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Theory and applications of motions of anisotropic interfacial networks

Research Project

Project/Area Number 18F18016
Research Category

Grant-in-Aid for JSPS Fellows

Allocation TypeSingle-year Grants
Section外国
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionKyoto University

Principal Investigator

SVADLENKA KAREL  京都大学, 理学研究科, 准教授 (60572188)

Co-Investigator(Kenkyū-buntansha) MOHAMMAD RHUDAINA  京都大学, 理学(系)研究科(研究院), 外国人特別研究員
Project Period (FY) 2018-07-25 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥2,300,000 (Direct Cost: ¥2,300,000)
Fiscal Year 2019: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2018: ¥1,200,000 (Direct Cost: ¥1,200,000)
Keywordsinterface dynamics / interfacial network / MBO scheme / level set method / volume preservation / cellular patterns / interface network / anisotropic energy
Outline of Annual Research Achievements

Considering the gradient flow of anisotropic surface energy constrained by volume preservation, we developed a level set-based method for realizing anisotropic motion of an interface network. First, we considered a variational approach to a vector-type Merriman-Bence-Osher (MBO) thresholding scheme with penalization technique, which realized volume-preserving crystalline motion with a smoothing technique but required an ad hoc scheme to satisfy the correct junction angles. Motivated by cellular pattern formations in sensory epithelium, we considered anisotropic motions driven by cell-cell adhesion. Due to the complexity of tricellular junctions, we then developed an MBO-type convolution scheme with localized auction dynamics which realizes correct cell contact angles and features good compatibility with level set representation and a solid mathematical background including stability and convergence. Here, cell-cell junctions are implicitly represented using level sets and succeeding dynamics are numerically determined by thresholding. We addressed several aspects pertinent to cell biology, e.g., our localization step prevents cells from unnatural splitting during rearrangement. Our method successfully reproduced development of cellular patterns in sensory systems, including cell sorting, total engulfment, and cell internalization. These simulations were implemented using C programming language and Matlab software. Results have been submitted for publication, as well as, presented and well received in local and overseas conferences.

Research Progress Status

令和元年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

令和元年度が最終年度であるため、記入しない。

Report

(2 results)
  • 2019 Annual Research Report
  • 2018 Annual Research Report
  • Research Products

    (14 results)

All 2020 2019 2018

All Presentation (14 results) (of which Int'l Joint Research: 13 results,  Invited: 10 results)

  • [Presentation] Modeling Cellular Dynamics in TissueMorphogenesis: A Level Set-based Approach2020

    • Author(s)
      Rhudaina MOHAMMAD
    • Organizer
      3rd International Workshop on Mathematical Biology, Philippines
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] On Mosaic Cellular Patterns of Sensory Epithelial Tissues: An Interface Evolution Problem2019

    • Author(s)
      Rhudaina MOHAMMAD
    • Organizer
      CAS Current Problems in Numerical Analysis, Prague, Czech Republic
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On Preserving Enclosed Volumes of Evolving Interfaces with Cell Motion Applications2019

    • Author(s)
      Rhudaina MOHAMMAD
    • Organizer
      CARMA Geometric Evolution Problems and Related Topics, Newcastle, Australia
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Numerical Simulation of Cellular Patterning in Sensory Epithelia2019

    • Author(s)
      Rhudaina MOHAMMAD
    • Organizer
      Kyoto Winter School “Quantifying Dynamics of Life”
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Modeling cell-to-cell adhesion dynamics in multicellular organisms2019

    • Author(s)
      Rhudaina MOHAMMAD
    • Organizer
      A3 Workshop on Soft Matter 2019, 東北大学
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Surface energy-driven interface dynamics with junctions and volume constraints2019

    • Author(s)
      Rhudaina MOHAMMAD
    • Organizer
      界面現象の数理・モデリング研究合宿,軽井沢
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] On Preserving Enclosed Volumes of Evolving Interfaces with Cell Motion Applications2019

    • Author(s)
      Rhudaina Mohammad
    • Organizer
      CARMA Workshop on Geometric Evolution Problems and Related Topics, Newcastle, Australia
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Mosaic Cellular Patterns of Sensory Epithelial Tissues: An Interface Evolution Problem2019

    • Author(s)
      Rhudaina Mohammad
    • Organizer
      Seminar on Current Problems in Numerical Analysis, Czech Academy of Sciences, Prague
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Numerical Simulation of Cellular Patterning in Sensory Epithelia2019

    • Author(s)
      Rhudaina Mohammad
    • Organizer
      Kyoto Winter School on “Quantifying Dynamics of Life”, Kyoto University, Japan
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Mathematics of Cellular Pattern Formation in Sensory Epithelia2019

    • Author(s)
      Karel Svadlenka
    • Organizer
      Kyoto Winter School 2019 "Quantifying Dynamics of Life", Kyoto University, Japan
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Numerical approach to filament dynamics2018

    • Author(s)
      Karel Svadlenka
    • Organizer
      Czech‐Japanese Seminar in Applied Mathematics 2018
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On some extensions of thresholding schemes2018

    • Author(s)
      Karel Svadlenka
    • Organizer
      The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Taipei, Taiwan
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Numerical approach to hyperbolic motions of co-dimension 22018

    • Author(s)
      Karel Svadlenka
    • Organizer
      The Seventh China-Japan-Korea Joint Conference on Numerical Mathematics,, Kanazawa, Japan
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Numerical simulation of sensory tissue formation2018

    • Author(s)
      Karel Svadlenka
    • Organizer
      A3 Soft matter workshop, Peking, China
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited

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Published: 2018-07-26   Modified: 2024-03-26  

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