156 research outputs found
Two-dimensional discrete solitons in rotating lattices
We introduce a two-dimensional (2D) discrete nonlinear Schr\"{o}dinger (DNLS)
equation with self-attractive cubic nonlinearity in a rotating reference frame.
The model applies to a Bose-Einstein condensate stirred by a rotating strong
optical lattice, or light propagation in a twisted bundle of nonlinear fibers.
Two species of localized states are constructed: off-axis fundamental solitons
(FSs), placed at distance from the rotation pivot, and on-axis (R=0) vortex
solitons (VSs), with vorticities and 2. At a fixed value of rotation
frequency , a stability interval for the FSs is found in terms of the
lattice coupling constant , , with monotonically
decreasing . VSs with S=1 have a stability interval,
\tilde{C}_{\mathrm{cr}%}^{(S=1)}(\Omega),
which exists for below a certain critical value,
. This implies that the VSs with S=1 are
\emph{destabilized} in the weak-coupling limit by the rotation. On the
contrary, VSs with S=2, that are known to be unstable in the standard DNLS
equation, with , are \emph{stabilized} by the rotation in region
%, with growing as a
function of . Quadrupole and octupole on-axis solitons are considered
too, their stability regions being weakly affected by .Comment: To be published in Physical Review
A PT PT -Symmetric Dual-Core System with the Sine-Gordon Nonlinearity and Derivative Coupling
As an extension of the class of nonlinear PT\u27\u3ePTPT -symmetric models, we propose a system of sine-Gordon equations, with the PT\u27\u3ePTPT symmetry represented by balanced gain and loss in them. The equations are coupled by sine-field terms and first-order derivatives. The sinusoidal coupling stems from local interaction between adjacent particles in coupled Frenkel–Kontorova (FK) chains, while the cross-derivative coupling, which was not considered before, is induced by three-particle interactions, provided that the particles in the parallel FK chains move in different directions. Nonlinear modes are then studied in this system. In particular, kink-kink (KK) and kink-anti-kink (KA) complexes are explored by means of analytical and numerical methods. It is predicted analytically and confirmed numerically that the complexes are unstable for one sign of the sinusoidal coupling and stable for another. Stability regions are delineated in the underlying parameter space. Unstable complexes split into free kinks and anti-kinks that may propagate or become quiescent, depending on whether they are subject to gain or loss, respectively
Solitary waves in the Ablowitz--Ladik equation with power-law nonlinearity
We introduce a generalized version of the Ablowitz-Ladik model with a power-law nonlinearity, as a discretization of the continuum nonlinear Schr¨odinger equation with the same type of the nonlinearity. The model
opens a way to study the interplay of discreteness and nonlinearity features. We identify stationary discretesoliton states for different values of nonlinearity power σ, and address changes of their stability as frequency
ω of the standing wave varies for given σ. Along with numerical methods, a variational approximation is
used to predict the form of the discrete solitons, their stability changes, and bistability features by means of
the Vakhitov-Kolokolov criterion (developed from the first principles). Development of instabilities and the
resulting asymptotic dynamics are explored by means of direct simulations.European Union AEI/FEDER MAT2016-79866-
Discrete solitons in nonlinear Schrödinger lattices with a power-law nonlinearity
We study the discrete nonlinear Schrödinger lattice model with the onsite nonlinearity of the general form, |u|2σu|u|2σu. We systematically verify the conditions for the existence and stability of discrete solitons in the one-dimensional version of the model predicted by means of the variational approximation (VA), and demonstrate the following: monostability of fundamental solitons (FSs) in the case of the weak nonlinearity, 2σ+1<3.682σ+1<3.68; bistability, in a finite range of values of the soliton’s power, for 3.68<2σ+1<53.68<2σ+1<5; and the presence of a threshold (minimum norm of the FS), for 2σ+1≥52σ+1≥5. We also perform systematic numerical simulations to study higher-order solitons in the same general model, i.e., bound states of the FSs. While all in-phase bound states are unstable, stability regions are identified for antisymmetric double solitons and their triple counterparts. These numerical findings are supplemented by an analytical treatment of the stability problem, which allows quantitively accurate predictions for the stability features of such multipulses. When these waveforms are found to be unstable, we show, by means of direct simulations, that they self-trap into a persistent lattice breather, or relax into a stable FS, or sometimes decay completely.MECD project FIS2004-01183
SORA Methodology for Multi-UAS Airframe Inspections in an Airport
Deploying Unmanned Aircraft Systems (UAS) in safety- and business-critical operations
requires demonstrating compliance with applicable regulations and a comprehensive understanding
of the residual risk associated with the UAS operation. To support these activities and enable the
safe deployment of UAS into civil airspace, the European Union Aviation Safety Agency (EASA) has
established a UAS regulatory framework that mandates the execution of safety risk assessment for
UAS operations in order to gain authorization to carry out certain types of operations. Driven by
this framework, the Joint Authorities for Rulemaking on Unmanned Systems (JARUS) released the
Specific Operation Risk Assessment (SORA) methodology that guides the systematic risk assessment
for UAS operations. However, existing work on SORA and its applications focuses mainly on single
UAS operations, offering limited support for assuring operations conducted with multiple UAS and
with autonomous features. Therefore, the work presented in this paper analyzes the application of
SORA for a Multi-UAS airframe inspection (AFI) operation, that involves deploying multiple UAS
with autonomous features inside an airport. We present the decision-making process of each SORA
step and its application to a multiple UAS scenario. The results shows that the procedures and safety
features included in the Multi-AFI operation such as workspace segmentation, the independent
multi-UAS AFI crew proposed, and the mitigation actions provide confidence that the operation can
be conducted safely and can receive a positive evaluation from the competent authorities. We also
present our key findings from the application of SORA and discuss how it can be extended to better
support multi-UAS operations.Unión Europea 10101725
Influence of Saharan dust in deposition fluxes of nutrients in Spain
Comunicación presentada en: 2012 European Aerosol Conference (EAC-2012), B-WG01S2P30, celebrada del 2 al 7 de septiembre de 2012 en Granada
Discrete solitons in optical BEC lattices. Effects of n-body interactions
In this poster we show some recent results concerning discrete solitons in strong optical lattices, which can be described by the Discrete Nonlinear Schrödinger equation. These results are related to a variation of this equation including saturable nonlinearity terms, a feature throughoutly studied in nonlinear optics. After presenting the derivation of the DNLS equation from the Gross-Pitaevskii equation in the presence of a strong optical lattice, we study the existence of thresholds in the quadratic norm of discrete solitons in the cubic DNLS, cubic-quintic DNLS and photorefractive-DNLS. The second part of the poster is devoted to moving discrete solitons in the photorefractive DNLS equation. In the one hand, we study the existence of radiationless moving discrete solitons; on the other hand, we study the collisions of moving discrete solitons
Lockdown Measures and their Impact on Single- and Two-age-structured Epidemic Model for the COVID-19 Outbreak in Mexico
The role of lockdown measures in mitigating COVID-19 in Mexico is investigated using a comprehensive
nonlinear ODE model. The model includes both asymptomatic and presymptomatic populations with the latter
leading to sickness (with recovery, hospitalization and death possibilities). We consider the situation involving
the imposed application of partial social distancing measures in the time series of interest and find optimal parametric fits to the time series of deaths (only), as well as to that of deaths and cumulative infections. We discuss
the merits and disadvantages of each approach, we interpret the parameters of the model and assess the realistic
nature of the parameters resulting from the optimization procedure. Importantly, we explore a model involving
two sub-populations (younger and older than a specific age), to more accurately reflect the observed impact as
concerns symptoms and behavior in different age groups. For definitiveness and to separate people that are (typically) in the active workforce, our partition of population is with respect to members younger vs. older than the
age of 65. The basic reproductive number of the model is computed for both the single- and the two-population
variant. Finally, we consider what would be the impact on the number of deaths and cumulative infections upon
imposition of partial lockdown (involving only the older population) and full lockdown (involving the entire
population)
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
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