452 research outputs found
Transition from anticipatory to lag synchronization via complete synchronization in time-delay systems
The existence of anticipatory, complete and lag synchronization in a single
system having two different time-delays, that is feedback delay and
coupling delay , is identified. The transition from anticipatory to
complete synchronization and from complete to lag synchronization as a function
of coupling delay with suitable stability condition is discussed. The
existence of anticipatory and lag synchronization is characterized both by the
minimum of similarity function and the transition from on-off intermittency to
periodic structure in laminar phase distribution.Comment: 14 Pages and 12 Figure
Nonlinear Dynamics of Moving Curves and Surfaces: Applications to Physical Systems
The subject of moving curves (and surfaces) in three dimensional space (3-D)
is a fascinating topic not only because it represents typical nonlinear
dynamical systems in classical mechanics, but also finds important applications
in a variety of physical problems in different disciplines. Making use of the
underlying geometry, one can very often relate the associated evolution
equations to many interesting nonlinear evolution equations, including soliton
possessing nonlinear dynamical systems. Typical examples include dynamics of
filament vortices in ordinary and superfluids, spin systems, phases in
classical optics, various systems encountered in physics of soft matter, etc.
Such interrelations between geometric evolution and physical systems have
yielded considerable insight into the underlying dynamics. We present a
succinct tutorial analysis of these developments in this article, and indicate
further directions. We also point out how evolution equations for moving
surfaces are often intimately related to soliton equations in higher
dimensions.Comment: Review article, 38 pages, 7 figs. To appear in Int. Jour. of Bif. and
Chao
A unification in the theory of linearization of second order nonlinear ordinary differential equations
In this letter, we introduce a new generalized linearizing transformation
(GLT) for second order nonlinear ordinary differential equations (SNODEs). The
well known invertible point (IPT) and non-point transformations (NPT) can be
derived as sub-cases of the GLT. A wider class of nonlinear ODEs that cannot be
linearized through NPT and IPT can be linearized by this GLT. We also
illustrate how to construct GLTs and to identify the form of the linearizable
equations and propose a procedure to derive the general solution from this GLT
for the SNODEs. We demonstrate the theory with two examples which are of
contemporary interest.Comment: 8 page
Stationary structures in two-dimensional continuous Heisenberg ferromagnetic spin system
Stationary structures in a classical isotropic two-dimensional continuous
Heisenberg ferromagnetic spin system are studied in the framework of the
(2+1)-dimensional Landau-Lifshitz model. It is established that in the case of
\vec S (\vec r, t)= \vec S (\vec r - \vec v t) the Landau-Lifshitz equation is
closely related to the Ablowitz-Ladik hierarchy. This relation is used to
obtain soliton structures, which are shown to be caused by joint action of
nonlinearity and spatial dispersion, contrary to the well-known one-dimensional
solitons which exist due to competition of nonlinearity and temporal
dispersion. We also present elliptical quasiperiodic stationary solutions of
the stationary (2+1)-dimensional Landau-Lifshitz equation.Comment: Archive version is already official Published by JNMP at
http://www.sm.luth.se/math/JNMP
Three dimensional quadratic algebras: Some realizations and representations
Four classes of three dimensional quadratic algebras of the type \lsb Q_0 ,
Q_\pm \rsb , \lsb Q_+ , Q_- \rsb ,
where are constants or central elements of the algebra, are
constructed using a generalization of the well known two-mode bosonic
realizations of and . The resulting matrix representations and
single variable differential operator realizations are obtained. Some remarks
on the mathematical and physical relevance of such algebras are given.Comment: LaTeX2e, 23 pages, to appear in J. Phys. A: Math. Ge
Suppression and Enhancement of Soliton Switching During Interaction in Periodically Twisted Birefringent Fiber
Soliton interaction in periodically twisted birefringent optical fibers has
been analysed analytically with refernce to soliton switching. For this purpose
we construct the exact general two-soliton solution of the associated coupled
system and investigate its asymptotic behaviour. Using the results of our
analytical approach we point out that the interaction can be used as a switch
to suppress or to enhance soliton switching dynamics, if one injects
multi-soliton as an input pulse in the periodically twisted birefringent fiber.Comment: 10 pages, 4 figures, Latex, submitted to Phys. Rev.
Dense Motion Estimation for Smoke
Motion estimation for highly dynamic phenomena such as smoke is an open
challenge for Computer Vision. Traditional dense motion estimation algorithms
have difficulties with non-rigid and large motions, both of which are
frequently observed in smoke motion. We propose an algorithm for dense motion
estimation of smoke. Our algorithm is robust, fast, and has better performance
over different types of smoke compared to other dense motion estimation
algorithms, including state of the art and neural network approaches. The key
to our contribution is to use skeletal flow, without explicit point matching,
to provide a sparse flow. This sparse flow is upgraded to a dense flow. In this
paper we describe our algorithm in greater detail, and provide experimental
evidence to support our claims.Comment: ACCV201
Intermittency transitions to strange nonchaotic attractors in a quasiperiodically driven Duffing oscillator
Different mechanisms for the creation of strange nonchaotic attractors (SNAs)
are studied in a two-frequency parametrically driven Duffing oscillator. We
focus on intermittency transitions in particular, and show that SNAs in this
system are created through quasiperiodic saddle-node bifurcations (Type-I
intermittency) as well as through a quasiperiodic subharmonic bifurcation
(Type-III intermittency). The intermittent attractors are characterized via a
number of Lyapunov measures including the behavior of the largest nontrivial
Lyapunov exponent and its variance as well as through distributions of
finite-time Lyapunov exponents. These attractors are ubiquitous in
quasiperiodically driven systems; the regions of occurrence of various SNAs are
identified in a phase diagram of the Duffing system.Comment: 24 pages, RevTeX 4, 12 EPS figure
XML data exchange:Consistency and query answering
Data exchange is the problem of finding an instance of a target schema, given an instance of a source schema and a specification of the relationship between the source and the target. Theoretical foundations of data exchange have recently been investigated for relational data. In this article, we start looking into the basic properties of XML data exchange, that is, restructuring of XML documents that conform to a source DTD under a target DTD, and answering queries written over the target schema. We define XML data exchange settings in which source-to-target dependencies refer to the hierarchical structure of the data. Combining DTDs and dependencies makes some XML data exchange settings inconsistent. We investigate the consistency problem and determine its exact complexity. We then move to query answering, and prove a dichotomy theorem that classifies data exchange settings into those over which query answering is tractable, and those over which it is coNP-complete, depending on classes of regular expressions used in DTDs. Furthermore, for all tractable cases we give polynomial-time algorithms that compute target XML documents over which queries can be answered
A generalized quantum nonlinear oscillator
We examine various generalizations, e.g. exactly solvable, quasi-exactly
solvable and non-Hermitian variants, of a quantum nonlinear oscillator. For all
these cases, the same mass function has been used and it has also been shown
that the new exactly solvable potentials possess shape invariance symmetry. The
solutions are obtained in terms of classical orthogonal polynomials
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