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Spontaneous flow pattern formation in fluids --- singularity and large scale flow phenomena

Research Project

Project/Area Number 24340016
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypePartial Multi-year Fund
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKyoto University

Principal Investigator

Yamada Michio  京都大学, 数理解析研究所, 教授 (90166736)

Co-Investigator(Kenkyū-buntansha) 林 祥介  神戸大学, 理学(系)研究科(研究院), 教授 (20180979)
竹広 真一  京都大学, 数理解析研究所, 准教授 (30274426)
岡本 久  京都大学, 数理解析研究所, 教授 (40143359)
Project Period (FY) 2012-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥17,940,000 (Direct Cost: ¥13,800,000、Indirect Cost: ¥4,140,000)
Fiscal Year 2016: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2015: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2014: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2013: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2012: ¥5,590,000 (Direct Cost: ¥4,300,000、Indirect Cost: ¥1,290,000)
Keywords回転流体 / ジェット流 / ロスピー波 / 応用数学 / 流体 / 波動乱流 / ベータ面 / ロスビー波
Outline of Final Research Achievements

Jet formation process on a beta plane and a rotating sphere was studied theoretically and numerically for incompressible two-dimensional fluids. The jet formation is observed in several situations including Jovian atmosphere, but its dynamical mechanism is not yet well understood. In this study, we have obtained an analytical description for the amount of jet acceleration on the beta plane by the use of the pseudo momentum given by the weakly nonlinear theory of Rossby waves, employing asymptotic forms of the eigenfunctions of the continuous modes in the linear stability problem of the jet flow. We also performed a numerical simulation of the fluid equation, and obtained a good agreement between the theoretical prediction and the numerically observed values for the jet acceleration.

Report

(6 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Annual Research Report
  • 2014 Annual Research Report
  • 2013 Annual Research Report
  • 2012 Annual Research Report
  • Research Products

    (55 results)

All 2017 2016 2015 2014 2013 2012 Other

All Int'l Joint Research (1 results) Journal Article (19 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 19 results,  Open Access: 5 results,  Acknowledgement Compliant: 5 results) Presentation (34 results) (of which Int'l Joint Research: 7 results,  Invited: 12 results) Funded Workshop (1 results)

  • [Int'l Joint Research] INPE/ITA/Univ. of Brasilia(Brazil)

    • Related Report
      2015 Annual Research Report
  • [Journal Article] Martian dust devil statistics from high-resolution large-eddy simulations2016

    • Author(s)
      Nishizawa, S., Odaka, M., Takahashi, Y. O., Sugiyama, K. Nakajima, K., Ishiwatari, M., Takehiro, S., Yashiro, H., Sato, Y., Tomita, H. and Hayashi, Y.-Y.
    • Journal Title

      Geophysical Research Letters

      Volume: 43 Issue: 9 Pages: 4180-4188

    • DOI

      10.1002/2016gl068896

    • NAID

      120005820904

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] A Numerical Study of Convection in a Condensing CO2 Atmosphere under Early Mars-Like Conditions2016

    • Author(s)
      Yamashita, T., Odaka, M., Sugiyama, K., Nakajima, K., Ishiwatari, M., Nishizawa, S., Takahashi, Y. O. and Hayashi, Y.
    • Journal Title

      Journal of the Atmospheric Sciences

      Volume: 73 Issue: 10 Pages: 4151-4169

    • DOI

      10.1175/jas-d-15-0132.1

    • NAID

      120005981527

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] The circulation pattern and day-night heat transport in the atmosphere of a synchronously rotating aquaplanet: Dependence on planetary rotation rate2015

    • Author(s)
      Noda, S., Ishiwatari, M., Nakajima, K., Takahashi, Y. O., Takehiro, S., Onishi, M., Hashimoto, G.. L., Kuramoto, K., and Hayashi, Y.-Y.
    • Journal Title

      Icarus

      Volume: 282 Pages: 1-18

    • DOI

      10.1016/j.icarus.2016.09.004

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Regeneration cycle and the covariant Lyapunov vectors in a minimal wall turbulence2015

    • Author(s)
      Masanobu Inubushi, Shin-ichi Takehiro, and Michio Yamada
    • Journal Title

      Physical Review E

      Volume: 92 Issue: 2 Pages: 023022-023022

    • DOI

      10.1103/physreve.92.023022

    • NAID

      120005672620

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Bifurcation structure of two-dimensional viscous zonal flows on a rotating sphere2015

    • Author(s)
      Eiichi Sasaki, Shin-ichi Takehiro and Michio Yamada
    • Journal Title

      Journal of Fluid Mechanics

      Volume: 774 Pages: 224-244

    • DOI

      10.1017/jfm.2015.262

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Reconstruction of chaotic saddles by classification of unstable periodic orbits: Kuramoto-Sivashinsky equation2015

    • Author(s)
      Yoshitaka Saiki, Michio Yamada, Abraham C.-L. Chian, Rodrigo A. Miranda and Erico L. Rempel
    • Journal Title

      Chaos

      Volume: 25 Issue: 10 Pages: 103123-103123

    • DOI

      10.1063/1.4933267

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Influence of surface displacement on solid state flow induced by horizontally heterogeneous Joule heating in the inner core of the Earth.2015

    • Author(s)
      S.Takehiro
    • Journal Title

      Physics of The Earth and Planetary Interiors

      Volume: 241 Pages: 15-20

    • DOI

      10.1016/j.pepi.2015.02.003

    • NAID

      120005575265

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Penetration of Alfven waves into an upper stably-stratified layer excited by magnetoconvection in rotating spherical shells.2015

    • Author(s)
      S.Takehiro
    • Journal Title

      Physics of The Earth and Planetary Interiors

      Volume: 241 Pages: 37-43

    • DOI

      10.1016/j.pepi.2015.02.005

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Equatorial symmetry of Boussinesq convective solutions in a rotating spherical shell allowing rotation of the inner and outer spheres2014

    • Author(s)
      K.Kimura, S.Takehiro, M.Yamada
    • Journal Title

      Physics of Fluids,

      Volume: 26 Issue: 8

    • DOI

      10.1063/1.4893374

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] SMILES L2 データ処理における逆問題の解析手法.2014

    • Author(s)
      眞子直弘, 鈴木睦, 佐野琢己, 光田千紘, 今井弘二,山田道夫, 竹広真一, 塩谷雅人
    • Journal Title

      宇宙科学情報解析論文誌,

      Volume: 3 Pages: 109-118

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Full sphere hydrodynamic and dynamo benchmarks2014

    • Author(s)
      Marti, P., Schaeffer, N., Hollerbach, R., Cebron, D., Nore, C., Luddens, F., Guermond, J.-L., Aubert, J., Takehiro, S., Sasaki, Y., Hayashi, Y.-Y., Simitev, R., Busse, F., Vantieghem, S., Jackson, A.
    • Journal Title

      Geophysical Journal International

      Volume: 197 Issue: 1 Pages: 119-134

    • DOI

      10.1093/gji/ggt518

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stability and bifurcation diagram of Boussinesq thermal convection in a moderately rotating spherical shell allowing rotation of the inner sphere2013

    • Author(s)
      Kimura, K., Takehiro, S., Yamada, M.
    • Journal Title

      Phys. Fluids

      Volume: 25 Issue: 8

    • DOI

      10.1063/1.4819140

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Liinear stability of viscous zonal jet flows on a rotating sphere2013

    • Author(s)
      E.Sasaki, S.Takehiro, M.Yamada
    • Journal Title

      Journal of the Physical Society of Japan

      Volume: 82 Issue: 9 Pages: 094402-094402

    • DOI

      10.7566/jpsj.82.094402

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Effects of latitudinally heterogeneous buoyancy flux conditions at the inner boundary on MHD dynamo in a rotating spherical shell2013

    • Author(s)
      Sasaki, Y., Takehiro, S., Nishizawa, S., Hayashi, Y.-Y.
    • Journal Title

      Phys. Earth Planet. Inter.

      Volume: 223 Pages: 55-61

    • DOI

      10.1016/j.pepi.2013.07.003

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Resonant interaction of Rossby waves in two-dimensional flow on a beta plane2013

    • Author(s)
      M. Yamada
    • Journal Title

      Physica D

      Volume: 245 Pages: 1-7

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Weak interaction between zonal jets on a beta plane2013

    • Author(s)
      K.Obuse, S.Takehiro and M.Yamada
    • Journal Title

      Japan Industrial and Applied Mathematics

      Volume: 30 Issue: 1 Pages: 111-127

    • DOI

      10.1007/s13160-012-0086-9

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A note on the stability of inviscid zonal jet flows on a rotating sphere2012

    • Author(s)
      E.Sasaki, S.Takehiro and M.Yamada
    • Journal Title

      J.Fluid Mech

      Volume: 710 Pages: 154-165

    • DOI

      10.1017/jfm.2012.356

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Torques on the inner and outer spheres induced by the Boussinesq thermal convection in a rotating spherical shell.2012

    • Author(s)
      Keiji Kimura
    • Journal Title

      Journal Physiical Society of Japan

      Volume: 81 Issue: 8 Pages: 84401-84401

    • DOI

      10.1143/jpsj.81.084401

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A coordinate-based proof of the scallop theorem2012

    • Author(s)
      K. Ishimoto, M. Yamada
    • Journal Title

      SIAM Journal on Applied Mathematics

      Volume: 72 Issue: 5 Pages: 1686-1694

    • DOI

      10.1137/110853297

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Presentation] “An effect of turbulence on zonal jet flows in forced 2D and quasi-geostrophic shallow water models on a beta plane2017

    • Author(s)
      Kiori Obuse, Shin-ichi Takehiro, and Michio Yamada
    • Organizer
      SIAM Computational science and Engineering (SCE) 17
    • Place of Presentation
      Hilton Atlanta (Atlanta, USA)
    • Year and Date
      2017-02-27
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Effect of turbulence on zonal jet flows in barotropic model and quasi-geostrophic shallow water model2017

    • Author(s)
      Kiori Obuse, Shin-ichi Takehiro, and Michio Yamada
    • Organizer
      Int.Conf. on Applied Mathematics and Computer Science (ICAMCS) 2017
    • Place of Presentation
      The Church Palace Hotel (Rome, Italy)
    • Year and Date
      2017-01-27
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] An effect of turbulence on a zonal jet flow on a β plane2016

    • Author(s)
      Kiori Obuse, Shin-ichi Takehiro, and Michio Yamada
    • Organizer
      The Computational Techniques and Applications Conference (CTAC)2016
    • Place of Presentation
      Monash University, Melbourne,Australia
    • Year and Date
      2016-11-27
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Penetration of mean zonal flows into an outer stable layer excited by MHD thermal convection in rotating spherical shells.2016

    • Author(s)
      Takehiro, S., Sasaki, Y.
    • Organizer
      The 15th symposium of Study for Earth Deep Interior (SEDI 2016)
    • Place of Presentation
      Nantes, France
    • Year and Date
      2016-07-24
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 2D Navier-Stokes equations on a sphere2016

    • Author(s)
      Michio Yamada
    • Organizer
      Naruto workshop on vortex dynamics
    • Place of Presentation
      Hotel Ad Inn Naruto, Japan
    • Year and Date
      2016-01-16
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 球面上の2次元Navier-Stokes流2015

    • Author(s)
      山田道夫
    • Organizer
      共共拠点研究会 RIMS1963-IMI2013
    • Place of Presentation
      九州大学マスフォアインダストリ研究所
    • Year and Date
      2015-12-07
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] 決定論的方程式に従う系における極値の統計2015

    • Author(s)
      山田道夫
    • Organizer
      統計数理研究所共同研究集会「極値理論の工学への応用」
    • Place of Presentation
      統計数理研究所
    • Year and Date
      2015-11-06
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Penetration of steady fluid motions into an outer stable layer excied by MHD thermal convection in a rotating spherical shell2015

    • Author(s)
      Shin-ichi Takehiro
    • Organizer
      Japan SEDI symposium 2015
    • Place of Presentation
      東京大学地震研究所
    • Year and Date
      2015-09-25
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Stability of one-directional flow on a rotating sphere2015

    • Author(s)
      Michio Yamada
    • Organizer
      ICIAM2014
    • Place of Presentation
      Beijing, China
    • Year and Date
      2015-08-11
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 2次元流の渦力学と帯状流2015

    • Author(s)
      山田道夫
    • Organizer
      研究会「渦を知る」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2015-04-17
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Reproduction of 2D unsteady flows on a rotating sphere2015

    • Author(s)
      E.Sasaki, S.Takehiro, M.Yamada
    • Organizer
      France-Japan Workshop 2015
    • Place of Presentation
      LIMSI-CNRS, Paris, France
    • Year and Date
      2015-03-04
    • Related Report
      2014 Annual Research Report
  • [Presentation] 2D zonal flows on a rotating sphere2015

    • Author(s)
      M.Yamada
    • Organizer
      ICCP9
    • Place of Presentation
      SNU, Singapore
    • Year and Date
      2015-01-09
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Covariant Lyapunov analysis and its application to Navier-Stokes flows2015

    • Author(s)
      M.Inubushi, S.Takehiro and M.Yamada
    • Organizer
      ICCP9
    • Place of Presentation
      SNU, Singapore
    • Year and Date
      2015-01-09
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Merging and disappearing processes of zonal jets in forced 2D Navier-Stokes turbulence on a rotating sphere.2015

    • Author(s)
      K.Obuse, S.Takehiro and M.Yamada
    • Organizer
      ICCP9
    • Place of Presentation
      SNU, Singapore
    • Year and Date
      2015-01-09
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] The regeneration cycle and the covariant Lyapunov vectors in a minimal wall turbulence,2014

    • Author(s)
      M.Inubushi, S.Takehiro and M.Yamada
    • Organizer
      Dynamics Days Asia-Pacific 2014
    • Place of Presentation
      IIT, Madras, Chennai, India
    • Year and Date
      2014-07-22
    • Related Report
      2014 Annual Research Report
  • [Presentation] 回転球殼ブシネスク対流におけるカオス解の対称性2013

    • Author(s)
      木村恵二
    • Organizer
      日本物理学会2013年年次大会
    • Place of Presentation
      広島大学
    • Year and Date
      2013-03-27
    • Related Report
      2012 Annual Research Report
  • [Presentation] ミニマルクエット乱流に見られる再生成サイクルの軌道不安定性について2013

    • Author(s)
      犬伏正信
    • Organizer
      日本物理学会2013年年次大会
    • Place of Presentation
      広島大学
    • Year and Date
      2013-03-26
    • Related Report
      2012 Annual Research Report
  • [Presentation] 回転球殼内の熱対流によって引き起こされる差分回転と角運動量輸送2013

    • Author(s)
      竹広真一
    • Organizer
      2013年日本天文学会春季大会
    • Place of Presentation
      埼玉大学
    • Year and Date
      2013-03-22
    • Related Report
      2012 Annual Research Report
  • [Presentation] Covariant Lyapunov Analysis of a Minimal Wall Turbulence.2013

    • Author(s)
      M. Inubushi
    • Organizer
      International Conference on Fluid Mechanics 2013
    • Place of Presentation
      Barcelona, Spain
    • Year and Date
      2013-02-27
    • Related Report
      2012 Annual Research Report
  • [Presentation] Bifurcations and Chaotic solutions of two-dimensia rotating sphere.2013

    • Author(s)
      E. Sasaki
    • Organizer
      International Conference on Fluid Mechanics 2013
    • Place of Presentation
      Barcelona, Spain
    • Year and Date
      2013-02-27
    • Related Report
      2012 Annual Research Report
  • [Presentation] Equatorial symmetry of chaotic solutions in Boussinesq convection in a rotating spherical shell.2013

    • Author(s)
      K. Kimura
    • Organizer
      International Conference on Fluid Mechanics 2013
    • Place of Presentation
      Barcelona, Spain
    • Year and Date
      2013-02-27
    • Related Report
      2012 Annual Research Report
  • [Presentation] ミニマル壁乱流の軌道不安定性について2013

    • Author(s)
      犬伏正信
    • Organizer
      RIMS共同研究集会「偏微分方程式の背後にある確率過程と解の族が示す統計力学的な現象の解析」
    • Place of Presentation
      京都大学
    • Year and Date
      2013-02-15
    • Related Report
      2012 Annual Research Report
  • [Presentation] 回転球面上の2次元Navier-Stokes方程式における帯状流解の分岐2013

    • Author(s)
      佐々木英一
    • Organizer
      RIMS共同研究集会「偏微分方程式の背後にある確率過程と解の族が示す統計力学的な現象の解析」
    • Place of Presentation
      京都大学
    • Year and Date
      2013-02-15
    • Related Report
      2012 Annual Research Report
  • [Presentation] 回転球面上の帯状流の分岐とカオス軌道2013

    • Author(s)
      佐々木英一
    • Organizer
      RIMS共同研究集会「多重物理・多重スケールの乱流現象の数理」
    • Place of Presentation
      京都大学
    • Year and Date
      2013-01-11
    • Related Report
      2012 Annual Research Report
  • [Presentation] 回転球殼ブシネスク熱対流問題におけるカオス解の対称性2013

    • Author(s)
      木村恵二
    • Organizer
      RIMS共同研究集会「多重物理・多重スケールの乱流現象の数理」
    • Place of Presentation
      京都大学
    • Year and Date
      2013-01-11
    • Related Report
      2012 Annual Research Report
  • [Presentation] ミニマルクエツト乱流に見られる再生成サイクルの軌道不安定性について2013

    • Author(s)
      犬伏正信
    • Organizer
      RIMS共同研究集会「多重物理・多重スケールの乱流現象の数理」
    • Place of Presentation
      京都大学
    • Year and Date
      2013-01-11
    • Related Report
      2012 Annual Research Report
  • [Presentation] Orbital instability of a minimal wall turbulence2012

    • Author(s)
      M. Yamada
    • Organizer
      Mathematical Theory of Turbulence via Harmonic Analysis and Computational Fluid Dynamics
    • Place of Presentation
      Nagoya University, Nagoya, Japan(招待講演)
    • Year and Date
      2012-12-07
    • Related Report
      2012 Annual Research Report
  • [Presentation] Differential rotation and angular momentum transport caused by thermal convection in rotating spherical shells.2012

    • Author(s)
      S. Takehiro
    • Organizer
      Progress in physics of the sun and stars : a new era in helio- and asteroseismology.
    • Place of Presentation
      Hakone, Japan(招待講演)
    • Year and Date
      2012-11-29
    • Related Report
      2012 Annual Research Report
  • [Presentation] Triaxial rotation of the inner and outer spheres driven by Boussinesq thermal convection in a rotating spherical shell.2012

    • Author(s)
      K. Kimura
    • Organizer
      The 13th Symposium of SEDI(Study of the Earth's Deep Interior).
    • Place of Presentation
      Leads, UK
    • Year and Date
      2012-07-01
    • Related Report
      2012 Annual Research Report
  • [Presentation] 2D zonal flows on a rotating sphere

    • Author(s)
      M.Yamada
    • Organizer
      Fundamental Aspects of Geophysical Turbulence
    • Place of Presentation
      Nagoya University, Japan
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 回転球面上の帯状流の分岐解とカオス軌道の平均量

    • Author(s)
      佐々木英一, 竹広真一, 山田道夫
    • Organizer
      2013年日本流体力学会年会
    • Place of Presentation
      東京農工大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] 回転球殻内の熱対流による角運動量輸送と太陽差分回転について.

    • Author(s)
      竹広真一,佐々木洋平,林祥介,山田道夫
    • Organizer
      2013 年日本流体力学会年会
    • Place of Presentation
      東京農工大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] Influence of surface displacement on fluid motions induced by horizontally heterogeneous Joule heating in the inner core of the earth.

    • Author(s)
      竹広真一
    • Organizer
      SEDI Pre-Symposium 2013
    • Place of Presentation
      湘南国際村センター
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 木星型惑星の表面パターンと大気循環モデル.

    • Author(s)
      竹広真一
    • Organizer
      系外惑星大気ワークショップ2014/惑星大気研究会
    • Place of Presentation
      国立天文台三鷹
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Funded Workshop] FDEPS20152015

    • Place of Presentation
      関西セミナーハウス(京都市左京区)
    • Year and Date
      2015-12-01
    • Related Report
      2015 Annual Research Report

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Published: 2012-04-24   Modified: 2019-07-29  

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