maintenance mechanism for the pillars are still not fully understood due to the complexity of the nonlinear radiation magneto-hydrodynamics (RMHD). Here, under laboratory laser-driven conditions, we studied the self-consistent dynamics of pillar structures in magnetic fields by means of two-dimensional (2D) and three-dimensional (3D) RMHD simulations, and these results also support our new experimental scheme. We find only when the magnetic pressure and ablation pressure are comparable, the magnetic field can significantly alter the plasma hydrodynamics. For medium magnetized cases (βinitial ≈ 3.5), the initial magnetic fields undergo compression and amplification. This amplification results in the magnetic pressure inside the pillar becoming large enough to support the sides of the pillar against radial collapse due to pressure from the surrounding hot plasma. This effect is particularly pronounced for the parallel component (By), which is consistent with observational results. In contrast, a strong perpendicular (Bx, Bz) magnetic field (βinitial Copyright © 2024, The Authors. All rights reserved.

关键词： Magnetoplasma

Thermoelastic properties of bridgmanite using deep-potential molecular dynamics

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Physical Review B 2024年第9期109卷 094101-094101页

作者： Tianqi Wan Chenxing Luo Yang Sun Renata M. Wentzcovitch Department of Applied Physics and Applied Mathematics Columbia University New York New York 10027 USA Department of Physics Xiamen University Xiamen 361005 China Department of Physics Iowa State University Ames Iowa 50011 USA Department of Earth and Environmental Sciences Columbia University New York New York 10027 USA Lamont–Doherty Earth Observatory Columbia University Palisades New York 10964 USA Data Science Institute Columbia University New York New York 10027 USA Center for Computational Quantum Physics Flatiron Institute New York New York 10010 USA

The high-pressure Pbnm-perovskite polymorph of MgSiO3, i.e., bridgmanite (Bm), plays a crucial role in the Earth's lower mantle. It is likely responsible for ∼75 vol. % of this region and its properties dominate the properties of this region, especially its elastic properties that are challenging to measure at ambient conditions. This study combines deep-learning potential (DP) with density-functional theory (DFT) to investigate the structural and elastic properties of Bm under lower-mantle conditions. To simulate this system, we developed a series of potentials capable of faithfully reproducing DFT calculations using different functionals, i.e., local density approximation (LDA), Perdew-Burke-Ernzerhof parametrization (PBE), revised PBE for solids (PBEsol), and strongly constrained and appropriately normed (SCAN) meta–generalized-gradient approximation functionals. Our predictions with DP-SCAN exhibit a remarkable agreement with experimental measurements of high-temperature equations of states and elastic properties and highlight its superior performance, closely followed by DP-LDA in accurately predicting. This hybrid computational approach offers a solution to the accuracy-efficiency dilemma in obtaining precise elastic properties at high pressure and temperature conditions for minerals like Bm, opening a way to study the Earth material's thermodynamic properties and related phenomena.

关键词： Elasticity Pressure effects Minerals Deep learning First-principles calculations Molecular dynamics

Implicit U-KAN2.0: Dynamic, Efficient and Interpretable Medical Image Segmentation

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arXiv 2025年

作者： Cheng, Chun-Wun Zhao, Yining Cheng, Yanqi Montoya, Javier Schönlieb, Carola-Bibiane Aviles-Rivero, Angelica I. Department of Applied Mathematics and Theoretical Physics University of Cambridge United Kingdom Siebel School of Computing and Data Science University of Illinois Urbana-Champaign United States Lucerne School of Computer Science and Information Technology Lucerne University of Applied Sciences and Arts United States Yau Mathematical Sciences Center Tsinghua University China

Image segmentation is a fundamental task in both image analysis and medical applications. State-of-the-art methods predominantly rely on encoder-decoder architectures with a U-shaped design, commonly referred to as U-Net. Recent advancements integrating transformers and MLPs improve performance but still face key limitations, such as poor interpretability, difficulty handling intrinsic noise, and constrained expressiveness due to discrete layer structures, often lacking a solid theoretical *** this work, we introduce Implicit U-KAN 2.0, a novel U-Net variant that adopts a two-phase encoder-decoder structure. In the SONO phase, we use a second-order neural ordinary differential equation (NODEs), called the SONO block, for a more efficient, expressive, and theoretically grounded modeling approach. In the SONO-MultiKAN phase, we integrate the second-order NODEs and MultiKAN layer as the core computational block to enhance interpretability and representation power. Our contributions are threefold. First, U-KAN 2.0 is an implicit deep neural network incorporating MultiKAN and second order NODEs, improving interpretability and performance while reducing computational costs. Second, we provide a theoretical analysis demonstrating that the approximation ability of the MultiKAN block is independent of the input dimension. Third, we conduct extensive experiments on a variety of 2D and a single 3D dataset, demonstrating that our model consistently outperforms existing segmentation networks. Copyright © 2025, The Authors. All rights reserved.

关键词： Deep neural networks

Strategies for enhancing interfacial built-in electric field strength in S-scheme heterojunction photocatalysts: A review

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Journal of Industrial and Engineering Chemistry 2025年 148卷 1-26页

作者： Ahmad, Irshad Lama Tamang, Tensangmu Ali, Ijaz Alanazi, Abdullah K. Farahim, Farha Ali, Talat Ahmad Khasawneh, Mohammad Rauf, Abdur Department of Physics University of Agriculture Faisalabad38040 Pakistan Department of Biotechnology Yeungnam University Gyeongbuk Gyeongsan38541 Korea Republic of Centre for Applied Mathematics and Bioinformatics Gulf University for Science and Technology Hawally32093 Kuwait Department of Chemistry College of Science Taif University Taif Saudi Arabia Department of Community Psychiatric and Mental Health Nursing King Khalid University Abha61413 Saudi Arabia Department of Basic Medical Sciences King Khalid University Abha61413 Saudi Arabia Department of Chemistry College of Science U.A.E. University Al-AinP.O. Box 15551 United Arab Emirates Institute of Physics Bahauddin Zakariya University Multan Pakistan

S-scheme heterojunctions, regarded as high-performance photocatalysts, have gained increasing attention in various applications due to their effective charge separation and migration, enhanced visible light absorption, high redox capacity, and remarkable stability. However, despite achieving effective charge separation, the built-in electric field (BIEF) driving charge separation process often lacks the desired strength. The BIEF strength is influenced by the Fermi level difference between the constituent semiconductors in an S-scheme heterojunction. Several emerging strategies have been explored to increase charge separation by enhancing the BIEF, particularly through modulation of band structure and Fermi levels. Despite significant progress in strengthening the BIEF, a review addressing these strategies is still lacking. This review consolidates recent advances in strategies to increase BIEF strength in S-scheme photocatalysts. Finally, the challenges and future perspectives for increasing BIEF strength through these strategies are discussed. This review provides valuable insights for researchers aiming to optimize charge separation and overall photocatalytic performance in S-scheme photocatalysts. © 2024 The Korean Society of Industrial and Engineering Chemistry

关键词： Fermi level

Mathematical Model of Asset and Liability Management in the Presence of Normative and Internal Constraints 5

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Mathematical Model of Asset and Liability Management in the ...

5th International Conference on Control Systems, Mathematical Modeling, Automation and Energy Efficiency, SUMMA 2023

作者： Zhukova, Aleksandra Flerova, Anna Chernov, Aleksey Pilnik, Nikolay FRC CSC of RAS Dept. of Mathematical Modelling of Economic Systems MIPT Moscow Russia FRC CSC RAS Dept. of Mathematical Modelling of Economic Systems Moscow Russia Moscow Institute of Physics and Technology MIPT-School of Applied Mathematics and Computer Science Moscow Russia

ISBN: (纸本)9798350309126

In this paper we present the mathematical formulation of the problem of planning the Asset Liability Management if the Presence of Normative and Internal Constraints. As a nonlinear optimal control problem, it has specifics due to the state constraints. The maximum principle involves verification of regularity property in order to apply computational methods. We reformulate the problem as the problem with convex objective function and linear, but mixed system of constraints. This enables application of optimization methods to compute the optimal controls, and study the dependence of controls on the parameters that describe the external environments and the management objective. © 2023 IEEE.

关键词： Optimal control systems

POINTWISE ESTIMATES FOR THE FUNDAMENTAL SOLUTIONS OF HIGHER ORDER SCHRÖDINGER EQUATIONS WITH FINITE RANK PERTURBATIONS

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arXiv 2025年

作者： Chen, Xinyi Cheng, Han Huang, Shanlin School of Mathematics and Statistics Huazhong University of Science and Technology Hubei Wuhan430074 China Institute of Applied Physics and Computational Mathematics Beijing100088 China Sun Yat-sen University Guangdong Zhuhai519082 China

This paper is dedicated to studying pointwise estimates of the fundamental solution for the higher order Schrödinger equation: i∂tu(x, t) = Hu(x, t), t ∈ R, x ∈ Rn, where the Hamiltonian H is defined as H = (-Δ)m + XN j=1 h , φjiφj, with each φj (1 ≤ j ≤ N) satisfying certain smoothness and decay conditions. We show that for any positive integer m > 1 and spatial dimension n ≥ 1, e-itHPac(H) has an integral kernel K(t, x, y) satisfying the following pointwise estimate: |K(t, x, y)| . |t|- n 2m (1 + |t|- 1 2m |x - y|)- n(m-1) 2m-1 , t , 0, x, y ∈ Rn. This estimate is consistent with the upper bounds in the free case. As an application, we derive Lp-Lq decay estimates for the propagator e-itHPac(H), where the pairs (1/p, 1/q) lie within a quadrilateral region in the plane. © 2025, CC BY.

关键词： Schrodinger equation

RerrFact: Reduced Evidence Retrieval Representations for Scientific Claim Verification

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RerrFact: Reduced Evidence Retrieval Representations for Sci...

2022 Workshop on Scientific Document Understanding, SDU 2022

作者： Rana, Ashish Khanna, Deepanshu Ghosal, Tirthankar Singh, Muskaan Singh, Harpreet Rana, Prashant Singh School of Business Informatics and Mathematics University of Mannheim Germany Department of Electronics & Communication Engineering Thapar Institute of Engineering & Technology India Institute of Formal and Applied Linguistics Faculty of Mathematics and Physics Charles University Czech Republic Department of Computer Science & Engineering Thapar Institute of Engineering & Technology India

Exponential growth in digital information outlets and the race to publish has made scientific misinformation more prevalent than ever. However, the task to fact-verify a given scientific claim is not straightforward even for researchers. Scientific claim verification requires in-depth knowledge and great labor from domain experts to substantiate supporting and refuting evidence from credible scientific sources. The SciFact dataset and corresponding task provide a benchmarking leaderboard to the community to develop automatic scientific claim verification systems via extracting and assimilating relevant evidence rationales from source abstracts. In this work, we propose a modular approach that sequentially carries out binary classification for every prediction subtask as in the SciFact leaderboard. Our simple classifier-based approach uses reduced abstract representations to retrieve relevant abstracts. These are further used to train the relevant rationale-selection model. Finally, we carry out two-step stance predictions that first differentiate non-relevant rationales and then identify supporting or refuting rationales for a given claim. Experimentally, our system RerrFact with no fine-tuning, simple design, and a fraction of model parameters fairs competitively on the leaderboard against large-scale, modular, and joint modeling approaches. © 2022 Copyright for this paper by its authors.

关键词： Abstracting

Uniform Anisotropic Regularity and Low Mach Number Limit of Non-isentropic Ideal MHD Equations with a Perfectly Conducting Boundary

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arXiv 2024年

作者： Ju, Qiangchang Wang, Jiawei Zhang, Junyan Institute of Applied Physics and Computational Mathematics Beijing China Hua Loo-Keng Center for Mathematical Sciences Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Department of Mathematics National University of Singapore Singapore

We prove the low Mach number limit of non-isentropic ideal magnetohydrodynamic (MHD) equations with general initial data in the half-space whose boundary satisfies the perfectly conducting wall condition. By observing a special structure contributed by Lorentz force in vorticity analysis, we establish uniform estimates in suitable anisotropic Sobolev spaces with weights of Mach number determined by the number of material derivatives. We also observe that the entropy has the enhanced regularity in the direction of the magnetic field. These two observations help us get rid of the loss of derivatives and weights of Mach number in vorticity analysis caused by the simultaneous appearance of entropy, general initial data and the magnetic field, which is one of the major difficulties that do not appear in Euler equations or the isentropic problems. By utilizing the technique of Alinhac good unknowns, the anti-symmetric structure is preserved in the tangential estimates for the system differenetiated by high-order material derivatives. © 2024, CC BY.

关键词： Euler equations