10 research outputs found
Dark-bright discrete solitons: a numerical study of existence, stability and dynamics
the present work, we numerically explore the existence and stability properties
of different types of configurations of dark-bright solitons, dark-bright soliton pairs
and pairs of dark-bright and dark solitons in discrete settings, starting from the
anti-continuum limit. We find that while single discrete dark-bright solitons have
similar stability properties to discrete dark solitons, their pairs may only be stable
if the bright components are in phase and are always unstable if the bright components
are out of phase. Pairs of dark-bright solitons with dark ones have similar
stability properties as individual dark or dark-bright ones. Lastly, we consider collisions
between dark-bright solitons and between a dark-bright one and a dark one.
Especially in the latter and in the regime where the underlying lattice structure
matters, we find a wide range of potential dynamical outcomes depending on the
initial soliton speed.MICINN project FIS2008-0484
Overdamped deterministic ratchets driven by multifrequency forces
Presented at the XVIII Marian Smoluchowski Symposium on Statistical Physics, Zakopane, Poland, September 3–6, 2005We investigate a dissipative, deterministic ratchet model in the overdamped regime driven by a rectangular force. Extensive numerical calculations are presented in a diagram depicting the drift velocity as a function of a wide range of the driving parameter values. We also present some theoretical considerations which explain some features of the mentioned diagram. In particular, we proof the existence of regions in the driving parameter space with bounded particle motion possessing zero current. Moreover, we present an explicit analytical expression for the drift velocity in the adiabatic limit.Ministerio de Educación y Ciencia of Spain (FIS2005-02884) and the Junta de Andalucía. Also acknowledges the Ministerio de Educación y Ciencia o f Spain for a contract under the Juan de la Cierva program
Discrete breathers collisions in nonlinear Schrödinger and Klein-Gordon lattices
Collisions between moving localized modes (moving breathers) in non-
integrable lattices present a rich outcome. In this paper, some features of the
interaction of moving breathers in Discrete Nonlinear Schrödinger and Klein-
Gordon lattices, together with some plausible explanations, are exposed
Nonsymmetric moving breather collisions in the Peyrard-Bishop DNA model
We study nonsymmetric collisions of moving breathers (MBs) in the Peyrard-Bishop DNA model. In this paper we have considered the following types of nonsymmetric collisions: head-on collisions of two breathers traveling with different velocities; collisions of moving breathers with a stationary trapped breather; and collisions of moving breathers traveling with the same direction. The various main observed phenomena are: one moving breather gets trapped at the collision region, and the other one is reflected; breather fusion without trapping, with the appearance of a new moving breather; and breather generation without trapping, with the appearance of new moving breathers traveling either with the same or different directions. For comparison we have included some results of a previous paper concerning to symmetric collisions, where two identical moving breathers traveling with opposite velocities collide. For symmetric collisions, the main observed phenomena are: breather generation with trapping, with the appearance of two new moving breathers with opposite velocities and a stationary breather trapped at the collision region; and breather generation without trapping, with the appearance of new moving breathers with opposite velocities. A common feature for all types of collisions is that the collision outcome depends on the internal structure of the moving breathers and the exact number of pair-bases that initially separates the stationary breathers when they are perturbed. As some nonsymmetric collisions result in the generation of a new stationary trapped breather of larger energy, the trapping phenomenon could play an important part of the complex mechanisms involved in the initiation of the DNA transcription processes.MICIN
New classes of stable exact solutions for a nonlinear rotational DNA model
We consider a system of two coupled nonlinear partial differential equations
for describing the rotational motions of bases in both polynucleotide
chains of the DNA molecule. The model was proposed by L.V. Yakushevich
and it is well known that the model supports, for some operating regimes,
traveling wave solutions as kink–(antikink) soliton solutions. We have tried
to make some progress by performing an analysis of the classical symmetries
of this model. Our study shows that the model does not have enough
symmetries as to reduce the equations to ordinary differential equations.
Nevertheless, the known symmetries have been useful for finding several
classes of exact solutions, by imposing adequate Ansätze. Some of them
are kink–(antikink) like solutions, but other ones are not traveling wave
solutions. For some of the new solutions, we have carried out a qualitative
study and analyzed some stability properties. We think that they could
be significant for the description of the DNA molecule as well as for some
other applications.DGYCYT project MTM2006-05031Junta de Andalucía FQM 201. P06-FQM-0144
Moving breather collisions in the Peyrard-Bishop DNA model
We consider collisions of moving breathers (MBs) in the
Peyrard-Bishop DNA model. Two identical stationary breathers, sep-
arated by a fixed number of pair-bases, are perturbed and begin to move
approaching to each other with the same module of velocity. The outcome
is strongly dependent of both the velocity of the MBs and the number
of pair-bases that initially separates the stationary breathers. Some col-
lisions result in the generation of a new stationary trapped breather of
larger energy. Other collisions result in the generation of two new MBs.
In the DNA molecule, the trapping phenomenon could be part of the
complex mechanisms involved in the initiation of the transcription pro-
cesses
Classical and quantum nonlinear localized excitations in discrete systems
Pre-pint tomado de ArxivDiscrete breathers, or intrinsic localized modes, are spatially localized, time–periodic, nonlinear
excitations that can exist and propagate in systems of coupled dynamical units. Recently, some
experiments show the sighting of a form of discrete breather that exist at the atomic scale in a
magnetic solid. Other observations of breathers refer to systems such as Josephson–junction arrays,
photonic crystals and optical-switching waveguide arrays. All these observations underscore their
importance in physical phenomena at all scales. The authors review some of their latest theoretical
contributions in the field of classical and quantum breathers, with possible applications to these
widely different physical systems and to many other such as DNA, proteins, quantum dots, quantum
computing, etc
Escape dynamics in the discrete repulsive φ4 model
We study deterministic escape dynamics of the discrete Klein-Gordon model with a repulsive quartic on-site potential. Using a combination of analytical techniques, based on differential and algebraic inequalities and selected numerical illustrations, we first derive conditions for collapse of an initially excited single-site unit, for both the Hamiltonian and the linearly damped versions of the system and showcase different potential fates of the single-site excitation, such as the possibility to be "pulled back" from outside the well or to "drive over" the barrier some of its neighbors. Next, we study the evolution of a uniform (small) segment of the chain and, in turn, consider the conditions that support its escape and collapse of the chain. Finally, our path from one to the few and finally to the many excited sites is completed by a modulational stability analysis and the exploration of its connection to the escape process for plane wave initial data. This reveals the existence of three distinct regimes, namely modulational stability, modulational instability without escape and, finally, modulational instability accompanied by escape. These are corroborated by direct numerical simulations. In each of the above cases, the variations of the relevant model parameters enable a consideration of the interplay of discreteness and nonlinearity within the observed phenomenology. © 2012 Elsevier B.V. All rights reserved