Quasiperiodic localized oscillating solutions in the discrete nonlinear Schr\"odinger equation with alternating on-site potential

We present what we believe to be the first known example of an exact quasiperiodic localized stable solution with spatially symmetric large-amplitude oscillations in a non-integrable Hamiltonian lattice model. The model is a one-dimensional discrete nonlinear Schr\"odinger equation with alternating on-site energies, modelling e.g. an array of optical waveguides with alternating widths. The solution bifurcates from a stationary discrete gap soliton, and in a regime of large oscillations its intensity oscillates periodically between having one peak at the central site, and two symmetric peaks at the neighboring sites with a dip in the middle. Such solutions, termed 'pulsons', are found to exist in continuous families ranging arbitrarily close both to the anticontinuous and continuous limits. Furthermore, it is shown that they may be linearly stable also in a regime of large oscillations.Comment: 4 pages, 4 figures, to be published in Phys. Rev. E. Revised version: change of title, added Figs. 1(b),(c), 4 new references + minor clarification

Regional Development: Factors of Unevenness and Forming of Periphery

Регіональний розвиток як суспільно-просторовий процес завжди є нерівномірним. Він формується способом взаємонакладання процесів територіального концентрування, просторової дифузії, територіального агломерування та районоутворення. Нерівномірність регіонального розвитку зумовлюється об’єктивними (передумови та самоорганізація) та суб’єктивними (управлінськими) чинниками. Зазвичай головний акцент у дослідженнях робиться на формуванні регіональних ядер, але не менш важливим об’єктом дослідження є периферійні території, які можна розділити на внутрішню і зовнішню периферії.Regional development as human-spatial process is always uneven. It is forming by overlapping of so processes as territorial concentration, spatial diffusion, territorial agglomerating and region forming. Uneven regional development is caused by objective (preconditions and self-organization) and subjective (management) factors. Usually the main focus in studies is the regional core forming, but peripheral territories are important as well, and can be divided on inner and outside peripheries

Investigation of ultrafast laser photonic material interactions: challenges for directly written glass photonics

Currently, direct-write waveguide fabrication is probably the most widely studied application of femtosecond laser micromachining in transparent dielectrics. Devices such as buried waveguides, power splitters, couplers, gratings and optical amplifiers have all been demonstrated. Waveguide properties depend critically on the sample material properties and writing laser characteristics. In this paper we discuss the challenges facing researchers using the femtosecond laser direct-write technique with specific emphasis being placed on the suitability of fused silica and phosphate glass as device hosts for different applications.Comment: 11 pages, 87 references, 11 figures. Article in revie

Discrete soliton mobility in two-dimensional waveguide arrays with saturable nonlinearity

We address the issue of mobility of localized modes in two-dimensional nonlinear Schr\"odinger lattices with saturable nonlinearity. This describes e.g. discrete spatial solitons in a tight-binding approximation of two-dimensional optical waveguide arrays made from photorefractive crystals. We discuss numerically obtained exact stationary solutions and their stability, focussing on three different solution families with peaks at one, two, and four neighboring sites, respectively. When varying the power, there is a repeated exchange of stability between these three solutions, with symmetry-broken families of connecting intermediate stationary solutions appearing at the bifurcation points. When the nonlinearity parameter is not too large, we observe good mobility, and a well defined Peierls-Nabarro barrier measuring the minimum energy necessary for rendering a stable stationary solution mobile.Comment: 19 pages, 4 figure

Two-dimensional discrete solitons in dipolar Bose-Einstein condensates

We analyze the formation and dynamics of bright unstaggered solitons in the disk-shaped dipolar Bose-Einstein condensate, which features the interplay of contact (collisional) and long-range dipole-dipole (DD) interactions between atoms. The condensate is assumed to be trapped in a strong optical-lattice potential in the disk's plane, hence it may be approximated by a two-dimensional (2D) discrete model, which includes the on-site nonlinearity and cubic long-range (DD) interactions between sites of the lattice. We consider two such models, that differ by the form of the on-site nonlinearity, represented by the usual cubic term, or more accurate nonpolynomial one, derived from the underlying 3D Gross-Pitaevskii equation. Similar results are obtained for both models. The analysis is focused on effects of the DD interaction on fundamental localized modes in the lattice (2D discrete solitons). The repulsive isotropic DD nonlinearity extends the existence and stability regions of the fundamental solitons. New families of on-site, inter-site and hybrid solitons, built on top of a finite background, are found as a result of the interplay of the isotropic repulsive DD interaction and attractive contact nonlinearity. By themselves, these solutions are unstable, but they evolve into robust breathers which exist on an oscillating background. In the presence of the repulsive contact interactions, fundamental localized modes exist if the DD interaction (attractive isotropic or anisotropic) is strong enough. They are stable in narrow regions close to the anticontinuum limit, while unstable solitons evolve into breathers. In the latter case, the presence of the background is immaterial

Accelerated magnetosheath flows caused by IMF draping: Dependence on latitude

In previous work we used a semi-analytical treatment to describe accelerated magnetosheath flows caused by the draping of interplanetary magnetic field (IMF) lines around the magnetosphere. Here, we use the same approach, i.e., modeling the magnetic field lines as elastic strings, to examine how the magnetic tension force, one of the two agents responsible for producing these flows, varies along field lines away from the equatorial plane. The bend in the field line caused by the draping mechanism propagates as two oppositely-directed waves to higher latitudes. For a due northward IMF - the case we consider here - these propagate symmetrically north/south of the equatorial plane. As a result, a two-peaked latitude velocity profile develops as we go further downtail and the velocity peaks migrate along the magnetic field line to higher latitudes. We examine this velocity-profile for two Alfvén Mach numbers (MA = 8 and 3), representative of conditions in the solar wind at 1 AU (“normal” solar wind and solar transients). Qualitatively, the picture is the same but quantitatively there are important differences: (i) the flows reach higher values for the lower MA (maximum V/VSW = 1.6) than for the higher MA (V/VSW= 1.3); (ii) asymptotic values are reached farther downstream of the dawn-dusk terminator for the lowerMA (∼−50 RE vs −15 RE); (iii) For the lower MAthe highest speeds are reached away from the equatorial plane. We predict two channels of fast magnetosheath flow next to the magnetopause at off-equatorial latitudes that exceed the solar wind speed

Effect of stellar wind induced magnetic fields on planetary obstacles of non-magnetized hot Jupiters

We investigate the interaction between the magnetized stellar wind plasma and the partially ionized hydrodynamic hydrogen outflow from the escaping upper atmosphere of non- or weakly magnetized hot Jupiters. We use the well-studied hot Jupiter HD 209458b as an example for similar exoplanets, assuming a negligible intrinsic magnetic moment. For this planet, the stellar wind plasma interaction forms an obstacle in the planet's upper atmosphere, in which the position of the magnetopause is determined by the condition of pressure balance between the stellar wind and the expanded atmosphere, heated by the stellar extreme ultraviolet (EUV) radiation. We show that the neutral atmospheric atoms penetrate into the region dominated by the stellar wind, where they are ionized by photo-ionization and charge exchange, and then mixed with the stellar wind flow. Using a 3D magnetohydrodynamic (MHD) model, we show that an induced magnetic field forms in front of the planetary obstacle, which appears to be much stronger compared to those produced by the solar wind interaction with Venus and Mars. Depending on the stellar wind parameters, because of the induced magnetic field, the planetary obstacle can move up to ~0.5-1 planetary radii closer to the planet. Finally, we discuss how estimations of the intrinsic magnetic moment of hot Jupiters can be inferred by coupling hydrodynamic upper planetary atmosphere and MHD stellar wind interaction models together with UV observations. In particular, we find that HD 209458b should likely have an intrinsic magnetic moment of 10-20% that of Jupiter.Comment: 8 pages, 6 figures, 2 tables, accepted to MNRA

Sub-critical regime of femtosecond inscription

We apply well known nonlinear diffraction theory governing focusing of a powerful light beam of arbitrary shape in medium with Kerr nonlinearity to the analysis of femtosecond (fs) laser processing of dielectric in sub-critical (input power less than the critical power of selffocusing) regime. Simple analytical expressions are derived for the input beam power and spatial focusing parameter (numerical aperture) that are required for achieving an inscription threshold. Application of non-Gaussian laser beams for better controlled fs inscription at higher powers is also discussed. © 2007 Optical Society of America

Turbulent broadening of optical spectra in ultralong Raman fiber lasers

We study the properties of radiation generated in ultralong fiber lasers and find an interesting link between these optical systems and the theory of weak wave turbulence. Experimental observations strongly suggest that turbulentlike weak interactions between the multitude of laser cavity modes are responsible for practical characteristics of ultralong fiber lasers such as spectra of the output radiation

KTM TOKAMAK OPERATION SCENARIOS SOFTWARE INFRASTRUCTURE

One of the largest problems for tokamak devices such as Kazakhstan Tokamak for Material Testing (KTM) is the operation scenarios' development and execution. Operation scenarios may be varied often, so a convenient hardware and software solution is required for scenario management and execution. Dozens of diagnostic and control subsystems with numerous configuration settings may be used in an experiment, so it is required to automate the subsystem configuration process to coordinate changes of the related settings and to prevent errors. Most of the diagnostic and control subsystems software at KTM was unified using an extra software layer, describing the hardware abstraction interface. The experiment sequence was described using a command language.The whole infrastructure was brought together by a universal communication protocol supporting various media, including Ethernet and serial links. The operation sequence execution infrastructure was used at KTM to carry out plasma experiments