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Journal of Statistical Physics

, Volume 158, Issue 1, pp 57–86 | Cite as

Dynamical Widom–Rowlinson Model and Its Mesoscopic Limit

  • Dmitri Finkelshtein
  • Yuri Kondratiev
  • Oleksandr Kutoviy
  • Maria João Oliveira
Article

Abstract

We consider the non-equilibrium dynamics for the Widom–Rowlinson model (without hard-core) in the continuum. The Lebowitz–Penrose-type scaling of the dynamics is studied and the system of the corresponding kinetic equations is derived. In the space-homogeneous case, the equilibrium points of this system are described. Their structure corresponds to the dynamical phase transition in the model. The bifurcation of the system is shown.

Keywords

Widom–Rowlinson model Stochastic dynamics in the continuum  Lebowitz–Penrose scaling Kinetic equations Bifurcation 

Mathematics Subject Classification

70F45 34A34 37A60 

Notes

Acknowledgments

Financial support of DFG through CRC 701, Research Group “Stochastic Dynamics: Mathematical Theory and Applications” at ZiF, and FCT through PTDC/MAT/100983/2008, PTDC/MAT-STA/1284/2012 and PEst OE/MAT/UI0209/2013 are gratefully acknowledged.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Dmitri Finkelshtein
    • 1
    • 2
  • Yuri Kondratiev
    • 3
  • Oleksandr Kutoviy
    • 3
    • 4
  • Maria João Oliveira
    • 5
    • 6
  1. 1.Department of MathematicsSwansea UniversitySwanseaUK
  2. 2.Institute of MathematicsKievUkraine
  3. 3.Fakultät für MathematikUniversität BielefeldBielefeldGermany
  4. 4.Department of MathematicsMITCambridgeUSA
  5. 5.Universidade AbertaLisbonPortugal
  6. 6.CMAFUniversity of LisbonLisbonPortugal

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