9,132 research outputs found
Critical behavior of a bounded Kardar-Parisi-Zhang equation
A host of spatially extended systems, both in physics and in other
disciplines, are well described at a coarse-grained scale by a Langevin
equation with multiplicative-noise. Such systems may exhibit non-equilibrium
phase transitions, which can be classified into universality classes. Here we
study in detail one of such classes that can be mapped into a
Kardar-Parisi-Zhang (KPZ) interface equation with a positive (negative)
non-linearity in the presence of a bounding lower (upper) wall. The wall limits
the possible values taken by the height variable, introducing a lower (upper)
cut-off, and induce a phase transition between a pinned (active) and a depinned
(absorbing) phase. This transition is studied here using mean field and field
theoretical arguments, as well as from a numerical point of view. Its main
properties and critical features, as well as some challenging theoretical
difficulties, are reported. The differences with other multiplicative noise and
bounded-KPZ universality classes are stressed, and the effects caused by the
introduction of ``attractive'' walls, relevant in some physical contexts, are
also analyzed.Comment: Invited paper to a special issue of the Brazilian J. of Physics. 5
eps Figures. 9 pagres. Revtex
Nonintegrability, Chaos, and Complexity
Two-dimensional driven dissipative flows are generally integrable via a
conservation law that is singular at equilibria. Nonintegrable dynamical
systems are confined to n*3 dimensions. Even driven-dissipative deterministic
dynamical systems that are critical, chaotic or complex have n-1 local
time-independent conservation laws that can be used to simplify the geometric
picture of the flow over as many consecutive time intervals as one likes. Those
conserevation laws generally have either branch cuts, phase singularities, or
both. The consequence of the existence of singular conservation laws for
experimental data analysis, and also for the search for scale-invariant
critical states via uncontrolled approximations in deterministic dynamical
systems, is discussed. Finally, the expectation of ubiquity of scaling laws and
universality classes in dynamics is contrasted with the possibility that the
most interesting dynamics in nature may be nonscaling, nonuniversal, and to
some degree computationally complex
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