PENG Linyu

写真a

Affiliation

Faculty of Science and Technology, Department of Mechanical Engineering (Yagami)

Position

Associate Professor

Related Websites

External Links
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Career 【 Display / hide 】

  • 2013.10
    -
    2015.03

    Waseda University, Junior Researcher

  • 2015.04
    -
    2017.03

    Waseda University , Assistant Professor

  • 2017.04
    -
    2020.03

    Waseda University, Assistant Professor

  • 2020.04
    -
    2023.03

    Keio University, Assistant Professor

  • 2023.04
    -
    Present

    Keio University , Associate Professor

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Academic Background 【 Display / hide 】

  • 2004.09
    -
    2008.06

    Beijing Institute of Technology

    University, Graduated

  • 2008.09
    -
    2010.07

    Beijing Institute of Technology

    Graduate School, Completed, Master's course

  • 2010.10
    -
    2013.07

    University of Surrey

    Graduate School, Completed, Doctoral course

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Academic Degrees 【 Display / hide 】

  • PhD, University of Surrey, Coursework, 2013.09

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Research Areas 【 Display / hide 】

  • Natural Science / Basic mathematics (Applied Mathematics)

  • Natural Science / Applied mathematics and statistics (Applied Mathematics)

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Research Keywords 【 Display / hide 】

  • Symmetries and conservation laws

  • Geometric mechanics

  • Geometric integration

  • Information geometry

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Books 【 Display / hide 】

  • Paving the Way for 5G Through the Convergence of Wireless Systems

    X. Zhang, Y. Cao, L. Peng, J. Li, IGI Global Publisher, 2019

    Scope: Enhancing Mobile Data Offloading With In-Network Caching,  Contact page： 250-270

  • An Elementary Introduction to Information Geometry

    H. Sun, Z. Zhang, L. Peng, X. Duan, Science Press, Beijing, 2016.03

  • Object Recognition

    F. Li, L. Peng, H. Sun, IntechOpen, 2011.04,  Page： 350

    Scope: Fibre Bundle Models and 3D Object Recognition,  Contact page： 317-332

  • Fibre Bundle Models and 3D Object Recognition

    2011

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Papers 【 Display / hide 】

  • 半離散方程式の対称性と群不変解

    彭林玉， 富田繁， 郡司士

    Jxiv, JST プレプリントサーバ  2024.11

    　View Summary

    半離散方程式（微分差分方程式ともいう）においては，連続独立変数と離散独立変数が非可換のため，対称性とならない非内在（non-intrinsic）（または不規則（irregular））な変換が生じるという問題があった．本論文では，この問題の解決方法を論じるとともに，半離散方程式における対称性理論について紹介する．具体例として，戸田型，ヴォルテラ型，5 点の伊藤・成田・ボゴヤヴレンスキー方程式などのリー点対称性（Lie point symmetry）を求め，群不変解（group-invariant solution）を導出する．

  • Discrete Dirac structures and discrete Lagrange--Dirac dynamical systems in mechanics

    Linyu Peng, Hiroaki Yoshimura

    arXiv preprint arXiv:2411.09530  2024.11

    　View Summary

    In this paper, we propose the concept of $(\pm)$-discrete Dirac structures
    over a manifold, where we define $(\pm)$-discrete two-forms on the manifold and
    incorporate discrete constraints using $(\pm)$-finite difference maps.
    Specifically, we develop $(\pm)$-discrete induced Dirac structures as discrete
    analogues of the induced Dirac structure on the cotangent bundle over a
    configuration manifold, as described by Yoshimura and Marsden (2006). We
    demonstrate that $(\pm)$-discrete Lagrange--Dirac systems can be naturally
    formulated in conjunction with the $(\pm)$-induced Dirac structure on the
    cotangent bundle. Furthermore, we show that the resulting equations of motion
    are equivalent to the $(\pm)$-discrete Lagrange--d'Alembert equations proposed
    in Cort\'es and Mart\'inez (2001) and McLachlan and Perlmutter (2006). We also
    clarify the variational structures of the discrete Lagrange--Dirac dynamical
    systems within the framework of the $(\pm)$-discrete
    Lagrange--d'Alembert--Pontryagin principle. Finally, we validate the proposed
    discrete Lagrange--Dirac systems with some illustrative examples of
    nonholonomic systems through numerical tests.

  • Information geometry and alpha-parallel prior of the beta-logistic distribution

    Lin Jiu, Linyu Peng

    Communications in Statistics - Theory and Methods  2024.08

    ISSN  03610926

    　View Summary

    The hyperbolic secant distribution has several generalizations with applications in, for example, finance. In this study, we explore the dual geometric structure of one such generalization: the beta-logistic distribution. Within this family, two special cases of random variables, as examples, are of particular interests: their moments, by some recent results, give the Bernoulli and Euler polynomials, which are important objects in many areas of mathematics. This current study also uncovers that the beta-logistic distribution admits a α-parallel prior for any real number α, that has the potential for application in geometric statistical inference.

  • Developing a cloud evidence method for dynamic early warning of tunnel construction safety risk in undersea environment

    H Zhou, B Gao, X Zhao, L Peng, S Bai

    Developments in the Built Environment 16, 100225 (Developments in the Built Environment)  16 2023.12

    ISSN  2666-1659

    　View Summary

    Traditional methods have limitations in achieving precise predictions of risk occurrence at an exact future time and have difficulties transforming between qualitative and quantitative indicators and handling multi-source heterogeneous risk data. This study quantifies and analyzes the multi-source construction safety risks classified into the categories of man, machine, material, method and environment (4M1E), and presents a cloud evidence method that integrates wavelet de-noising algorithm, cloud model, and Dempster-Shafer (D-S) evidence theory. A real-time risk prediction and warning is provided using this method after the fusion of multi-source uncertain information and the transformation between qualitative and quantitative indicators, enabling the timely detection of potential risks for project managers. This method analyzing “uncertainty” with “certainty” is verified by an undersea tunnel construction project. The result shows that this method is effective in early warning risks two days before their actual occurrence, providing reference significance for risk early warning of the tunnel construction project.

  • The difference variational bicomplex and multisymplectic systems

    Linyu Peng, Peter E. Hydon

    arXiv preprint arXiv:2307.13935 (arXiv)   2023.07

    　View Summary

    The difference variational bicomplex, which is the natural setting for
    systems of difference equations, is constructed and used to examine the
    geometric and algebraic properties of various systems. Exactness of the
    bicomplex gives a coordinate-free setting for finite difference variational
    problems, Euler--Lagrange equations and Noether's theorem. We also examine the
    connection between the condition for existence of a Hamiltonian and the
    multisymplecticity of systems of partial difference equations. Furthermore, we
    define difference multimomentum maps of multisymplectic systems, which yield
    their conservation laws. To conclude, we demonstrate how multisymplectic
    integrators can be comprehended even on non-uniform meshes through a
    generalized difference variational bicomplex.

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Papers, etc., Registered in KOARA 【 Display / hide 】

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Presentations 【 Display / hide 】

  • Discrete Lagrangian multiforms on the difference variational bicomplex

    Linyu Peng

    BIRS Workshop Lagrangian Multiform Theory and Pluri-Lagrangian Systems, 

    2023.10

  • The modified formal variational formulation for general differential equations and applications

    Linyu Peng

    持続的環境エネルギー社会共創研究機構　研究所間交流会, 

    2023.09

  • Applications of Bures-Wasserstein geometry of HPD matrices to signal detection

    Y. Ono, L. Peng

    10th International Congress on Industrial and Applied Mathematics (ICIAM2023), 

    2023.08

  • A discretization of Dirac structures and Lagrange-Dirac dynamical systems

    H. Yoshimura, L. Peng

    10th International Congress on Industrial and Applied Mathematics (ICIAM2023), 

    2023.08

  • The influence of accuracy of initial values on the discrete energy in variational integrator

    M. Gunji, Y. Ono, L. Peng

    IUTAM Symposium on Nonlinear Dynamics for Design of Mechanical Systems across Different Length/Time Scales (IUTAM2023), 

    2023.07
    -
    2023.08
    , 

    Poster presentation

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Research Projects of Competitive Funds, etc. 【 Display / hide 】

  • Symmetry Methods for Discrete Equations and Their Applications

    2024.04
    -
    2028.03

    Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Principal investigator

    　View Summary

    Symmetries have proven to be of great importance in various fields, owing to the versatile applications in elucidating solution properties to physical models. Many scholars made substantial contributions to the study of symmetry methods for discrete equations, giving rise to a plethora of subsequent research and applications. Despite these advancements, a multitude of unresolved questions continued to challenge the field. The primary objective of the current project is to tackle some of the unresolved questions concerning the symmetries of discrete equations and to explore their applications.

  • Multisymplectic Geometry and Geometric Numerical Integrator for Variational Problems

    2020.04
    -
    Present

    Keio University, Grants-in-Aid for Scientific Research, Linyu Peng, Grant-in-Aid for Early-Career Scientists, Research grant, Principal investigator

    　View Summary

    Geometric integrator is among one of the most efficient numerical methods for differential equations. In this project, we establish a unified and systematical analogue for understanding both continuous and discrete multisymplectic structures of arbitrary order variational differential equations.

  • 複雑な流体現象のモデリング，マルチスケール構造の解明と数理解析

    2016.04
    -
    2019.03

    Waseda University, Grants-in-Aid for Scientific Research, Hiroaki Yoshimura, Grant-in-Aid for Scientific Research (B), Research grant, Coinvestigator(s)

    　View Summary

    We have explored mathematical modeling of complex fluid phenomena, mathematical analysis of partial differential equations and stochastic differential equations associated to multi-scale phenomena as well as applications of nonlinear mechanics. For the mathematical modeling, we have studied a Lagrangian variational formulation of nonequilibrium thermodynamics, modeling of cloud cavitation and with experiments, elucidation of LCS (Lagrangian coherent structures) for Rayleigh-Benard convection as well as a stochastic variational formulation of single bubble dynamics. For the mathematical analysis, we have researched on the existence and uniqueness of Navier-Stokes equations for two-phase flows, stochastic KPZ equations and modified KdV equations. Further we have shown some applications of LCS analysis to space mission design.

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Courses Taught 【 Display / hide 】

  • INDEPENDENT STUDY ON SCIENCE FOR OPEN AND ENVIRONMENTAL SYSTEMS

    2024

  • INDEPENDENT STUDIES IN MECHANICAL ENGINEERING

    2024

  • GRADUATE RESEARCH ON SCIENCE FOR OPEN AND ENVIRONMENTAL SYSTEMS 2

    2024

  • GRADUATE RESEARCH ON SCIENCE FOR OPEN AND ENVIRONMENTAL SYSTEMS 1

    2024

  • FACTORY VISITING

    2024

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Memberships in Academic Societies 【 Display / hide 】

  • Institute of Electrical and Electronics Engineers, 

    2021.07
    -
    Present

  • The Japan Society of Mechanical Engineers, 

    2021.01
    -
    Present

  • The Mathematical Society of Japan, 

    2018.10
    -
    Present

  • The Japan Society for Industrial and Applied Mathematics, 

    2018.06
    -
    Present
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