Eur. Phys. J. Special Topics 216, 139-151 (2013)
https://doi.org/10.1140/epjst/e2013-01737-y

Regular Article

Boundary-driven phase transitions in open driven systems with an umbilic point

¹ Dipartimento di Fisica e Astronomia, Università di Firenze, via G. Sansone 1, 50019 Sesto Fiorentino, Italy
² Max-Planck-Institute for Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany

^a e-mail: popkov@fi.infn.it

Received: 30 November 2012
Revised: 6 December 2012
Published online: 31 January 2013

Abstract

Different phases in open driven systems are governed by either shocks or rarefaction waves. A presence of an isolated umbilic point in bidirectional systems of interacting particles stabilizes an unusual large scale excitation, an umbilic shock (U-shock). We show that in open systems the U-shock governs a large portion of phase space, and drives a new discontinuous transition between the two rarefaction-controlled phases. This is in contrast to strictly hyperbolic case where such a transition is always continuous. Also, we describe another robust phase which takes place at the phase governed by the U-shock, if the umbilic point is not isolated.