11,474 research outputs found
PT-symmetric sine-Gordon breathers
In this work, we explore a prototypical example of a genuine continuum
breather (i.e., not a standing wave) and the conditions under which it can
persist in a -symmetric medium. As our model of interest, we
will explore the sine-Gordon equation in the presence of a -
symmetric perturbation. Our main finding is that the breather of the
sine-Gordon model will only persist at the interface between gain and loss that
-symmetry imposes but will not be preserved if centered at the
lossy or at the gain side. The latter dynamics is found to be interesting in
its own right giving rise to kink-antikink pairs on the gain side and complete
decay of the breather on the lossy side. Lastly, the stability of the breathers
centered at the interface is studied. As may be anticipated on the basis of
their "delicate" existence properties such breathers are found to be
destabilized through a Hopf bifurcation in the corresponding Floquet analysis
Motion of discrete solitons assisted by nonlinearity management
We demonstrate that periodic modulation of the nonlinearity coefficient in
the discrete nonlinear Schr\"{o}dinger (DNLS) equation can strongly facilitate
creation of traveling solitons in the lattice. We predict this possibility in
an analytical form, and test it in direct simulations. Systematic simulations
reveal several generic dynamical regimes, depending on the amplitude and
frequency of the time modulation, and on initial thrust which sets the soliton
in motion. These regimes include irregular motion, regular motion of a decaying
soliton, and regular motion of a stable one. The motion may occur in both the
straight and reverse directions, relative to the initial thrust. In the case of
stable motion, extremely long simulations in a lattice with periodic boundary
conditions demonstrate that the soliton keeps moving as long as we can monitor
without any visible loss. Velocities of moving stable solitons are in good
agreement with the analytical prediction, which is based on requiring a
resonance between the ac drive and motion of the soliton through the periodic
potential. All the generic dynamical regimes are mapped in the model's
parameter space. Collisions between moving stable solitons are briefly
investigated too, with a conclusion that two different outcomes are possible:
elastic bounce, or bounce with mass transfer from one soliton to the other. The
model can be realized experimentally in a Bose-Einstein condensate trapped in a
deep optical lattice
Nucleation of breathers via stochastic resonance in nonlinear lattices
By applying a staggered driving force in a prototypical discrete model with a
quartic nonlinearity, we demonstrate the spontaneous formation and destruction
of discrete breathers with a selected frequency due to thermal fluctuations.
The phenomenon exhibits the striking features of stochastic resonance (SR): a
nonmonotonic behavior as noise is increased and breather generation under
subthreshold conditions. The corresponding peak is associated with a matching
between the external driving frequency and the breather frequency at the
average energy given by ambient temperature.Comment: Added references, figure 5 modified to include new dat
Coupled backward- and forward-propagating solitons in a composite right/left-handed transmission line
We study the coupling between backward- and forward-propagating wave modes,
with the same group velocity, in a composite right/left-handed nonlinear
transmission line. Using an asymptotic multiscale expansion technique, we
derive a system of two coupled nonlinear Schr{\"o}dinger equations governing
the evolution of the envelopes of these modes. We show that this system
supports a variety of backward- and forward propagating vector solitons, of the
bright-bright, bright-dark and dark-bright type. Performing systematic
numerical simulations in the framework of the original lattice that models the
transmission line, we study the propagation properties of the derived vector
soliton solutions. We show that all types of the predicted solitons exist, but
differ on their robustness: only bright-bright solitons propagate undistorted
for long times, while the other types are less robust, featuring shorter
lifetimes. In all cases, our analytical predictions are in a very good
agreement with the results of the simulations, at least up to times of the
order of the solitons' lifetimes
Speed-of-light pulses in a nonlinear Weyl equation
We introduce a prototypical nonlinear Weyl equation, motivated by recent
developments in massless Dirac fermions, topological semimetals and photonics.
We study the dynamics of its pulse solutions and find that a localized one-hump
initial condition splits into a localized two-hump pulse, while an associated
phase structure emerges in suitable components of the spinor field. For times
larger than a transient time this pulse moves with the speed of light (or
Fermi velocity in Weyl semimetals), effectively featuring linear wave dynamics
and maintaining its shape (both in two and three dimensions). We show that for
the considered nonlinearity, this pulse represents an exact solution of the
nonlinear Weyl (NLW) equation. Finally, we comment on the generalization of the
results to a broader class of nonlinearities and on their emerging potential
for observation in different areas of application.Comment: 7 pages, 6 figure
Vibrational Instabilities in Resonant Electron Transport through Single-Molecule Junctions
We analyze various limits of vibrationally coupled resonant electron
transport in single-molecule junctions. Based on a master equation approach, we
discuss analytic and numerical results for junctions under a high bias voltage
or weak electronic-vibrational coupling. It is shown that in these limits the
vibrational excitation of the molecular bridge increases indefinitely, i.e. the
junction exhibits a vibrational instability. Moreover, our analysis provides
analytic results for the vibrational distribution function and reveals that
these vibrational instabilities are related to electron-hole pair creation
processes.Comment: 19 pages, 3 figure
An energy-based stability criterion for solitary traveling waves in Hamiltonian lattices
In this work, we revisit a criterion, originally proposed in [Nonlinearity
{\bf 17}, 207 (2004)], for the stability of solitary traveling waves in
Hamiltonian, infinite-dimensional lattice dynamical systems. We discuss the
implications of this criterion from the point of view of stability theory, both
at the level of the spectral analysis of the advance-delay differential
equations in the co-traveling frame, as well as at that of the Floquet problem
arising when considering the traveling wave as a periodic orbit modulo a shift.
We establish the correspondence of these perspectives for the pertinent
eigenvalue and Floquet multiplier and provide explicit expressions for their
dependence on the velocity of the traveling wave in the vicinity of the
critical point. Numerical results are used to corroborate the relevant
predictions in two different models, where the stability may change twice. Some
extensions, generalizations and future directions of this investigation are
also discussed
Reaction-diffusion spatial modeling of COVID-19: Greece and Andalusia as case examples
We examine the spatial modeling of the outbreak of COVID-19 in two regions:
the autonomous community of Andalusia in Spain and the mainland of Greece. We
start with a 0D compartmental epidemiological model consisting of Susceptible,
Exposed, Asymptomatic, (symptomatically) Infected, Hospitalized, Recovered, and
deceased populations. We emphasize the importance of the viral latent period
and the key role of an asymptomatic population. We optimize model parameters
for both regions by comparing predictions to the cumulative number of infected
and total number of deaths via minimizing the norm of the difference
between predictions and observed data. We consider the sensitivity of model
predictions on reasonable variations of model parameters and initial
conditions, addressing issues of parameter identifiability. We model both
pre-quarantine and post-quarantine evolution of the epidemic by a
time-dependent change of the viral transmission rates that arises in response
to containment measures. Subsequently, a spatially distributed version of the
0D model in the form of reaction-diffusion equations is developed. We consider
that, after an initial localized seeding of the infection, its spread is
governed by the diffusion (and 0D model "reactions") of the asymptomatic and
symptomatically infected populations, which decrease with the imposed
restrictive measures. We inserted the maps of the two regions, and we imported
population-density data into COMSOL, which was subsequently used to solve
numerically the model PDEs. Upon discussing how to adapt the 0D model to this
spatial setting, we show that these models bear significant potential towards
capturing both the well-mixed, 0D description and the spatial expansion of the
pandemic in the two regions. Veins of potential refinement of the model
assumptions towards future work are also explored.Comment: 28 pages, 16 figures and 2 movie
Waiting time distribution for electron transport in a molecular junction with electron-vibration interaction
On the elementary level, electronic current consists of individual electron
tunnelling events that are separated by random time intervals. The waiting time
distribution is a probability to observe the electron transfer in the detector
electrode at time given that an electron was detected in the same
electrode at earlier time . We study waiting time distribution for quantum
transport in a vibrating molecular junction. By treating the electron-vibration
interaction exactly and molecule-electrode coupling perturbatively, we obtain
master equation and compute the distribution of waiting times for electron
transport. The details of waiting time distributions are used to elucidate
microscopic mechanism of electron transport and the role of electron-vibration
interactions. We find that as nonequilibrium develops in molecular junction,
the skewness and dispersion of the waiting time distribution experience
stepwise drops with the increase of the electric current. These steps are
associated with the excitations of vibrational states by tunnelling electrons.
In the strong electron-vibration coupling regime, the dispersion decrease
dominates over all other changes in the waiting time distribution as the
molecular junction departs far away from the equilibrium
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