Equation of Motion for Incompressible Mixed Fluid Driven by Evaporation and Its Application to Online Rankings

• Hattori Kumiko

  Tokyo Metropolitan University

• Hattori Tetsuya

  Keio University

抄録

We consider a system of partial differential equations for the densities of components of one dimensional incompressible fluid mixture whose motion is driven by evaporation. We prove existence and give explicit form of unique global classical non-negative solution to initial value problem for the system. The solution is known to be an infinite particle limit of stochastic ranking processes, which is a simple stochastic model of time evolutions of Amazon Sales Ranks. As a practical application, we collected data from the web and performed statistical fits to our formula. The results suggest that the system of equations and solutions, though very simple, may have applications in the analysis of online rankings.

収録刊行物

• Funkcialaj Ekvacioj

  Funkcialaj Ekvacioj 52 (3), 301-319, 2009

  日本数学会函数方程式論分科会

キーワード

• Evaporation driven fluid
• Non-linear wave
• Stochastic ranking process
• Long tail
• Online ranking

詳細情報

• CRID: 1390001205112189184
• NII論文ID: 130000161973
• DOI: 10.1619/fesi.52.301
• MRID: 2589658
• ISSN: 05328721
• Web Site: http://www.jstage.jst.go.jp/article/fesi/52/3/52_3_301/_pdf
• 本文言語コード: en
• データソース種別:
  • JaLC
  • Crossref
  • CiNii Articles
• 抄録ライセンスフラグ: 使用不可