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A SPECTRAL LEVENBERG-MARQUARDT-DEFLATION METHOD FOR MULTIPLE SOLUTIONS OF SEMILINEAR ELLIPTIC SYSTEMS

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arXiv 2025年

作者： Li, Lin Zhou, Yuheng Xie, Pengcheng Li, Huiyuan School of Mathematics and Physics University of South China Hengyang China Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory 1 Cyclotron Road BerkeleyCA94720 United States State Key Laboratory of Computer Science Laboratory of Parallel Computing Institute of Software Chinese Academy of Sciences Beijing100190 China

Many nonlinear differential equations arising from practical problems may permit nontrivial multiple solutions relevant to applications, and these multiple solutions are helpful to deeply understand these practical problems and to improve some applications. Developing an efficient numerical method for finding multiple solutions is very necessary due to the nonlinearity and multiple solutions of these equations. Moreover, providing an efficient iteration plays an important role in successfully obtaining multiple solutions with fast and stable convergence. In the current paper, an efficient algorithm for finding multiple solutions of semilinear elliptic systems is proposed, where the trust region Levenberg-Marquardt method is firstly used to iterate the resulted nonlinear algebraic system. When the nonlinear term in these equations has only the first derivative, our algorithm can efficiently find multiple solutions as well. Several numerical experiments are tested to show the efficiency of our algorithm, and some solutions which have not been shown in the literature are also found and *** Codes 65N35, 65N22, 65F05, 65L10 Copyright © 2025, The Authors. All rights reserved.

关键词： Nonlinear equations

Detecting the Most Probable High Dimensional Transition Pathway Based on Optimal Control Theory

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SSRN

SSRN 2023年

作者： Chen, Jianyu Gao, Ting Li, Yang Duan, Jinqiao School of Mathematics and Statistics Center for Mathematical Sciences Huazhong University of Science and Technology Wuhan430074 China School of Automation Nanjing University of Science and Technology Nanjing210094 China Department of Applied Mathematics Department of Physics Illinois Institute of Technology ChicagoIL60616 United States

Many natural systems exhibit transitions when external environmental conditions spark a shift to a new and sometimes quite different state. Therefore, detecting the most probable transition pathway between metastable states of a stochastic dynamical system is a significant topic. The most probable transition pathway is the minimizer of the associated Onsager-Machlup action functional. We convert this variational problem for computing the most probable transition pathway into a deterministic optimal control problem. One traditional variational approach for an optimal control problem is via the Pontryagin’s Maximum Principle, but it is a challenge in high dimensional systems. In this paper, we devise a method to detect the most probable transition pathway for stochastic dynamical systems, by combining the Pontryagin’s Maximum Principle with a successive approximation scheme and a nested neural network technique. We validate our method with three stochastic dynamical systems, including a double well system, a Maier-Stein system and a Nutrient-Phytoplankton-Zooplanktonr system. Specifically, we test the error and convergence of our method, in order to illustrate its effectiveness. Our method contributes to better understanding of transition phenomena in complex systems under random fluctuations. © 2023, The Authors. All rights reserved.

关键词： Maximum principle

Operando Spectroscopic Analysis of Axial Oxygen-Coordinated Single-Sn-Atom Sites for Electrochemical CO2 Reduction

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Journal of the American Chemical Society 2023年第13期145卷 7242-7251页

作者： Deng, Yachen Zhao, Jian Wang, Shifu Chen, Ruru Ding, Jie Tsai, Hsin-Jung Zeng, Wen-Jing Hung, Sung-Fu Xu, Wei Wang, Junhu Jaouen, Frédéric Li, Xuning Huang, Yanqiang Liu, Bin State Key Laboratory of Catalysis Dalian Institute of Chemical Physics Chinese Academy of Sciences Dalian116023 China University of Chinese Academy of Sciences Beijing100049 China Department of Chemical Physics University of Science and Technology of China Hefei230026 China School of Chemistry Chemical Engineering and Biotechnology Nanyang Technological University 62 Nanyang Drive Singapore637459 Singapore Department of Applied Chemistry National Yang Ming Chiao Tung University Hsinchu300 Taiwan Beijing Synchrotron Radiation Facility Institute of High Energy Physics Beijing100049 China RICMASS Rome International Center for Materials Science Superstripes Rome0185 Italy Center for Advanced Mössbauer Spectroscopy Mössbauer Effect Data Center Dalian Institute of Chemical Physics Chinese Academy of Sciences Dalian116023 China Institut Charles Gerhardt Montpellier University of Montpellier CNRS ENSCM Montpellier34095 France Department of Materials Science and Engineering City University of Hong Kong Hong Kong SAR Kowloon999077 Hong Kong

Sn-based materials have been demonstrated as promising catalysts for the selective electrochemical CO2 reduction reaction (CO2RR). However, the detailed structures of catalytic intermediates and the key surface species remain to be identified. In this work, a series of single-Sn-atom catalysts with well-defined structures is developed as model systems to explore their electrochemical reactivity toward CO2RR. The selectivity and activity of CO2 reduction to formic acid on Sn-single-atom sites are shown to be correlated with Sn(IV)-N4 moieties axially coordinated with oxygen (O-Sn-N4), reaching an optimal HCOOH Faradaic efficiency of 89.4% with a partial current density (jHCOOH) of 74.8 mA·cm-2 at −1.0 V vs reversible hydrogen electrode (RHE). Employing a combination of operando X-ray absorption spectroscopy, attenuated total reflectance surface-enhanced infrared absorption spectroscopy, Raman spectroscopy, and 119Sn Mössbauer spectroscopy, surface-bound bidentate tin carbonate species are captured during CO2RR. Moreover, the electronic and coordination structures of the single-Sn-atom species under reaction conditions are determined. Density functional theory (DFT) calculations further support the preferred formation of Sn-O-CO2 species over the O-Sn-N4 sites, which effectively modulates the adsorption configuration of the reactive intermediates and lowers the energy barrier for the hydrogenation of *OCHO species, as compared to the preferred formation of *COOH species over the Sn-N4 sites, thereby greatly facilitating CO2-to-HCOOH conversion. © 2023 American Chemical Society.

关键词： Atoms

Extraction of binary neutron star gravitational wave waveforms from Einstein Telescope using deep learning

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arXiv 2024年

作者： Ma, CunLiang Yu, XinYao Cao, Zhoujian Jia, Mingzhen School of Information Engineering Jiangxi University of Science and Technology Ganzhou341000 China Jiangxi Provincial Key Laboratory of Multidimensional Intelligent Perception and Control Ganzhou341000 China Institute of Applied Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Fundamental Physics and Mathematical Sciences Hangzhou Institute for Advanced Study UCAS Hangzhou310024 China

In the future, the third generation (3G) gravitational wave (GW) detectors, exemplified by the Einstein Telescope (ET), will be operational. The detection rate of GW from binary neutron star (BNS) is expected to reach approximately 104 per year. To address the challenges posed by BNS GW data processing for 3G GW detectors, this paper explores the extraction of BNS waveforms from ET. Drawing inspiration from SPIIR’s matched filtering approach, we introduce a novel framework leveraging deep learning for BNS waveform extraction. By integrating denoised outputs of time-delayed strain, we can reconstruct the embedded BNS waveform. We have established three distinct BNS GW denoising models, each tailored to address the early inspiral, later inspiral, and merger phases of BNS GW, respectively. To further regulate the waveform shape, we propose the Amplitude Regularity Model that takes denoised output as input and regulated waveform as output. The experiments conducted on test data demonstrate the efficacy of the denoising models, the Amplitude Regularity Models, as well as the overall waveform construction method. To the best of our knowledge, this marks the first instance of deep learning being utilized for the task of BNS waveform extraction. We believe that the proposed method holds promise for early warning, searching, and localization of BNS GWs. Copyright © 2024, The Authors. All rights reserved.

关键词： Gravity waves

Chirality-selective transparency induced by lattice resonance in bilayer metasurfaces

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Photonics Research 2021年第4期9卷 484-493页

作者： Shuxia Zhao Lei Shao Jianfang Wang Hai-Qing Lin Wei Zhang Institute of Applied Physics and Computational Mathematics Beijing 100088China Beijing Computational Science Research Center Beijing 100193China Department of Physics The Chinese University of Hong KongShatinHong Kong SARChina

Chiral optical responses of bilayer metasurfaces made of twisted metallic nanorods are investigated in detail with focus on the collective effect due to lattice resonance(LR).Using an analytical approach based on the coupled dipole method(supported by full wave simulation),we find optical chirality is dramatically increased by the coupling between localized surface plasmon resonances and *** collective effect results in significant chiral signal even for metasurfaces made of achiral unit *** interlayer coupling generally destroys the Wood’s anomaly and the associated *** making use of Pancharatnam–Berry(PB)phase and propagation phase,one can modulate the optical activity effectively and achieve chirality-selective transparency induced by LR in a designed structure with a g-factor of absorption as high as 1.99(close to the upper limit of 2).Our studies not only reveal a new mechanism of modulating chiral optical response by combination effects from PB phase,propagation phase,and LR,but also give a quantitative relationship between the geometry configuration and chiral optical properties,thus providing helpful guidance for device design.

关键词： transparency chiral lattice

Evidence for Magnetic Fractional Excitations in a Kitaev Quantum-Spin-Liquid Candidate α-RuCl_(3)

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Chinese physics Letters 2022年第2期39卷 72-77页

作者： Kejing Ran Jinghui Wang Song Bao Zhengwei Cai Yanyan Shangguan Zhen Ma Wei Wang Zhao-Yang Dong P.Cermak A.Schneidewind Siqin Meng Zhilun Lu Shun-Li Yu Jian-Xin Li Jinsheng Wen School of Physical Science and Technology and ShanghaiTech Laboratory for Topological PhysicsShanghaiTech UniversityShanghai 200031China National Laboratory of Solid State Microstructures and Department of Physics Nanjing UniversityNanjing 210093China Institute for Advanced Materials Hubei Normal UniversityHuangshi 435002China School of Science Nanjing University of Posts and TelecommunicationsNanjing 210023China Department of Applied Physics Nanjing University of Science and TechnologyNanjing 210094China Julich Centre for Neutron Science(JCNS)at Heinz Maier-Leibnitz Zentrum(MLZ) Forschungszentrum Jülich GmbHLichtenbergstr.185748 GarchingGermany Charles University Faculty of Mathematics and PhysicsDepartment of Condensed Matter PhysicsKe Karlovu 512116PrahaCzech Republic Helmholtz-Zentrum Berlin fur Materialien und Energie GmbH Hahn-Meitner-Platz 1D-14109BerlinGermany China Institute of Atomic Energy(CIAE) Beijing 102413China The Henry Royce Institute and Department of Materials Science and Engineering The University of SheffieldSir Robert Hadfield BuildingSheffieldS13JDUnited Kingdom Collaborative Innovation Center of Advanced Microstructures Nanjing UniversityNanjing 210093China

It is known that α-RuCl_(3) has been studied extensively because of its proximity to the Kitaev quantum-spin-liquid(QSL)phase and the possibility of approaching it by tuning the competing *** we present the first polarized inelastic neutron scattering study on α-RuCl_(3) single crystals to explore the scattering continuum around the Γ point at the Brillouin zone center,which was hypothesized to be resulting from the Kitaev QSL state but without concrete *** polarization analyses,we find that,while the spin-wave excitations around the Γ point vanish above the transition temperature T_(N),the pure magnetic continuous excitations around the Γ point are robust against ***,by calculating the dynamical spin-spin correlation function using the cluster perturbation theory,we derive magnetic dispersion spectra based on the K-Γ model,which involves with a ferromagnetic Kitaev interaction of −7.2 meV and an off-diagonal interaction of 5.6 *** find this model can reproduce not only the spin-wave excitation spectra around the Γ point,but also the non-spin-wave continuous magnetic excitations around the Γ *** results provide evidence for the existence of fractional excitations around the Γ point originating from the Kitaev QSL state,and further support the validity of the K-Γ model as the effective minimal spin model to describe α-RuCl_(3).

关键词： temperature excitation diagonal

A self-induced mechanism of large-scale helical structures in compressible turbulent flows

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arXiv 2024年

作者： Yan, Zheng Wang, Jianchun Wang, Lifeng Lei, Zhu Wu, Junfeng Duan, Junyi Tong, Fulin Li, Xinliang Yu, Changping Institute of Applied Physics and Computational Mathematics Beijing100094 China Department of Mechanics and Aerospace Engineering Southern University of Science and Technology Guangdong Shenzhen518055 China Center for Applied Physics and Technology HEDPS Peking University Beijing100871 China LHD Institute of Mechanics Chinese Academy of Sciences Beijing100190 China School of Engineering Science University of Chinese Academy of Sciences Beijing100049 China State Key Laboratory of Aerodynamics China Aerodynamics Research and Development Center Mianyang621000 China

A novel self-sustaining mechanism is proposed for large-scale helical structures in compressible turbulent flows. The existence of two channels of subgrid-scale and viscosity terms for large-scale helicity evolution is confirmed for the first time, through selecting a physical definition of the large-scale helicity in compressible turbulence. Under the influence of the fluid element expansion, it is found that the helicity is generated at small scales via the second-channel viscosity, and the inverse cross-scale helicity transfers at inertial scales through the second-channel helicity flux. Together, they form a self-induced mechanism, which provides a physical insight into the long-period characteristic of large-scale helical structures in the evolution of compressible flow systems. © 2024, CC0.

关键词： Turbulent flow

Macroscopic Auxiliary Asymptotic Preserving Neural Networks for the Linear Radiative Transfer Equations

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SSRN

SSRN 2023年

作者： Li, Hongyan Jiang, Song Sun, Wenjun Xu, Liwei Zhou, Guanyu School of Mathematical Sciences University of Electronic Science and Technology of China Sichuan Chengdu611731 China Institute of Applied Physics and Computational Mathematics Beijing100094 China Institute of Fundamental and Frontier Sciences University of Electronic Science and Technology of China Sichuan Chengdu611731 China

We develop a Macroscopic Auxiliary Asymptotic-Preserving Neural Network (MA-APNN) method to solve the time-dependent linear radiative transfer equations (LRTEs), which have a multi-scale nature and high dimensionality. To achieve this, we utilize the physics-Informed Neural Networks (PINNs) framework and design a new adaptive exponentially weighted Asymptotic-Preserving (AP) loss function, which incorporates the macroscopic auxiliary equation that is derived from the original transfer equation directly and explicitly contains the information of the diffusion limit equation. Thus, as the scale parameter tends to zero, the loss function gradually transitions from the transport state to the diffusion limit state. In addition, the initial data, boundary conditions, and conservation laws serve as the regularization terms for the loss. We present several numerical examples to demonstrate the effectiveness of MA-APNNs. © 2023, The Authors. All rights reserved.

关键词： Radiative transfer

Cosmological cutting rules for Bogoliubov initial states

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arXiv 2024年

作者： Ghosh, Diptimoy Pajer, Enrico Ullah, Farman Indian Institute of Science Education and Research Pune Dr. Homi Bhabha Road Pune411008 India Department of Applied Mathematics and Theoretical Physics University of Cambridge Wilberforce Road CambridgeCB3 0WA United Kingdom

The field theoretic wavefunction in cosmological spacetimes has received much attention as a fundamental object underlying the generation of primordial perturbations in our universe. Assuming an initial Bunch-Davies state, unitary time evolution implies an infinite set of cutting rules for the wavefunction to all orders in perturbation theory, collectively known as the cosmological optical theorem. In this work, we generalise these results to the case of Bogoliubov initial states, accounting for both parity-even and parity-odd interactions. We confirm our findings in a few explicit examples, assuming IR-finite interactions. In these examples, we preserve scale invariance by adiabatically turning on interactions in the infinite past rather than imposing a Bogoliubov state at some finite initial time. Finally, we give a prescription for computing Bogoliubov wavefunction coefficients from the corresponding Bunch-Davies coefficients for both n-point contact and four-point exchange diagrams. © 2024, CC BY.

关键词： Point contacts