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New trends of energy gradient flow: mathematical aspects and various phenomena and applications

Research Project

Project/Area Number 20KK0058
Research Category

Fund for the Promotion of Joint International Research (Fostering Joint International Research (B))

Allocation TypeMulti-year Fund
Review Section Medium-sized Section 12:Analysis, applied mathematics, and related fields
Research InstitutionKanazawa University

Principal Investigator

木村 正人  金沢大学, 数物科学系, 教授 (70263358)

Co-Investigator(Kenkyū-buntansha) 大塚 浩史  金沢大学, 数物科学系, 教授 (20342470)
野津 裕史  金沢大学, 数物科学系, 教授 (00588783)
POZAR Norbert  金沢大学, 数物科学系, 准教授 (00646523)
VANMEURS PATRICK  金沢大学, 数物科学系, 助教 (20815378)
Project Period (FY) 2020-10-27 – 2025-03-31
Project Status Granted (Fiscal Year 2023)
Budget Amount *help
¥8,450,000 (Direct Cost: ¥6,500,000、Indirect Cost: ¥1,950,000)
Fiscal Year 2024: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2023: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2022: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2021: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2020: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords勾配流 / 変分法 / 混相流 / 移動境界問題 / ODENet / 粒子系 / フェーズ・フィールド・モデル / 亀裂進展 / 形状最適化 / 転位ダイナミクス / 数理モデリング
Outline of Research at the Start

新しい勾配流の数学理論が次々に生み出されている状況を受け、アイントホーフェン工科大学の協力を得て、金沢大学で強力に推進している勾配流構造を持つ様々な魅力的な現象の数理モデルの解析を行うものである。新たな勾配流理論や数理モデルの持つ勾配流構造の多様さは、古典的なおとなしく退屈な勾配流のイメージを一変させるものであり、亀裂進展や結晶成長など様々な空間スケールにおける物理現象にとどまらず、形状最適化などある種の工学的アルゴリズムや、ニューラルネットワーク・深層学習などのアルゴリズムにも応用が期待される。

Outline of Annual Research Achievements

本研究計画は、一般化された意味での新しい勾配流の数学理論が次々に生み出されている状況を受け、アイントホーフェン工科大学のマーク・ペレティエ教授の協力を得て、金沢大学で強力に推進している勾配流構造を持つ様々な魅力的な現象の数理モデルの解析を行うものである。2023年度は、オンライン会議や電子メールによる研究打ち合わせを密に行うとともに、アイントホーフェン工科大学から金沢大学に、マーク・ペレティエ教授が短期訪問し、また大学院生1名が長期訪問した。また、金沢大学からもアイントホーフェン工科大学を研究者が訪問し、粒子系に関する共同研究を推進した。このように、双方向の渡航を伴う質の高い共同研究が実施できた。2023年度の成果としては、「粒子の相互作用・転位モデル」に関してヴァンマースなどが中心となり3編、「結晶成長・界面・流体・最適形状」分野で木村・野津が中心となり3編、「機械学習・工学アルゴリズム」分野で木村と大学院生を中心に1 編、「変分法・固有値問題」分野で、大塚が中心となり1編、計8編の論文の出版に至った。2023年度はこれまでの研究をさらに推進し、粒子の相互作用・転位モデル・最適形状・混相流方程式などのテーマで成果を挙げ、論文として順調に発表することができた。また新たに、木村と大学院生が中心となり、ODENetおよびResNetなどの機械学習分野や、スモルコフスキー凝集方程式の解析などにおいても成果を挙げ、勾配流の新しい応用の方向性を広げることに成功した。

Current Status of Research Progress
Current Status of Research Progress

1: Research has progressed more than it was originally planned.

Reason

これまでのCOVID19の影響にもかかわらず、研究計画・渡航計画の適切な見直しなどを行うと同時に、オンライン会議による研究打ち合わせなどの方策を積極的に実施した結果、2021年度の9編、2022年度の10編の論文の発表に続き、2023年度には8編の論文を発表できた。最終年の2024年度についてもさらに進んだ研究推進の見通しを立てることができている。

Strategy for Future Research Activity

大学院生などの協力を得ることで、2023年度以降の研究計画を一部前倒しして実施したため、コロナ禍による渡航制限の影響は今のところ最低限に抑えられた。 2024年度には、アイントホーフェン工科大学の若手研究者が金沢大学に短期滞在予定であるほか、金沢大のメンバーが複数名アイントホーフェン工科大学を訪問す る予定で計画を立てており、順調に研究推進できる見通しである。一方、万が 一、ウクライナ情勢の影響などにより、渡航中止になることも 想定し、その場合でも研究推進に支障がなるべく出ないよう研究計画をコントロールする。1つの方策として、アイントホーフェン工科大学側を含めた研究メンバーによる、オンラインセミナーを定期的に開催し、複数の研究テーマ間のアイデア・情報の交換を推進する。

Report

(4 results)
  • 2023 Research-status Report
  • 2022 Research-status Report
  • 2021 Research-status Report
  • 2020 Research-status Report
  • Research Products

    (40 results)

All 2024 2023 2022 2021 2020 Other

All Int'l Joint Research (4 results) Journal Article (29 results) (of which Int'l Joint Research: 24 results,  Peer Reviewed: 29 results,  Open Access: 21 results) Presentation (6 results) (of which Int'l Joint Research: 3 results) Funded Workshop (1 results)

  • [Int'l Joint Research] アイントホーフェン工科大学(オランダ)

    • Related Report
      2023 Research-status Report
  • [Int'l Joint Research] アイントホーフェン工科大学(オランダ)

    • Related Report
      2022 Research-status Report
  • [Int'l Joint Research] アイントホーフェン工科大学(オランダ)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] アイントホーフェン工科大学(オランダ)

    • Related Report
      2020 Research-status Report
  • [Journal Article] Universal approximation properties for an ODENet and a ResNet: Mathematical analysis and numerical experiments2024

    • Author(s)
      Aizawa Yuto, Kimura Masato, Matsui Kazunori
    • Journal Title

      Discrete and Continuous Dynamical Systems - B

      Volume: 29 Issue: 1 Pages: 351-376

    • DOI

      10.3934/dcdsb.2023099

    • Related Report
      2023 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] An energy estimate and a stabilized Lagrange-Galerkin scheme for a multiphase flow model2024

    • Author(s)
      Rudiawan Aufa, Zak Alexander, Benes Michal, Kimura Masato, Notsu Hirofumi
    • Journal Title

      Applied Mathematics Letters

      Volume: 153 Pages: 109059-109059

    • DOI

      10.1016/j.aml.2024.109059

    • Related Report
      2023 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Refinement of asymptotic behavior of the eigenvalues for the linearized Liouville-Gel’fand problem2024

    • Author(s)
      Ohtsuka Hiroshi, Sato Tomohiko
    • Journal Title

      Nonlinear Analysis

      Volume: 240 Pages: 113464-113464

    • DOI

      10.1016/j.na.2023.113464

    • Related Report
      2023 Research-status Report
    • Peer Reviewed
  • [Journal Article] Generalized Moment Method for Smoluchowski Coagulation Equation and Mass Conservation Property2023

    • Author(s)
      Islam Md. Sahidul, Kimura Masato, Miyata Hisanori
    • Journal Title

      Mathematics

      Volume: 11 Issue: 12 Pages: 2770-2770

    • DOI

      10.3390/math11122770

    • Related Report
      2023 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Numerical Solution to a Free Boundary Problem for the Stokes Equation Using the Coupled Complex Boundary Method in Shape Optimization Setting2023

    • Author(s)
      Rabago Julius Fergy Tiongson、Notsu Hirofumi
    • Journal Title

      Applied Mathematics & Optimization

      Volume: 89 Issue: 1 Pages: 2-2

    • DOI

      10.1007/s00245-023-10065-7

    • Related Report
      2023 Research-status Report
    • Peer Reviewed
  • [Journal Article] Convergence rates for energies of interacting particles whose distribution spreads out as their number increases2023

    • Author(s)
      van Meurs Patrick、Tanaka Ken'ichiro
    • Journal Title

      ESAIM: Control, Optimisation and Calculus of Variations

      Volume: 29 Pages: 1-28

    • DOI

      10.1051/cocv/2022083

    • Related Report
      2023 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] A simple, accurate scheme for the flow of an electric charge distribution2023

    • Author(s)
      Lalita Apisornpanich, Patrick van Meurs
    • Journal Title

      The Science Reports of Kanazawa University

      Volume: 66 Pages: 1-16

    • Related Report
      2023 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Constant-speed interface flow from unbalanced Glauber-Kawasaki dynamics2023

    • Author(s)
      Funaki Tadahisa、van Meurs Patrick、Sethuraman Sunder、Tsunoda Kenkichi
    • Journal Title

      Ensaios Matematicos

      Volume: 38 Issue: 8 Pages: 223-248

    • DOI

      10.21711/217504322023/em388

    • Related Report
      2023 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] A Two-Step Lagrange?Galerkin Scheme for the Shallow Water Equations with a Transmission Boundary Condition and Its Application to the Bay of Bengal Region?Part I: Flat Bottom Topography2023

    • Author(s)
      Rasid Md Mamunur、Kimura Masato、Murshed Md Masum、Wijayanti Erny Rahayu、Notsu Hirofumi
    • Journal Title

      Mathematics

      Volume: 11 Issue: 7 Pages: 1633-1633

    • DOI

      10.3390/math11071633

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Motion by Mean Curvature from Glauber-Kawasaki Dynamics with Speed Change2023

    • Author(s)
      Funaki Tadahisa、van Meurs Patrick、Sethuraman Sunder、Tsunoda Kenkichi
    • Journal Title

      Journal of Statistical Physics

      Volume: 190 Issue: 3 Pages: 1-30

    • DOI

      10.1007/s10955-022-03044-9

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Motion by crystalline-like mean curvature: A survey2022

    • Author(s)
      Giga Yoshikazu、Pozar Norbert
    • Journal Title

      Bulletin of Mathematical Sciences

      Volume: 12 Issue: 02 Pages: 1-68

    • DOI

      10.1142/s1664360722300043

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] A Mass-Preserving Two-Step Lagrange?Galerkin Scheme for Convection-Diffusion Problems2022

    • Author(s)
      Futai Kouta、Kolbe Niklas、Notsu Hirofumi、Suzuki Tasuku
    • Journal Title

      Journal of Scientific Computing

      Volume: 92 Issue: 2 Pages: 37-37

    • DOI

      10.1007/s10915-022-01885-w

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] A convective boundary condition for the Navier-Stokes equations2022

    • Author(s)
      Simon John Sebastian H.、Notsu Hirofumi
    • Journal Title

      Applied Mathematics Letters

      Volume: 128 Pages: 107876-107876

    • DOI

      10.1016/j.aml.2021.107876

    • Related Report
      2022 Research-status Report 2021 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Comoving mesh method for certain classes of moving boundary problems2022

    • Author(s)
      Sunayama Yosuke、Kimura Masato、Rabago Julius Fergy T.
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: 39 Issue: 3 Pages: 973-1001

    • DOI

      10.1007/s13160-022-00524-z

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] A shape design problem for the Navier?Stokes flow with a convective boundary condition2022

    • Author(s)
      Simon J. S. H、Notsu Hirofumi
    • Journal Title

      Computational and Applied Mathematics

      Volume: 41 Issue: 4 Pages: 167-167

    • DOI

      10.1007/s40314-022-01876-5

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Numerical crack path selection problem based on energy profiles2022

    • Author(s)
      Alifian Mahardhika Maulana、Kimura Masato、Alfat Sayahdin
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: 39 Issue: 3 Pages: 817-841

    • DOI

      10.1007/s13160-022-00523-0

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Discrete-to-Continuum Convergence of Charged Particles in 1D with Annihilation2022

    • Author(s)
      van Meurs Patrick、Peletier Mark A.、Pozar Norbert
    • Journal Title

      Archive for Rational Mechanics and Analysis

      Volume: 246 Issue: 1 Pages: 241-297

    • DOI

      10.1007/s00205-022-01812-1

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Boundary-Layer Analysis of Repelling Particles Pushed to an Impenetrable Barrier2022

    • Author(s)
      van Meurs Patrick
    • Journal Title

      SIAM Journal on Mathematical Analysis

      Volume: 54 Issue: 2 Pages: 1742-1774

    • DOI

      10.1137/21m1420198

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] A shape optimization problem constrained with the Stokes equations to address maximization of vortices2022

    • Author(s)
      Simon John Sebastian、Notsu Hirofumi
    • Journal Title

      Evolution Equations & Control Theory

      Volume: - Issue: 6 Pages: 1873-1902

    • DOI

      10.3934/eect.2022003

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Phase Field Models for Thermal Fracturing and Their Variational Structures2022

    • Author(s)
      Alfat Sayahdin、Kimura Masato、Maulana Alifian Mahardhika
    • Journal Title

      Materials

      Volume: 15 Issue: 7 Pages: 2571-2571

    • DOI

      10.3390/ma15072571

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] The lewy-stampacchia inequality for the fractional Laplacian and its application to anomalous unidirectional diffusion equations2022

    • Author(s)
      Kow Pu-Zhao、Kimura Masato
    • Journal Title

      Discrete & Continuous Dynamical Systems - B

      Volume: 27 (6) Issue: 6 Pages: 2935-2957

    • DOI

      10.3934/dcdsb.2021167

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Second-Order Finite Difference Approximations of the Upper-Convected Time Derivative2021

    • Author(s)
      Medeiros Debora D.、Notsu Hirofumi、Oishi Cassio M.
    • Journal Title

      SIAM Journal on Numerical Analysis

      Volume: 59 Issue: 6 Pages: 2955-2988

    • DOI

      10.1137/20m1364990

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Twin vortex computer in fluid flow2021

    • Author(s)
      Goto Ken、Nakajima Kohei、Notsu Hirofumi
    • Journal Title

      New Journal of Physics

      Volume: 23 Issue: 6 Pages: 063051-063051

    • DOI

      10.1088/1367-2630/ac024d

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Weak solutions for unidirectional gradient flows: existence, uniqueness, and convergence of time discretization schemes2021

    • Author(s)
      Kimura Masato、Negri Matteo
    • Journal Title

      Nonlinear Differential Equations and Applications NoDEA

      Volume: 28 Issue: 6

    • DOI

      10.1007/s00030-021-00720-9

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Particle Dynamics with Elastic Collision at the Boundary: Existence and Partial Uniqueness of Solutions2021

    • Author(s)
      Kimura M.、van Meurs P.、Yang Z. X.
    • Journal Title

      Acta Applicandae Mathematicae

      Volume: 174 Issue: 1 Pages: 1-26

    • DOI

      10.1007/s10440-021-00423-4

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Irreversible phase field models for crack growth in industrial applications: thermal stress, viscoelasticity, hydrogen embrittlement2021

    • Author(s)
      Kimura Masato、Takaishi Takeshi、Alfat Sayahdin、Nakano Takumi、Tanaka Yoshimi
    • Journal Title

      SN Applied Sciences

      Volume: 3 Issue: 9

    • DOI

      10.1007/s42452-021-04593-6

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Quantitative Estimate of the Continuum Approximations of Interacting Particle Systems in One Dimension2021

    • Author(s)
      Kimura Masato、van Meurs Patrick
    • Journal Title

      SIAM Journal on Mathematical Analysis

      Volume: 53 Issue: 1 Pages: 681-709

    • DOI

      10.1137/20m1322054

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Discrete-to-continuum limits of planar disclinations2021

    • Author(s)
      Cesana Pierluigi、van Meurs Patrick
    • Journal Title

      ESAIM: Control, Optimisation and Calculus of Variations

      Volume: 27 Pages: 23-23

    • DOI

      10.1051/cocv/2021025

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Atomistic origins of continuum dislocation dynamics2020

    • Author(s)
      Hudson Thomas、van Meurs Patrick、Peletier Mark
    • Journal Title

      Mathematical Models and Methods in Applied Sciences

      Volume: 30 Issue: 13 Pages: 2557-2618

    • DOI

      10.1142/s0218202520500505

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Presentation] Zener型粘弾性波動方程式の弱解の一意存在と漸近挙動2024

    • Author(s)
      木村正人, 李敬潼, 劉逸侃, 中村玄, 野津裕史, 上田好寛
    • Organizer
      日本数学会2024年度年会 応用数学分科会
    • Related Report
      2023 Research-status Report
  • [Presentation] On the linear response of equilibrium vortices2021

    • Author(s)
      Hiroshi Ohtsuka
    • Organizer
      TU/e - KU Math Symposia ``Stochastic particle systems with singular interactions''
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research
  • [Presentation] Comoving mesh method:移動境界問題に対する汎用型有限要素法2021

    • Author(s)
      砂山 洋祐、木村 正人、Rabago Julius Fergy
    • Organizer
      日本応用数理学会 2021年度 年会
    • Related Report
      2021 Research-status Report
  • [Presentation] Quasi-stationary Stefan-type scheme for solving shape identification problems2021

    • Author(s)
      Rabago Julius Fergy、木村 正人
    • Organizer
      日本応用数理学会 2021年度 年会
    • Related Report
      2021 Research-status Report
  • [Presentation] A variational approach to modeling thermoelastic problems2020

    • Author(s)
      Sayahdin Alfat and Masato Kimura
    • Organizer
      The Second Russia-Japan Workshop "Mathematical analysis of fracture phenomena for elastic structures and its applications"
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research
  • [Presentation] Variational approach on crack path selection problem2020

    • Author(s)
      Alifian Mahardhika Maulana and Masato Kimura
    • Organizer
      The Second Russia-Japan Workshop "Mathematical analysis of fracture phenomena for elastic structures and its applications"
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research
  • [Funded Workshop] TU/e - KU international math symposia2021

    • Related Report
      2021 Research-status Report

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Published: 2020-10-29   Modified: 2024-12-25  

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