1,253 research outputs found
Integrable (2+1)-Dimensional Spin Models with Self-Consistent Potentials
Integrable spin systems possess interesting geometrical and gauge invariance
properties and have important applications in applied magnetism and
nanophysics. They are also intimately connected to the nonlinear Schr\"odinger
family of equations. In this paper, we identify three different integrable spin
systems in (2 + 1) dimensions by introducing the interaction of the spin field
with more than one scalar potential, or vector potential, or both. We also
obtain the associated Lax pairs. We discuss various interesting reductions in
(2 + 1) and (1 + 1) dimensions. We also deduce the equivalent nonlinear
Schr\"odinger family of equations, including the (2 + 1)-dimensional version of
nonlinear Schr\"odinger--Hirota--Maxwell--Bloch equations, along with their Lax
pairs.Comment: 21 page
Matter wave switching in Bose-Einstein condensates via intensity redistribution soliton interactions
Using time dependent nonlinear (s-wave scattering length) coupling between
the components of a weakly interacting two component Bose-Einstein condensate
(BEC), we show the possibility of matter wave switching (fraction of atoms
transfer) between the components via shape changing/intensity redistribution
(matter redistribution) soliton interactions. We investigate the exact
bright-bright N-soliton solution of an effective one-dimensional (1D) two
component BEC by suitably tailoring the trap potential, atomic scattering
length and atom gain or loss. In particular, we show that the effective 1D
coupled Gross-Pitaevskii (GP) equations with time dependent parameters can be
transformed into the well known completely integrable Manakov model described
by coupled nonlinear Schr\"odinger (CNLS) equations by effecting a change of
variables of the coordinates and the wave functions under certain conditions
related to the time dependent parameters. We obtain the one-soliton solution
and demonstrate the shape changing/matter redistribution interactions of two
and three soliton solutions for the time independent expulsive harmonic trap
potential, periodically modulated harmonic trap potential and kink-like
modulated harmonic trap potential. The standard elastic collision of solitons
occur only for a specific choice of soliton parameters.Comment: 11 pages, 14 figures, 1 tabl
Bright-dark solitons and their collisions in mixed N-coupled nonlinear Schr\"odinger equations
Mixed type (bright-dark) soliton solutions of the integrable N-coupled
nonlinear Schr{\"o}dinger (CNLS) equations with mixed signs of focusing and
defocusing type nonlinearity coefficients are obtained by using Hirota's
bilinearization method. Generally, for the mixed N-CNLS equations the bright
and dark solitons can be split up in ways. By analysing the collision
dynamics of these coupled bright and dark solitons systematically we point out
that for , if the bright solitons appear in at least two components,
non-trivial effects like onset of intensity redistribution, amplitude dependent
phase-shift and change in relative separation distance take place in the bright
solitons during collision. However their counterparts, the dark solitons,
undergo elastic collision but experience the same amplitude dependent
phase-shift as that of bright solitons. Thus in the mixed CNLS system there
co-exist shape changing collision of bright solitons and elastic collision of
dark solitons with amplitude dependent phase-shift, thereby influencing each
other mutually in an intricate way.Comment: Accepted for publication in Physical Review
EFFECT OF CHLORHEXIDINE MOUTHWASH ON TASTE ALTERATION
Objective: Chlorhexidine (CHX) mouthwash is used as an antibacterial mouthwash since it is active against Gram-positive and Gram-negativeorganisms, anaerobes, aerobes, and yeast. It helps in reduction of dental plaque and is used to help treat gingivitis. Adverse effects of chlorohexidineare increased staining of teeth, burning sensation and most importantly taste alteration. This study will be based on the change of taste perceptionafter rinsing with 0.2% CHX. To study the effect of 0.2% CHX mouthwash on taste perception.Methods: Patients were exposed to different tastes using four samples-sweet, sour, bitter and saltiness and using a visual analog scale the intensity oftaste perception was noted before and after CHX rinses. This study was performed on 100 patients from Saveetha Dental College.Results: Sweet taste was the same for 59% of the cases while 31% of them had mild decrease in sweetness. In the case of sourness, 76% had samewhile 17% had mild reduction in sour sensation. For bitterness 2% of the cases had same, 25% had mild decrease, 63% had moderate decrease and4% had severe decrease for the taste. While in saltiness, 9% of the cases had same, 58% had mild decresase and 26% had severe decrease.Conclusion: It was found that 0.2% CHX has reduced the intensity of bitterness and saltiness quite drastically while sweetness and sourness hadshown very less to no reduction in an intensity of taste perception.Keywords: Chlorhexidine, Mouthwash, Taste, Dysguesia
Scaling and synchronization in a ring of diffusively coupled nonlinear oscillators
Chaos synchronization in a ring of diffusively coupled nonlinear oscillators
driven by an external identical oscillator is studied. Based on numerical
simulations we show that by introducing additional couplings at -th
oscillators in the ring, where is an integer and is the maximum
number of synchronized oscillators in the ring with a single coupling, the
maximum number of oscillators that can be synchronized can be increased
considerably beyond the limit restricted by size instability. We also
demonstrate that there exists an exponential relation between the number of
oscillators that can support stable synchronization in the ring with the
external drive and the critical coupling strength with a scaling
exponent . The critical coupling strength is calculated by numerically
estimating the synchronization error and is also confirmed from the conditional
Lyapunov exponents (CLEs) of the coupled systems. We find that the same scaling
relation exists for couplings between the drive and the ring. Further, we
have examined the robustness of the synchronous states against Gaussian white
noise and found that the synchronization error exhibits a power-law decay as a
function of the noise intensity indicating the existence of both noise-enhanced
and noise-induced synchronizations depending on the value of the coupling
strength . In addition, we have found that shows an
exponential decay as a function of the number of additional couplings. These
results are demonstrated using the paradigmatic models of R\"ossler and Lorenz
oscillators.Comment: Accepted for Publication in Physical Review
Comment on ``Intermittent Synchronization in a Pair of Coupled Chaotic Pendula"
The main aim of this comment is to emphasize that the conditional Lyapunov
exponents play an important role in distinguishing between intermittent and
persistent synchronization, when the analytic criteria for asymptotic stability
are not uniformly obeyed.Comment: 2 pages, RevTeX 4, 1 EPS figur
Bifurcations and Chaos in Time Delayed Piecewise Linear Dynamical Systems
We reinvestigate the dynamical behavior of a first order scalar nonlinear
delay differential equation with piecewise linearity and identify several
interesting features in the nature of bifurcations and chaos associated with it
as a function of the delay time and external forcing parameters. In particular,
we point out that the fixed point solution exhibits a stability island in the
two parameter space of time delay and strength of nonlinearity. Significant
role played by transients in attaining steady state solutions is pointed out.
Various routes to chaos and existence of hyperchaos even for low values of time
delay which is evidenced by multiple positive Lyapunov exponents are brought
out. The study is extended to the case of two coupled systems, one with delay
and the other one without delay.Comment: 34 Pages, 14 Figure
Global phase synchronization in an array of time-delay systems
We report the identification of global phase synchronization (GPS) in a
linear array of unidirectionally coupled Mackey-Glass time-delay systems
exhibiting highly non-phase-coherent chaotic attractors with complex
topological structure. In particular, we show that the dynamical organization
of all the coupled time-delay systems in the array to form GPS is achieved by
sequential synchronization as a function of the coupling strength. Further, the
asynchronous ones in the array with respect to the main sequentially
synchronized cluster organize themselves to form clusters before they achieve
synchronization with the main cluster. We have confirmed these results by
estimating instantaneous phases including phase difference, average phase,
average frequency, frequency ratio and their differences from suitably
transformed phase coherent attractors after using a nonlinear transformation of
the original non-phase-coherent attractors. The results are further
corroborated using two other independent approaches based on recurrence
analysis and the concept of localized sets from the original non-phase-coherent
attractors directly without explicitly introducing the measure of phase.Comment: 11 pages, 13 figures, Appear in Physical Review
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
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