371 research outputs found
Resonances in a trapped 3D Bose-Einstein condensate under periodically varying atomic scattering length
Nonlinear oscillations of a 3D radial symmetric Bose-Einstein condensate
under periodic variation in time of the atomic scattering length have been
studied analytically and numerically. The time-dependent variational approach
is used for the analysis of the characteristics of nonlinear resonances in the
oscillations of the condensate. The bistability in oscillations of the BEC
width is invistigated. The dependence of the BEC collapse threshold on the
drive amplitude and parameters of the condensate and trap is found. Predictions
of the theory are confirmed by numerical simulations of the full
Gross-Pitaevski equation.Comment: 17 pages, 10 figures, submitted to Journal of Physics
Interaction of pulses in nonlinear Schroedinger model
The interaction of two rectangular pulses in nonlinear Schroedinger model is
studied by solving the appropriate Zakharov-Shabat system. It is shown that two
real pulses may result in appearance of moving solitons. Different limiting
cases, such as a single pulse with a phase jump, a single chirped pulse,
in-phase and out-of-phase pulses, and pulses with frequency separation, are
analyzed. The thresholds of creation of new solitons and multi-soliton states
are found.Comment: 9 pages, 7 figures. Accepted to Phys. Rev. E, 200
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Some Case Example Exact Solutions for Quadratically Nonlinear Optical Media with PT-Symmetric Potentials
In the present paper we consider an optical system with a χ (2)-type nonlinearity and unspecified PT -symmetric potential functions. Considering this as an inverse problem and positing a family of exact solutions in terms of cnoidal functions, we solve for the resulting potential functions in a way that ensures the potentials obey the requirements of PT -symmetry. We then focus on case examples of soliton and periodic solutions for which we present a stability analysis as a function of their amplitude parameters. Finally, we numerically explore the nonlinear dynamics of the associated waveforms to identify the outcome of the relevant dynamical instabilities of localized and extended states
Negative thermal expansion of MgB in the superconducting state and anomalous behavior of the bulk Gr\"uneisen function
The thermal expansion coefficient of MgB is revealed to change
from positive to negative on cooling through the superconducting transition
temperature . The Gr\"uneisen function also becomes negative at
followed by a dramatic increase to large positive values at low temperature.
The results suggest anomalous coupling between superconducting electrons and
low-energy phonons.Comment: 5 figures. submitted to Phys. Rev. Let
Modulational and Parametric Instabilities of the Discrete Nonlinear Schr\"odinger Equation
We examine the modulational and parametric instabilities arising in a
non-autonomous, discrete nonlinear Schr{\"o}dinger equation setting. The
principal motivation for our study stems from the dynamics of Bose-Einstein
condensates trapped in a deep optical lattice. We find that under periodic
variations of the heights of the interwell barriers (or equivalently of the
scattering length), additionally to the modulational instability, a window of
parametric instability becomes available to the system. We explore this
instability through multiple-scale analysis and identify it numerically. Its
principal dynamical characteristic is that, typically, it develops over much
larger times than the modulational instability, a feature that is qualitatively
justified by comparison of the corresponding instability growth rates
Theory of Nonlinear Dispersive Waves and Selection of the Ground State
A theory of time dependent nonlinear dispersive equations of the Schroedinger
/ Gross-Pitaevskii and Hartree type is developed. The short, intermediate and
large time behavior is found, by deriving nonlinear Master equations (NLME),
governing the evolution of the mode powers, and by a novel multi-time scale
analysis of these equations. The scattering theory is developed and coherent
resonance phenomena and associated lifetimes are derived. Applications include
BEC large time dynamics and nonlinear optical systems. The theory reveals a
nonlinear transition phenomenon, ``selection of the ground state'', and NLME
predicts the decay of excited state, with half its energy transferred to the
ground state and half to radiation modes. Our results predict the recent
experimental observations of Mandelik et. al. in nonlinear optical waveguides
Wannier functions analysis of the nonlinear Schr\"{o}dinger equation with a periodic potential
In the present Letter we use the Wannier function basis to construct lattice
approximations of the nonlinear Schr\"{o}dinger equation with a periodic
potential. We show that the nonlinear Schr\"{o}dinger equation with a periodic
potential is equivalent to a vector lattice with long-range interactions. For
the case-example of the cosine potential we study the validity of the so-called
tight-binding approximation i.e., the approximation when nearest neighbor
interactions are dominant. The results are relevant to Bose-Einstein condensate
theory as well as to other physical systems like, for example, electromagnetic
wave propagation in nonlinear photonic crystals.Comment: 5 pages, 1 figure, submitted to Phys. Rev.
The Efimov's effect for a model of a three particle discrete Shr\"odinger operator
In the paper we study existance of infinitly many egenvalues for a model of a
three particle discrete Shr\"odinger operator.Comment: Russia
Stable spinning optical solitons in three dimensions
We introduce spatiotemporal spinning solitons (vortex tori) of the
three-dimensional nonlinear Schrodinger equation with focusing cubic and
defocusing quintic nonlinearities. The first ever found completely stable
spatiotemporal vortex solitons are demonstrated. A general conclusion is that
stable spinning solitons are possible as a result of competition between
focusing and defocusing nonlinearities.Comment: 4 pages, 6 figures, accepted to Phys. Rev. Let
The effect of sexual differences on the clinical course of type 1 diabetes in children with autoimmune thyroiditis as parts of autoimmune polyglandular type 3 syndrome
The article discusses the effect of sexual differences on the clinical course of type 1 diabetes in children of autoimmune thyroiditis in the autoimmune polyglandular type 3 syndrome. A cross-sectional study was conducted, with the formation of a comparison group. A definite difference in the level of HbA1c% and the incidence of late complications of diabetes. According to the results of this study, it became clear that the female sex is the worst course of type 1 diabetes in combination with autoimmune thyroiditis.В статье обсуждается влияние половых различий на клиническое течение сахарного диабета 1 типа у детей аутоиммунного тиреоидита в составе аутоиммунного полигландулярного синдрома 3 типа. Проведено поперечное исследование, с формированием группы сравнения. Определена разница в уровне HbA1c% и частоте проявлений поздних осложнений диабета. По результатам данного исследования стало понятно, что женский пол характеризуется худшим течением сахарного диабета 1 типа в сочетании с аутоиммунным тиреоидитом
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