TY  - JOUR
A1  - Mulansky, Mario
A1  - Ahnert, Karsten
A1  - Pikovskij, Arkadij
A1  - Shepelyansky, Dima L.
T1  - Dynamical thermalization of disordered nonlinear lattices
N2  - We study numerically how the energy spreads over a finite disordered nonlinear one-dimensional lattice, where all linear modes are exponentially localized by disorder. We establish emergence of dynamical thermalization characterized as an ergodic chaotic dynamical state with a Gibbs distribution over the modes. Our results show that the fraction of thermalizing modes is finite and grows with the nonlinearity strength.
Y1  - 2009
UR  - http://pre.aps.org/
U6  - https://doi.org/10.1103/Physreve.80.056212
SN  - 1539-3755
ER  - 
TY  - JOUR
A1  - Shepelyansky, Dima L.
A1  - Pikovskij, Arkadij
A1  - Schmidt, Jürgen
A1  - Spahn, Frank
T1  - Synchronization mechanism of sharp edges in rings of Saturn
N2  - We propose a new mechanism which explains the existence of enormously sharp edges in the rings of Saturn. This mechanism is based on the synchronization phenomenon due to which the epicycle rotational phases of particles in the ring, under certain conditions, become synchronized with the phase of external satellite, e. g. with the phase of Mimas in the case of the outer B ring edge. This synchronization eliminates collisions between particles and suppresses the diffusion induced by collisions by orders of magnitude. The minimum of the diffusion is reached at the centre of the synchronization regime corresponding to the ratio 2:1 between the orbital frequency at the edge of B ring and the orbital frequency of Mimas. The synchronization theory gives the sharpness of the edge in a few tens of meters that is in agreement with available observations.
Y1  - 2009
UR  - http://www3.interscience.wiley.com/cgi-bin/issn?DESCRIPTOR=PRINTISSN&VALUE=0035-8711
U6  - https://doi.org/10.1111/j.1365-2966.2009.14719.x
SN  - 0035-8711
ER  -