101 research outputs found
Information Technology of Generalized Model Creation of Complex Technical Objects
The paper introduces a knowledge representation framework for design and geometrical modelling of complex technical objects such as ships, aircrafts, cars, etc. The design process cannot be fully automated yet because of a lot of technical and economical factors that influence the decisions during that process. In order to make the process more efficient, a knowledge modelling framework is suggested. The basic principles of conceptual knowledge modelling and data exchange framework are presented. A practical use case of aircraft ramp modelling is provided
Asymmetric Wave Propagation Through Nonlinear PT-symmetric Oligomers
In the present paper, we consider nonlinear PT-symmetric dimers and trimers
(more generally, oligomers) embedded within a linear Schr{\"o}dinger lattice.
We examine the stationary states of such chains in the form of plane waves, and
analytically compute their reflection and transmission coefficients through the
nonlinear PT symmetric oligomer, as well as the corresponding rectification
factors which clearly illustrate the asymmetry between left and right
propagation in such systems. We examine not only the existence but also the
dynamical stability of the plane wave states and interestingly find them to be
generically unstable. Lastly, we generalize our numerical considerations to the
more physically relevant case of Gaussian initial wavepackets and confirm that
the asymmetry in the transmission properties persists in the case of such
wavepackets, as well
Bound states in Bose-Einstein condensates with radially-periodic spin-orbit coupling
We consider Bose-Einstein condensate (BEC) subject to the action of
spin-orbit-coupling (SOC) periodically modulated in the radial direction. In
contrast to the commonly known principle that periodic potentials do not create
bound states, the binary BEC maintains multiple localized modes in the linear
limit, with their chemical potential falling into spectral gaps of the
(numerically found) radial band structure induced by the spatial modulation of
the SOC. In the presence of the repulsive nonlinearity, the SOC modulation
supports fundamental gap solitons of the semi-vortex types, as well as
higher-order vortex gap solitons. The localization degree and stability of the
gap solitons strongly depend on the location of their chemical potential in the
gap. Stability intervals for vortex gap solitons in a broad range of the
intrinsic vorticity, from -2 to 3, are identified. Thus, the analysis reveals
the previously unexplored mechanism of linear and nonlinear localization
provided by the spatially periodic modulation of SOC, which may be extended to
other settings, such as those for optical beams and polaritons. Unlike the
commonly known quartets of eigenvalues for small perturbations, in the present
system the instability is accounted for by shifted complex eigenvalue pairs.Comment: 7pages, 4 figures, to be published in Chaos, Solitons & Fractal
Topological edge states in Rashba-Dresselhaus spin-orbit-coupled atoms in a Zeeman lattice
We address the impact of spin-orbit coupling on the existence and properties of topological edge states of cold neutral atoms and Bose-Einstein condensates loaded in honeycomb Zeeman lattices—lattices where the spinor components are placed in potentials having opposite signs. We find that the type of spin-orbit-coupling mechanism has profound effect on the emergence of topological edge states. We also reveal that edge states persist when interatomic interactions are present and that they become metastable in Bose-Einstein condensates.Peer ReviewedPostprint (author's final draft
-symmetric coupler with nonlinearity
We introduce the notion of a -symmetric dimer with a
nonlinearity. Similarly to the Kerr case, we argue that such a nonlinearity
should be accessible in a pair of optical waveguides with quadratic
nonlinearity and gain and loss, respectively. An interesting feature of the
problem is that because of the two harmonics, there exist in general two
distinct gain/loss parameters, different values of which are considered herein.
We find a number of traits that appear to be absent in the more standard cubic
case. For instance, bifurcations of nonlinear modes from the linear solutions
occur in two different ways depending on whether the first or the second
harmonic amplitude is vanishing in the underlying linear eigenvector. Moreover,
a host of interesting bifurcation phenomena appear to occur including
saddle-center and pitchfork bifurcations which our parametric variations
elucidate. The existence and stability analysis of the stationary solutions is
corroborated by numerical time-evolution simulations exploring the evolution of
the different configurations, when unstable.Comment: 12 pages, 11 figure
Localized and periodic exact solutions to the nonlinear Schrodinger equation with spatially modulated parameters: Linear and nonlinear lattices
Using similarity transformations we construct explicit solutions of the
nonlinear Schrodinger equation with linear and nonlinear periodic potentials.
We present explicit forms of spatially localized and periodic solutions, and
study their properties. We put our results in the framework of the exploited
perturbation techniques and discuss their implications on the properties of
associated linear periodic potentials and on the possibilities of stabilization
of gap solitons using polychromatic lattices.Comment: 17 pages, 5 figure
Solitons in one-dimensional photonic crystals
We report results of a systematic analysis of spatial solitons in the model
of 1D photonic crystals, built as a periodic lattice of waveguiding channels,
of width D, separated by empty channels of width L-D. The system is
characterized by its structural "duty cycle", DC = D/L. In the case of the
self-defocusing (SDF) intrinsic nonlinearity in the channels, one can predict
new effects caused by competition between the linear trapping potential and the
effective nonlinear repulsive one. Several species of solitons are found in the
first two finite bandgaps of the SDF model, as well as a family of fundamental
solitons in the semi-infinite gap of the system with the self-focusing
nonlinearity. At moderate values of DC (such as 0.50), both fundamental and
higher-order solitons populating the second bandgap of the SDF model suffer
destabilization with the increase of the total power. Passing the
destabilization point, the solitons assume a flat-top shape, while the shape of
unstable solitons gets inverted, with local maxima appearing in empty layers.
In the model with narrow channels (around DC =0.25), fundamental and
higher-order solitons exist only in the first finite bandgap, where they are
stable, despite the fact that they also feature the inverted shape
Matter rogue wave in Bose-Einstein condensates with attractive atomic interaction
We investigate the matter rogue wave in Bose-Einstein Condensates with
attractive interatomic interaction analytically and numerically. Our results
show that the formation of rogue wave is mainly due to the accumulation of
energy and atoms toward to its central part; Rogue wave is unstable and the
decay rate of the atomic number can be effectively controlled by modulating the
trapping frequency of external potential. The numerical simulation demonstrate
that even a small periodic perturbation with small modulation frequency can
induce the generation of a near-ideal matter rogue wave. We also give an
experimental protocol to observe this phenomenon in Bose-Einstein Condensates
PT-Symmetric Dimer in a Generalized Model of Coupled Nonlinear Oscillators
Abstract In the present work, we explore the case of a general PT -symmetric dimer in the context of two both linearly and nonlinearly coupled cubic oscillators. To obtain an analytical handle on the system, we first explore the rotating wave approximation converting it into a discrete nonlinear Schrödinger type dimer. In the latter context, the stationary solutions and their stability are identified numerically but also wherever possible analytically. Solutions stemming from both symmetric and anti-symmetric special limits are identified. A number of special cases are explored regarding the ratio of coefficients of nonlinearity between oscillators over the intrinsic one of each oscillator. Finally, the considerations are extended to the original oscillator model, where periodic orbits and their stability are obtained. When the solutions are found to be unstable their dynamics is monitored by means of direct numerical simulations
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