Dissipative Dynamics of Matter Wave Soliton in Nonlinear Optical Lattice

Dynamics and stability of solitons in two-dimensional (2D) Bose-Einstein condensates (BEC), with low-dimensional (1D) conservative plus dissipative nonlinear optical lattices are investigated. In the case of focusing media (with attractive atomic systems) the collapse of the wave packet is arrested by the dissipative periodic nonlinearity. The adiabatic variation of the background scattering length leads to metastable matter-wave solitons. When the atom feeding mechanism is used, a dissipative soliton can exist in focusing 2D media with 1D periodic nonlinearity. In the defocusing media (repulsive BEC case) with harmonic trap in one dimension and one dimensional nonlinear optical lattice in other direction, the stable soliton can exist. This prediction of variational approach is confirmed by the full numerical simulation of 2D Gross-Pitaevskii equation.Comment: 9 pages, 8 figure

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

Examination of nanosecond laser melting thresholds in refractory metals by shear wave acoustics

Nanosecond laser pulse-induced melting thresholds in refractory (Nb, Mo, Ta and W) metals are measured using detected laser-generated acoustic shear waves. Obtained melting threshold values were found to be scaled with corresponding melting point temperatures of investigated materials displaying dissimilar shearing behavior. The experiments were conducted with motorized control of the incident laser pulse energies with small and uniform energy increments to reach high measurement accuracy and real-time monitoring of the epicentral acoustic waveforms from the opposite side of irradiated sample plates. Measured results were found to be in good agreement with numerical finite element model solving coupled elastodynamic and thermal conduction governing equations on structured quadrilateral mesh. Solid-melt phase transition was handled by means of apparent heat capacity method. The onset of melting was attributed to vanished shear modulus and rapid radial molten pool propagation within laser-heated metal leading to preferential generation of transverse acoustic waves from sources surrounding the molten mass resulting in the delay of shear wave transit times. Developed laser-based technique aims for applications involving remote examination of rapid melting processes of materials present in harsh environment (e.g. spent nuclear fuels) with high spatio-temporal resolution. © 2017 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). [http://dx.doi.org/10.1063/1.4993591

Matter-wave 2D solitons in crossed linear and nonlinear optical lattices

It is demonstrated the existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with linear OL in the $x-$direction and nonlinear OL (NOL) in the $y-$direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance. In particular, we show that such crossed linear and nonlinear OL allows to stabilize two-dimensional (2D) solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach (VA), with the Vakhitov-Kolokolov (VK) necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation (GPE). Very good agreement of the results corresponding to both treatments is observed.Comment: 8 pages (two-column format), with 16 eps-files of 4 figure

Effects of plant growth regulators on callogenesis and embryogenesis in sarnav and desiree potato (Solanum tuberosum L.) varieties

Somatic embryos play a pivotal role in the production of high-quality potatoes and seed breeding. This study focused on determining the concentrations of 1-naphthaleneacetic acid (NAA) and 6-benzyl amino purine (BAP) in the formation of callus tissue and callus induction. Our goal was to assess the efficiency of potato explants with the highest potential for somatic embryo production. To achieve this, we cultivated Sarnav and Desiree potato varieties under in vitro tissue culture conditions, utilizing the obtained tissue cultures for subsequent experiments. The MS nutrient media were enriched with NAA and BAP at ratios of 1.5: 1, 1: 1.5, and 1: 1 mg/L, along with NAA concentrations of 1.5, 1, or 2 mg/L. Somatic embryogenesis experiments were conducted using various MS nutrient media, enriched with BAP and GA3 at concentrations of 1: 0.5, 0.4: 0.1, 0.5: 0.2, and 0.1: 0.1 mg/L of plant growth regulators. During the course of the study, diverse callus formations were observed in both leaf and internodal stem explants. Among the nutrient media, the M2 medium enriched with 1: 1.5 mg/L of NAA and BAP yielded the highest callus formation rates: 92% for the Desiree variety and 100% for the Sarnav variety, specifically in internodal stem explants. Notably, the index of embryo formation in leaf explants selected for somatic embryogenesis within the SE4 medium was 70% for the Sarnav variety and 65% for the Desiree variety. The inclusion of BAP and GA3 at a ratio of 0.1: 0.1 mg/l in the SE4 nutrient medium resulted in somatic embryogenesis in 80% of calli for the Sarnav variety and 78% for the Desiree variety. These findings underscore the potential for regenerating plants through somatic embryogenesis in the Sarnav potato variety, a significant development with implications for genetic transformation studies involving this particular variety

Criteria for integro-differential modeling of plane-parallel flow of viscous incompressible fluid

For a liquid with a nonmonotonic flow curve in the stationary case in the region of the descending branch, setting the velocity at the boundary does not uniquely determine the shear stress, strain rate distribution, and velocity profile that arise since the problem is known to have many unstable solutions. At the same time, the problem of the motion of such fluid under the action of a given pressure difference has no more than three solutions, two of which are stable, and the third is unstable and not reproducible. Which of the two stable solutions is realized depends on the loading history. The problem of determining the velocity profile for a fluid characterized by a nonmonotonic rheological flow curve between parallel planes is considered. The existence of a solution is realized by reducing the problem posed to a singular integral equation of normal type, which is known by the Carleman – Vekua regularization method developed by S.G. Mikhlin and M.M. Smirnov equivalently reduces to the Fredholm integral equation of the second kind, and the solvability of the latter follows from the uniqueness of the solution delivered problem describing of criteria for integro–differential modeling of a plane-parallel flow of a viscous incompressible fluid

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

Maximal width of the separatrix chaotic layer

The main goal of the paper is to find the {\it absolute maximum} of the width of the separatrix chaotic layer as function of the frequency of the time-periodic perturbation of a one-dimensional Hamiltonian system possessing a separatrix, which is one of the major unsolved problems in the theory of separatrix chaos. For a given small amplitude of the perturbation, the width is shown to possess sharp peaks in the range from logarithmically small to moderate frequencies. These peaks are universal, being the consequence of the involvement of the nonlinear resonance dynamics into the separatrix chaotic motion. Developing further the approach introduced in the recent paper by Soskin et al. ({\it PRE} {\bf 77}, 036221 (2008)), we derive leading-order asymptotic expressions for the shape of the low-frequency peaks. The maxima of the peaks, including in particular the {\it absolute maximum} of the width, are proportional to the perturbation amplitude times either a logarithmically large factor or a numerical, still typically large, factor, depending on the type of system. Thus, our theory predicts that the maximal width of the chaotic layer may be much larger than that predicted by former theories. The theory is verified in simulations. An application to the facilitation of global chaos onset is discussed.Comment: 18 pages, 16 figures, submitted to PR

On the unique solvability of a nonlocal boundary value problem with the poincaré condition

As is known, it is customary in the literature to divide degenerate equations of mixed type into equations of the first and second kind. In the case of an equation of the second kind, in contrast to the first, the degeneracy line is simultaneously the envelope of a family of characteristics, i.e. is itself a characteristic, which causes additional difficulties in the study of boundary value problems for equations of the second kind. In this paper, in order to establish the unique solvability of one nonlocal problem with the Poincaré condition for an elliptic-hyperbolic equation of the second kind developed a new principle extremum, which helps to prove the uniqueness of resolutions as signed problem. The existence of a solution is realized by reducing the problem posed to a singular integral equation of normal type, which known by the Carleman-Vekua regularization method developed by S.G. Mikhlin and M.M. Smirnov equivalently reduces to the Fredholm integral equation of the second kind, and the solvability of the latter follows from the uniqueness of the solution delivered problem

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