Abstract
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 appli cation, 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.
| Original language | English |
|---|---|
| Pages (from-to) | 301-319 |
| Number of pages | 19 |
| Journal | Funkcialaj Ekvacioj |
| Volume | 52 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2009 |
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Keywords
- Evaporation driven fluid
- Long tail
- Non-linear wave
- Online ranking
- Stochastic ranking process
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory
- Geometry and Topology
Cite this
Equation of Motion for Incompressible Mixed Fluid Driven by Evaporation and Its Application to Online Rankings. / Hattori, Kumiko; Hattori, Tetsuya.
In: Funkcialaj Ekvacioj, Vol. 52, No. 3, 2009, p. 301-319.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Equation of Motion for Incompressible Mixed Fluid Driven by Evaporation and Its Application to Online Rankings
AU - Hattori, Kumiko
AU - Hattori, Tetsuya
PY - 2009
Y1 - 2009
N2 - 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 appli cation, 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.
AB - 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 appli cation, 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.
KW - Evaporation driven fluid
KW - Long tail
KW - Non-linear wave
KW - Online ranking
KW - Stochastic ranking process
UR - http://www.scopus.com/inward/record.url?scp=84877084688&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84877084688&partnerID=8YFLogxK
U2 - 10.1619/fesi.52.301
DO - 10.1619/fesi.52.301
M3 - Article
AN - SCOPUS:84877084688
VL - 52
SP - 301
EP - 319
JO - Funkcialaj Ekvacioj
JF - Funkcialaj Ekvacioj
SN - 0532-8721
IS - 3
ER -