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

Antisymmetric distribution of permanent refractive index change in β-BaB2O4 crystal under exposure of femtosecond pulses

We have observed unusual asymmetrical refractive index change as a result of femtosecond laser inscription in a crystal without center of inversion. Profile of the refractive index change exhibits sign turn within the domain of femtosecond pulse exposure

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

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

The First World War as part of the historical and sociological concept of Michael Mann

В статье рассматриваются историко-социологический подход к Первой мировой войне и ее характеристика в рамках общеисторической концепции британского исследователя Майкла Манна.This paper examines the historical and sociological approach to the First World War and characteristics of this war in the framework of the general historical concept of british scientist Michael Mann

Phase transformation under direct laser writing in a YAG single crystal

The transformation from Y3Al5O12 to perovskite YAlO3 crystal phase was observed during ultrafast laser writing in the bulk of a Y3Al5O12 single crystal. The control of the phase transformation was demonstrated by tuning parameters of laser writing. The phenomenon is interpreted in terms of structural changes in the overheated garnet melt under laser heating followed by rapid solidification, and at least 1-ms dwell time of overheated melt is required to start spontaneous crystallization. The appearance of the perovskite phase was confirmed by Raman spectroscopy, quantitative phase and polarization microscopies

Lewis Mumford and the Birth of the City

The article discusses the views of the American philosopher and sociologist Lewis Mumford about the city as a historical phenomenon and his concept of the emergence of the city as a crystallization of certain social and cultural needs of people.В статье рассматриваются представления американского философа и социолога Льюиса Мамфорда о городе как историческом феномене и его концепция возникновения города как кристаллизации определенных социальных и культурных потребностей людей