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GLOBALLY BOUNDED IN-TIME SOLUTIONS TO A PARABOLIC-ELLIPTIC SYSTEM MODELLING CHEMOTAXIS

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Acta Mathematica Scientia 2007年第2期27卷 421-429页

作者：钟新华江松 Department of Basic Courses Beijing Information Technology Institute LCP Institute of Applied Physics and Computational Mathematics

In this article, the globally bounded in-time pointwise estimate of solutions to the simplified Keller-Segel system modelling chemotaxis are derived. Moreover, a local existence theorem is obtained.

关键词： Keller-Segel system chemotaxis globally bounded

Fast-slow neural networks for learning singularly perturbed dynamical systems

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Journal of computational physics 2025年 537卷

作者： Serino, Daniel A. Alvarez Loya, Allen Burby, J.W. Kevrekidis, Ioannis G. Tang, Qi Los Alamos National Laboratory Los Alamos NM United States Department of Physics University of Texas at Austin Austin TX United States Department of Chemical and Biomolecular Engineering and Department of Applied Mathematics and Statistics Johns Hopkins University Baltimore MD United States School of Computational Science and Engineering Georgia Institute of Technology Atlanta GA United States

Singularly perturbed dynamical systems play a crucial role in climate dynamics and plasma physics. A powerful and well-known tool to address these systems is the Fenichel normal form, which significantly simplifies fast dynamics near slow manifolds through a transformation. However, this normal form is difficult to realize in conventional numerical algorithms. In this work, we explore an alternative way of realizing it through structure-preserving machine learning. Specifically, a fast-slow neural network (FSNN) is proposed for learning data-driven models of singularly perturbed dynamical systems with dissipative fast timescale dynamics. Our method enforces the existence of a trainable, attracting invariant slow manifold as a hard constraint. Closed-form representation of the slow manifold enables efficient integration on the slow time scale and significantly improves prediction accuracy beyond the training data. We demonstrate the FSNN on examples including the Grad moment system, two-scale Lorenz96 equations, and Abraham-Lorentz dynamics modeling radiation reaction of electrons. © 2025 Elsevier Inc.

关键词： Closures Model reduction Singularly perturbed dynamical systems Slow manifold

A Weakly Nonlinear Model for Kelvin-Helmholtz Instability in Incompressible Fluids

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Chinese physics Letters 2009年第7期26卷 211-214页

作者：王立锋叶文华范征锋薛创李英骏 Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing 100088 Center for Applied Physics and Technology Peking University Beijing 100871 Department of Physics Zhejiang University Hangzhou 310028 China University of Mining and Technology Beijing 100083

A weakly nonlinear model is proposed for the Kelvin-Helmholtz instability in two-dimensional incompressible fluids by expanding the perturbation velocity potential to third order. The third-order harmonic generation effects of single-mode perturbation are analyzed, as well as the nonlinear correction to the exponential growth of the fundamental modulation. The weakly nonlinear results are supported by numerical simulations. Density and resonance effects exist in the development of mode coupling.

关键词： Fluid dynamics

Determination of Landé gJ factor and Zeeman coefficients in ground-state 171Yb+ and their applications to quantum frequency standards

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arXiv 2025年

作者： Han, Jize Lu, Benquan Yu, Yanmei Li, Jiguang Huang, Zhiguo Wen, Jingwei Qian, Ling Wang, Lijun State Key Laboratory of Precision Measurement Technology and Instruments Department of Precision Instrument Tsinghua University Beijing100084 China Software Technology Company Limited Suzhou215163 China National Time Service Center Chinese Academy of Sciences Xi’an710600 China Beijing National Laboratory for Condensed Matter Physics Institute of Physics Chinese Academy of Sciences Beijing100190 China University of Chinese Academy of Sciences Beijing100049 China Institute of Applied Physics and Computational Mathematics Beijing100088 China Department of Physics Tsinghua University Beijing100084 China

We report the determination of the Landé gJ factor and Zeeman coefficients for the ground-state of 171Yb+, relevant to microwave quantum frequency standards (QFSs). The gJ factor is obtained by using two independent methods: multiconfiguration Dirac-Hartree-Fock and multireference configuration interaction, yielding a consistent value of 2.002615(70). The first- and second-order Zeeman coefficients are determined as 14,010.78(49) Hz/µT and 31.0869(22) mHz/µT2, respectively, based on the calculated gJ factor. These coefficients enable reduced magnetic-field-induced uncertainties, improving the accuracy of the 171Yb+ microwave QFSs. The results reported in this work also offer potential for improved constraints on variations in fundamental constants through frequency comparisons, and advancing trapped-ion quantum computers based on the ground-state hyperfine splitting of 171Yb+ © 2025, CC BY.

关键词： Trapped ions

New developments in MatCont: delay equation importer and Lyapunov exponents

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arXiv 2025年

作者： Liessi, Davide Santi, Enrico Vermiglio, Rossana Thakur, Mayank Meijer, Hil G.E. Scarabel, Francesca CDLab – Computational Dynamics Laboratory Department of Mathematics Computer Science and Physics University of Udine Italy Department of Applied Mathematics University of Twente Netherlands School of Mathematics University of Leeds United Kingdom CDLab – Computational Dynamics Laboratory University of Udine Italy

MatCont is a powerful toolbox for numerical bifurcation analysis focussing on smooth ODEs. A user can study equilibria, periodic and connecting orbits, and their stability and bifurcations. Here, we report on additional features in version 7p6. The first is a delay equation importer enabling MatCont users to study a much larger class of models, namely delay equations with finite delay (including delay differential and renewal equations). This importer translates the delay equation into a system of ODEs using a pseudospectral approximation with an order specified by the user. We also implemented Lyapunov exponent computations, event functions for Poincaré maps, and enhanced homoclinic continuation. We demonstrate these features with test cases, such as the Mackey–Glass equation and a renewal equation, and provide additional examples in online tutorials. © 2025, CC BY.

关键词： Bifurcation (mathematics)

Study on Non-Sequential Double Ionization of Aligned Diatomic Molecules in Strong Laser Fields

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Chinese physics Letters 2007年第5期24卷 1231-1233页

作者：李燕陈京杨世平刘杰 Department of Physics Hebei Normal University Shijiazhuang 050016 Institute of Applied Physics and Computational Mathematics PO Box 8009 Beijing 100088

We develop a semiclassical model to describe the non-sequential double ionization of aligned diatomic molecules in an intense linearly polarized field. It is found that in the tunnelling regime, the oriented molecule shows geometric effects on double ionization process when aligned parallel and perpendicular to the external field. Our results are qualitatively consistent with the recent experimental observations.

关键词： ABOVE-THRESHOLD-IONIZATION RESCATTERING DYNAMICS PULSES

Existence and Stability of Static Solutions of the Landau-Lifshitz Equation with Multi-direct Effective Field

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Acta Mathematica Sinica,English Series 2004年第6期20卷 1135-1152页

作者： Bo Ling GUO Gan Shan YANG Institute of Applied Physics and Computational Mathematics Center for Nonlinear Studies Department of Mathematics Yunnan Nationalities University Graduate School of Chinese Academy of Engineering Physics

We prove the existence of solutions of the static Landau-Lifshitz equation with multi- direct effective field and with Dirichlet boundary condition,and establish the stability of the solution of Landau-Lifshitz equati... 详细信息

关键词： Landau-Lifshitz equation Liapunov stable Multi-direct effective field

Integrating Chain-of-Thought and Retrieval Augmented Generation Enhances Rare Disease Diagnosis from Clinical Notes

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arXiv 2025年

作者： Wu, Da Wang, Zhanliang Nguyen, Quan Wang, Kai Raymond G. Perelman Center for Cellular and Molecular Therapeutics Children's Hospital of Philadelphia PhiladelphiaPA19104 United States Applied Mathematics and Computational Science Graduate Program University of Pennsylvania PhiladelphiaPA19104 United States Bioengineering Graduate Program University of Pennsylvania PhiladelphiaPA19104 United States Department of Pathology and Laboratory Medicine Perelman School of Medicine University of Pennsylvania PhiladelphiaPA19104 United States

Background: Several studies show that large language models (LLMs) struggle with phenotype-driven gene prioritization for rare diseases. These studies typically use Human Phenotype Ontology (HPO) terms to prompt foundation models like GPT and LLaMA to predict candidate genes. However, in real-world settings, foundation models are not optimized for domain-specific tasks like clinical diagnosis, yet inputs are unstructured clinical notes rather than standardized terms. How LLMs can be instructed to predict candidate genes or disease diagnosis from unstructured clinical notes remains a major challenge. Methods: We introduce RAG-driven CoT and CoT-driven RAG, two methods that combine Chain-of-Thought (CoT) and Retrieval Augmented Generation (RAG) to analyze clinical notes. A five-question CoT protocol mimics expert reasoning, while RAG retrieves data from sources like HPO and OMIM (Online Mendelian Inheritance in Man). We evaluated these approaches on rare disease datasets, including 5,980 Phenopacket-derived notes, 255 literature-based narratives, and 220 in-house clinical notes from Children’s Hospital of Philadelphia. Results: We found that recent foundations models, including Llama 3.3-70B-Instruct and DeepSeek-R1-Distill-Llama-70B, outperformed earlier versions such as Llama 2 and GPT-3.5. We also showed that RAG-driven CoT and CoT-driven RAG both outperform foundation models in candidate gene prioritization from clinical notes;in particular, both methods with DeepSeek backbone resulted in a top-10 gene accuracy of over 40% on Phenopacket-derived clinical notes. RAG-driven CoT works better for high-quality notes, where early retrieval can anchor the subsequent reasoning steps in domain-specific evidence, while CoT-driven RAG has advantage when processing lengthy and noisy notes. Conclusions: Integrating CoT and RAG enhances LLMs’ understanding of clinical notes in the context of rare disease diagnosis, and can facilitate various downstream medical tasks. © 2025, CC

关键词： Chains

Ultradense Sphere Packings Derived From Disordered Stealthy Hyperuniform Ground States

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arXiv 2025年

作者： Kim, Jaeuk Torquato, Salvatore Princeton Materials Institute Department of Physics Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Chemistry Department of Physics Princeton Materials Institute Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Disordered stealthy hyperuniform (SHU) packings are an emerging class of exotic amorphous two-phase materials endowed with novel optical, transport, and mechanical properties. Such packings of identical spheres have been created from SHU ground-state point patterns via a modified collective-coordinate optimization scheme that includes a soft-core repulsion, besides the standard "stealthy" pair potential. To explore maximal ranges of the packing fraction , we investigate the distributions of minimum pair distances as well as nearest-neighbor distances of ensembles of SHU point patterns without and with soft-core repulsions in the first three space dimensions as a function of the stealthiness parameter χ and number of particles N within a hypercubic simulation box under periodic boundary conditions. Within the disordered regime (χ max(χ, d), decrease to zero on average as N increases if there are no soft-core repulsions. By contrast, the inclusion of soft-core repulsions results in very large max(χ, d) independent of N, reaching up to max(χ, d) = 1.0, 0.86, 0.63 in the zero-χ limit and decreasing to max(χ, d) = 1.0, 0.67, 0.47 at χ = 0.45 for d = 1, 2, 3, respectively. We obtain explicit formulas for max(χ, d) as functions of χ and N for a given value of d in both cases with and without soft-core repulsions. In two and three dimensions, our soft-core SHU ground-state packings for small χ become configurationally very close to the corresponding jammed hard-particle packings created by fast compression algorithms, as measured by their pair statistics. As χ increases beyond 0.20, the packings form fewer contacts and linear polymer-like chains as χ tends to 1/2. The resulting structure factors S(k) and pair correlation functions g2(r) reveal that soft-core repulsions significantly alter the short- and intermediate-range correlations in the SHU ground states. We show that the degree of large-scale order of the soft-core SHU ground states increases as χ increases from 0 to

关键词： Digital arithmetic