Bulk induced phase transition in driven diffusive systems

This paper studies a weakly and asymmetrically coupled three-lane driven diffusive system. A non-monotonically changing density profile in the middle lane has been observed. When the extreme value of the density profile reaches ρ = 0.5, a bulk induced phase transition occurs which exhibits a shock and a continuously and smoothly decreasing density profile which crosses ρ = 0.5 upstream or downstream of the shock. The existence of double shocks has also been observed. A mean-field approach has been used to interpret the numerical results obtained by Monte Carlo simulations. The current minimization principle has excluded the occurrence of two or more bulk induced shocks in the general case of nonzero lane changing rates.

[1]  R. Juhasz.  Weakly coupled, antiparallel, totally asymmetric simple exclusion processes. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  V. Popkov,et al.  Steady-state selection in driven diffusive systems with open boundaries , 1999, cond-mat/0002242.

[3]  A B Kolomeisky,et al.  Localization of shocks in driven diffusive systems without particle number conservation. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Enrique D. Andjel.  The asymmetric simple exclusion process on Zd , 1981 .

[5]  Peter F. Arndt,et al.  First-Order Phase Transitions in One-Dimensional Steady States , 1997 .

[6]  Robin Stinchcombe,et al.  Ideal and disordered two-lane traffic models , 2005 .

[7]  R. A. Blythe,et al.  Nonequilibrium steady states of matrix-product form: a solver's guide , 2007, 0706.1678.

[8]  T. Reichenbach,et al.  Driven transport on parallel lanes with particle exclusion and obstruction. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  David P. Landau,et al.  Phase transitions and critical phenomena , 1989, Computing in Science & Engineering.

[10]  T. Chou,et al.  Non-equilibrium statistical mechanics: from a paradigmatic model to biological transport , 2011, 1110.1783.

[11]  R. K. P. Zia,et al.  Driven diffusive systems. An introduction and recent developments , 1998 .

[12]  J. Koenderink.  Q… , 2014, Les noms officiels des communes de Wallonie, de Bruxelles-Capitale et de la communaute germanophone.

[13]  V Popkov,et al.  Symmetry breaking and phase coexistence in a driven diffusive two-channel system. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  M. Hu,et al.  Strong Asymmetric Coupling of Two Parallel Exclusion Processes , 2011 .

[15]  J. Krug,et al.  Minimal current phase and universal boundary layers in driven diffusive systems. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  K. Nishinari,et al.  Exact solution of a heterogeneous multilane asymmetric simple exclusion process. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  M. Hu,et al.  Weak and strong coupling in a two-lane asymmetric exclusion process. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  G. Schütz,et al.  Phase diagram of one-dimensional driven lattice gases with open boundaries , 1998 .

[19]  D. Mukamel,et al.  PHASE SEPARATION IN ONE-DIMENSIONAL DRIVEN DIFFUSIVE SYSTEMS , 1998 .

[20]  Anomalous nucleation far from equilibrium. , 2005, Physical review letters.

[21]  Erwin Frey,et al.  Exclusion processes with internal states. , 2006, Physical review letters.

[22]  M. R. Evans,et al.  Phase diagrams of two-lane driven diffusive systems , 2011, 1103.4677.

[23]  G. Schütz.  1 – Exactly Solvable Models for Many-Body Systems Far from Equilibrium , 2001 .

[24]  J Török,et al.  Criterion for phase separation in one-dimensional driven systems. , 2002, Physical review letters.

[25]  Krug,et al.  Boundary-induced phase transitions in driven diffusive systems. , 1991, Physical review letters.

[26]  Rui Jiang,et al.  Phase Separation in a Bidirectional Two-Lane Asymmetric Exclusion Process , 2009 .

[27]  asymmetric simple exclusion process , 2016 .

[28]  L. Santen,et al.  Shock dynamics of two-lane driven lattice gases , 2010, 1005.1504.

[29]  Evans,et al.  Spontaneous symmetry breaking in a one dimensional driven diffusive system. , 1995, Physical review letters.

[30]  Erwin Frey,et al.  Phase coexistence in driven one-dimensional transport. , 2003, Physical review letters.

[31]  B. Derrida.  AN EXACTLY SOLUBLE NON-EQUILIBRIUM SYSTEM : THE ASYMMETRIC SIMPLE EXCLUSION PROCESS , 1998 .

[32]  Erwin Frey,et al.  Bulk-driven nonequilibrium phase transitions in a mesoscopic ring. , 2006, Physical review letters.

[33]  A. Kolomeisky,et al.  Inhomogeneous coupling in two-channel asymmetric simple exclusion processes , 2008 .

[34]  M. Hu,et al.  Asymmetric coupling in multi-channel simple exclusion processes , 2008 .