Generalized Neighbor-Interaction Models Induced by Nonlinear Lattices

It is shown that the tight-binding approximation of the nonlinear Schr\"odinger equation with a periodic linear potential and periodic in space nonlinearity coefficient gives rise to a number of nonlinear lattices with complex, both linear and nonlinear, neighbor interactions. The obtained lattices present non-standard possibilities, among which we mention a quasi-linear regime, where the pulse dynamics obeys essentially the linear Schr{\"o}dinger equation. We analyze the properties of such models both in connection with their modulational stability, as well as in regard to the existence and stability of their localized solitary wave solutions

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

Telomerization reaction of ethylene with ethanol

The research's main aim is to synthesize saturated alcohols containing four or more carbon atoms in the chain from ethylene and ethanol, which are products of natural gas processing. During of investigation, isobutyl and isohexyl alcohols were synthesized, and the optimal conditions for the process were determined. The dependence of the product yield on various factors has been studied

Modulational instability in cigar shaped Bose-Einstein condensates in optical lattices

A self consistent theory of a cigar shaped Bose-Einstein condensate (BEC) periodically modulated by a laser beam is presented. We show, both theoretically and numerically, that modulational instability/stability is the mechanism by which wavefunctions of soliton type can be generated in cigar shaped BEC subject to a 1D optical lattice. The theory explains why bright solitons can exist in BEC with positive scattering length and why condensate with negative scattering length can be stable and give rise to dark solitary pulses.Comment: Submitted, 4 pages, 3 figures. Revised versio

Dynamics of positive- and negative-mass solitons in optical lattices and inverted traps

We study the dynamics of one-dimensional solitons in the attractive and repulsive Bose-Einstein condensates (BECs) loaded into an optical lattice (OL), which is combined with an external parabolic potential. First, we demonstrate analytically that, in the repulsive BEC, where the soliton is of the gap type, its effective mass is \emph{negative}. This gives rise to a prediction for the experiment: such a soliton cannot be not held by the usual parabolic trap, but it can be captured (performing harmonic oscillations) by an anti-trapping inverted parabolic potential. We also study the motion of the soliton a in long system, concluding that, in the cases of both the positive and negative mass, it moves freely, provided that its amplitude is below a certain critical value; above it, the soliton's velocity decreases due to the interaction with the OL. At a late stage, the damped motion becomes chaotic. We also investigate the evolution of a two-soliton pulse in the attractive model. The pulse generates a persistent breather, if its amplitude is not too large; otherwise, fusion into a single fundamental soliton takes place. Collisions between two solitons captured in the parabolic trap or anti-trap are considered too. Depending on their amplitudes and phase difference, the solitons either perform stable oscillations, colliding indefinitely many times, or merge into a single soliton. Effects reported in this work for BECs can also be formulated for optical solitons in nonlinear photonic crystals. In particular, the capture of the negative-mass soliton in the anti-trap implies that a bright optical soliton in a self-defocusing medium with a periodic structure of the refractive index may be stable in an anti-waveguide.Comment: 22pages, 9 figures, submitted to Journal of Physics

Nonlinear excitations in arrays of Bose-Einstein condensates

The dynamics of localized excitations in array of Bose-Einstein condensates is investigated in the framework of the nonlinear lattice theory. The existence of temporarily stable ground states displaying an atomic population distributions localized on very few lattice sites (intrinsic localized modes), as well as, of atomic population distributions involving many lattice sites (envelope solitons), is studied both numerically and analytically. The origin and properties of these modes are shown to be inherently connected with the interplay between macroscopic quantum tunnelling and nonlinearity induced self-trapping of atoms in coupled BECs. The phenomenon of Bloch oscillations of these excitations is studied both for zero and non zero backgrounds. We find that in a definite range of parameters, homogeneous distributions can become modulationally unstable. We also show that bright solitons and excitations of shock wave type can exist in BEC arrays even in the case of positive scattering length. Finally, we argue that BEC array with negative scattering length in presence of linear potentials can display collapse.Comment: Submitted to Phys. Rev.

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

Glassy dynamics in thin films of polystyrene

Glassy dynamics was investigated for thin films of atactic polystyrene by complex electric capacitance measurements using dielectric relaxation spectroscopy. During the isothermal aging process the real part of the electric capacitance increased with time, whereas the imaginary part decreased with time. It follows that the aging time dependences of real and imaginary parts of the electric capacitance were primarily associated with change in volume (film thickness) and dielectric permittivity, respectively. Further, dielectric permittivity showed memory and rejuvenation effects in a similar manner to those observed for poly(methyl methacrylate) thin films. On the other hand, volume did not show a strong rejuvenation effect.Comment: 7 pages, 7 figures. Phys. Rev. E (in press

Telomerization reaction of ethylene with ethanol

The research's main aim is to synthesize saturated alcohols containing four or more carbon atoms in the chain from ethylene and ethanol, which are products of natural gas processing. During of investigation, isobutyl and isohexyl alcohols were synthesized, and the optimal conditions for the process were determined. The dependence of the product yield on various factors has been studied