Skip to main content
Top

2015 | OriginalPaper | Chapter

Sticky Particles and Stochastic Flows

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Gawȩdzki and Horvai have studied a model for the motion of particles carried in a turbulent fluid and shown that in a limiting regime with low levels of viscosity and molecular diffusivity, pairs of particles exhibit the phenomena of stickiness when they meet. In this paper we characterise the motion of an arbitrary number of particles in a simplified version of their model.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference R. Bass, A stochastic differential equation with a sticky point. Electron. J. Probab. 19(32), 1–22 (2014)MathSciNet R. Bass, A stochastic differential equation with a sticky point. Electron. J. Probab. 19(32), 1–22 (2014)MathSciNet
2.
go back to reference R.J. Chitashvili, On the nonexistence of a strong solution in the boundary problem for a sticky Brownian motion. Centrum voor Wiskunde en Informatica (1989) R.J. Chitashvili, On the nonexistence of a strong solution in the boundary problem for a sticky Brownian motion. Centrum voor Wiskunde en Informatica (1989)
3.
go back to reference H. Engelbert, G. Peskir, Stochastic differential equations for sticky Brownian motion. Stochastics 86(6), 993–1021 (2014)MathSciNet H. Engelbert, G. Peskir, Stochastic differential equations for sticky Brownian motion. Stochastics 86(6), 993–1021 (2014)MathSciNet
4.
go back to reference K. Gawȩdzki, P. Horvai, Sticky behavior of fluid particles in the compressible Kraichnan model. J. Stat. Phys. 116(5–6), 1247–1300 (2004)CrossRef K. Gawȩdzki, P. Horvai, Sticky behavior of fluid particles in the compressible Kraichnan model. J. Stat. Phys. 116(5–6), 1247–1300 (2004)CrossRef
5.
go back to reference C.J. Howitt, J. Warren, Consistent families of Brownian motions and stochastic flows of kernels. Ann. Probab. 37(4), 1237–1272 (2009)MATHMathSciNetCrossRef C.J. Howitt, J. Warren, Consistent families of Brownian motions and stochastic flows of kernels. Ann. Probab. 37(4), 1237–1272 (2009)MATHMathSciNetCrossRef
7.
go back to reference Y. Le Jan, S. Lemaire, Products of Beta matrices and sticky flows. Probab. Theory Relat. Fields 130(1), 109–134 (2004)MATH Y. Le Jan, S. Lemaire, Products of Beta matrices and sticky flows. Probab. Theory Relat. Fields 130(1), 109–134 (2004)MATH
10.
go back to reference Y. Le Jan, O. Raimond, Sticky flows on the circle and their noises. Probab. Theory Relat. Fields 129(1), 63–82 (2004)MATHCrossRef Y. Le Jan, O. Raimond, Sticky flows on the circle and their noises. Probab. Theory Relat. Fields 129(1), 63–82 (2004)MATHCrossRef
11.
go back to reference G. Peskir, On boundary behaviour of one-dimensional diffusions: from Brown to Feller and beyond (2014); Research Report No. 8 (2014); Probab. Statist. Group Manchester (14 pp.). To appear in Selected Works of William Feller (Springer) G. Peskir, On boundary behaviour of one-dimensional diffusions: from Brown to Feller and beyond (2014); Research Report No. 8 (2014); Probab. Statist. Group Manchester (14 pp.). To appear in Selected Works of William Feller (Springer)
12.
go back to reference E. Schertzer, R. Sun, J.M. Swart, Stochastic flows in the Brownian web and net. Mem. Am. Math. Soc. 227(1065) (2014) E. Schertzer, R. Sun, J.M. Swart, Stochastic flows in the Brownian web and net. Mem. Am. Math. Soc. 227(1065) (2014)
13.
go back to reference J. Warren, Branching processes, the Ray-Knight theorem, and sticky Brownian motion, in Séminaire de Probabilités XXXI (Springer, Berlin, 1997), pp. 1–15 J. Warren, Branching processes, the Ray-Knight theorem, and sticky Brownian motion, in Séminaire de Probabilités XXXI (Springer, Berlin, 1997), pp. 1–15
14.
go back to reference J. Warren, An elliptic pde with convex solutions (2014) [arXiv:1407.3985] J. Warren, An elliptic pde with convex solutions (2014) [arXiv:1407.3985]
Metadata
Title
Sticky Particles and Stochastic Flows
Author
Jon Warren
Copyright Year
2015
DOI
https://doi.org/10.1007/978-3-319-18585-9_2