TY - JOUR
T1 - Front depinning by deterministic and stochastic fluctuations
T2 - A comparison
AU - Alvarez-Socorro, A. J.
AU - Clerc, Marcel G.
AU - Ferré, M. A.
AU - Knobloch, Edgar
N1 - Funding Information:
The authors are very grateful to Professor Georg Gottwald for his insightful comments on the topic of this paper. This work was supported by CONICYT under Grant No. CONICYT-USA PII20150011. M.G.C. and M.A.F. also thank the Millennium Institute for Research in Optics (MIRO) for financial support. A.J.A.-S. gratefully acknowledges financial support from Becas Conicyt 2015, Contract No. 21151618.
Publisher Copyright:
© 2019 American Physical Society.
PY - 2019/6/27
Y1 - 2019/6/27
N2 - Driven dissipative many-body systems are described by differential equations for macroscopic variables which include fluctuations that account for ignored microscopic variables. Here, we investigate the effect of deterministic fluctuations, drawn from a system in a state of phase turbulence, on front dynamics. We show that despite these fluctuations a front may remain pinned, in contrast to fronts in systems with Gaussian white noise fluctuations, and explore the pinning-depinning transition. In the deterministic case, this transition is found to be robust but its location in parameter space is complex, generating a fractal-like structure. We describe this transition by deriving an equation for the front position, which takes the form of an overdamped system with a ratchet potential and chaotic forcing; this equation can, in turn, be transformed into a linear parametrically driven oscillator with a chaotically oscillating frequency. The resulting description provides an unambiguous characterization of the pinning-depinning transition in parameter space. A similar calculation for noise-driven front propagation shows that the pinning-depinning transition is washed out.
AB - Driven dissipative many-body systems are described by differential equations for macroscopic variables which include fluctuations that account for ignored microscopic variables. Here, we investigate the effect of deterministic fluctuations, drawn from a system in a state of phase turbulence, on front dynamics. We show that despite these fluctuations a front may remain pinned, in contrast to fronts in systems with Gaussian white noise fluctuations, and explore the pinning-depinning transition. In the deterministic case, this transition is found to be robust but its location in parameter space is complex, generating a fractal-like structure. We describe this transition by deriving an equation for the front position, which takes the form of an overdamped system with a ratchet potential and chaotic forcing; this equation can, in turn, be transformed into a linear parametrically driven oscillator with a chaotically oscillating frequency. The resulting description provides an unambiguous characterization of the pinning-depinning transition in parameter space. A similar calculation for noise-driven front propagation shows that the pinning-depinning transition is washed out.
UR - http://www.scopus.com/inward/record.url?scp=85068353937&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.99.062226
DO - 10.1103/PhysRevE.99.062226
M3 - Article
C2 - 31330663
AN - SCOPUS:85068353937
VL - 99
JO - Physical Review E
JF - Physical Review E
SN - 2470-0045
IS - 6
M1 - 062226
ER -