19 research outputs found
Universality classes in nonequilibrium lattice systems
This work is designed to overview our present knowledge about universality
classes occurring in nonequilibrium systems defined on regular lattices. In the
first section I summarize the most important critical exponents, relations and
the field theoretical formalism used in the text. In the second section I
briefly address the question of scaling behavior at first order phase
transitions. In section three I review dynamical extensions of basic static
classes, show the effect of mixing dynamics and the percolation behavior. The
main body of this work is given in section four where genuine, dynamical
universality classes specific to nonequilibrium systems are introduced. In
section five I continue overviewing such nonequilibrium classes but in coupled,
multi-component systems. Most of the known nonequilibrium transition classes
are explored in low dimensions between active and absorbing states of
reaction-diffusion type of systems. However by mapping they can be related to
universal behavior of interface growth models, which I overview in section six.
Finally in section seven I summarize families of absorbing state system
classes, mean-field classes and give an outlook for further directions of
research.Comment: Updated comprehensive review, 62 pages (two column), 29 figs
included. Scheduled for publication in Reviews of Modern Physics in April
200
Tracking azimuthons in nonlocal nonlinear media
We study the formation of azimuthons, i.e., rotating spatial solitons, in
media with nonlocal focusing nonlinearity. We show that whole families of these
solutions can be found by considering internal modes of classical non-rotating
stationary solutions, namely vortex solitons. This offers an exhaustive method
to identify azimuthons in a given nonlocal medium. We demonstrate formation of
azimuthons of different vorticities and explain their properties by considering
the strongly nonlocal limit of accessible solitons.Comment: 11 pages, 7 figure