Skip to main content
SpringerLink
Log in

Dynamical Phase Transition in Slowed Exclusion Processes

  • Conference paper
  • First Online:
Modeling, Dynamics, Optimization and Bioeconomics I

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 73))

  • 1176 Accesses

Abstract

In this work, we present symmetric simple exclusion processes with a finite number of bonds whose dynamics is slowed down in order to difficult the passage of particles at those bonds. We study the influence of the rate of passage of mass at those bonds in the macroscopic hydrodynamic equation. As a consequence, we exhibit a dynamical phase transition that goes from smooth profiles to the development of discontinuities.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Evans, L.: Partial differential equations. In: Graduate Studies in Mathematics. American Mathematical Society, Providence (1998)

    MATH  Google Scholar 

  2. Faggionato, A., Jara, M., Landim, C.: Hydrodynamic behavior of one dimensional subdiffusive exclusion processes with random conductances. Probab. Theor Relat. Field 144(3–4), 633–667 (2008)

    MathSciNet  Google Scholar 

  3. Franco, T., Landim, C.: Hydrodynamic limit of gradient exclusion processes with conductances. Arch. Ration. Mech. Anal. 195, 409–439 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  4. Franco, T., Neumann, A., Valle, G.: Hydrodynamic limit for a class of exclusion type process in dimension ≥ 2. J. Appl. Probab. 49.2, 333–351 (2011)

    Article  MathSciNet  Google Scholar 

  5. Franco, T., Gonçalves, P., Neumann, A.: Hydrodynamical behavior of symmetric exclusion with slow bonds. Annales de l’Institut Henri Poincaré Probab. Stat. B 49(2), 402–427 (2013)

    Article  MATH  Google Scholar 

  6. Guo, M.Z., Papanicolau, G.C., Varadhan, S.R.S.: Nonlinear diffusion limit for a system with nearest neighbor interactions. Commun. Math. Phys. 118, 31–59 (1988)

    Article  MATH  Google Scholar 

  7. Jara, M., Landim, C.: Non equilibrium central limit theorem for a tagged particle in symmetric simple exclusion. Annales de l’Institute Henri Poincaré Probab. Stat. 42(5), 567–577 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  8. Kipnis, C., Landim, C.: Scaling Limits of Interacting Particle Systems. Springer, New York (1999)

    Book  MATH  Google Scholar 

  9. Leoni, G.: A First Course in Sobolev Spaces. In: Graduate Studies in Mathematics. American Mathematical Society, Providence (2009)

    MATH  Google Scholar 

  10. Ravishankar, K.: Fluctuations from the hydrodynamical limit for the symmetric simple exclusion in \(\mathbb{Z}^{d}\). Stoch. Process. Appl. 42, 31–37 (1992)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors thank FCT (Portugal) and Capes (Brazil) for the financial support through the research project “Non-Equilibrium Statistical Mechanics of Stochastic Lattice Systems”. PG thanks FCT (Portugal) for support through the research project “Non-Equilibrium Statistical Physics” PTDC/MAT/109844/2009. PG thanks the Research Centre of Mathematics of the University of Minho, for the financial support provided by “FEDER” through the “Programa Operacional Factores de Competitividade COMPETE” and by FCT through the research project PEst-C/MAT/UI0013/2011.

Author information

Authors and Affiliations

  1. Instituto de Matemática, Universidade Federal da Bahia, Av. Adhemar de Barros S/N, Ondina, CEP 40170-110, Salvador, Brazil

    Tertuliano Franco

  2. PUC-RIO, Departamento de Matemática, Rua Marquês de São Vicente, no. 225, 22453-900, Gávea, Rio de Janeiro, Brazil

    Patrícia Gonçalves

  3. Centro de Matemática da Universidade do Minho, Campus de Gualtar, 4710-057, Braga, Portugal

    Patrícia Gonçalves

  4. Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil

    Adriana Neumann

Authors
  1. Tertuliano Franco
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Patrícia Gonçalves
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Adriana Neumann
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tertuliano Franco .

Editor information

Editors and Affiliations

  1. University of Porto, Department of Mathematics, Porto, Portugal

    Alberto Adrego Pinto

  2. Univ. of California, Dept. of Agricultural and Resource Economics, Berkeley, California, USA

    David Zilberman

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Franco, T., Gonçalves, P., Neumann, A. (2014). Dynamical Phase Transition in Slowed Exclusion Processes. In: Pinto, A., Zilberman, D. (eds) Modeling, Dynamics, Optimization and Bioeconomics I. Springer Proceedings in Mathematics & Statistics, vol 73. Springer, Cham. https://doi.org/10.1007/978-3-319-04849-9_16

Download citation

Publish with us

Policies and ethics

Search

Navigation