Coupled Ostrovsky equations for internal waves in a shear flow

In the context of fluid flows, the coupled Ostrovsky equations arise when two distinct linear long wave modes have nearly coincident phase speeds in the presence of background rotation. In this paper, nonlinear waves in a stratified fluid in the presence of shear flow are investigated both analytically, using techniques from asymptotic perturbation theory, and through numerical simulations. The dispersion relation of the system, based on a three-layer model of a stratified shear flow, reveals various dynamical behaviours, including the existence of unsteady and steady envelope wave packets.Comment: 47 pages, 39 figures, accepted to Physics of Fluid

Policentricity as a way to sustainable development of the city (The case-study of the city of kazan)

© SGEM 2017. The article is devoted to the study of the polycentric city structure. The large area of the city combined with territorial-functional differentiation, growing interest of the population in recreation, leisure time, family rest, and the desire to attract tourists are all components of the emerging polycentricity of city life. Polycentricity of city structure assumes the formation of not one but several local centers on the basis of socio-ecological functions in combination with economic activities of a post-industrial nature (trade, entertainment, creative industries, education). Polycentricity allows creating a general brand of the city consisted of local brands, thereby increasing the attractiveness of the urban environment due to its diversity in different areas. The City of of Kazan has an area of more than 600 sq.km and a population of more than 1.2 million people. In administrative terms, the city is divided into seven districts. The historical center of the The City of Kazan has historical and cultural significance - the Kazan Kremlin (UNESCO site) - and natural sites - the Kaban lakes, the embankments of the Kazanka and Volga rivers. The analysis of the territorial differentiation of the city and the functional-territorial characteristics of the administrative districts of Kazan with the use of cartographic and statistical methods is carried out. It is shown that for each district there is a potential for the formation of a center on the base of existing social and environmental factors, and for the city as a whole - a polycentric territorial structure. The importance of creating pedestrian accessibility of these centers and the formation of walking and pedestrian networks of the districts is determined, taking into account the preservation of the region's uniqueness, expressed through existing environmental objects, natural objects, social functions, which is generally the basis of the sustainable development of the city

Intramolecular non-covalent interactions as a strategy towards controlled photoluminescence in copper(i) complexes

In this work, we describe a new strategy for designing photoluminescent Cu(i) complexes. At its core are simple cyclophane inspired N-donor ligands featuring intramolecular interactions between aromatic units within a single molecule. Variation of the steric bulk inflicted a change in intramolecular stacking distances that in turn affected the emission colour of copper(i) complexes tunable in a 0.5 eV range from green to red. As the interactions driving emission are confined to the single molecule, no intermolecular aggregation is required to enable photoluminescence in solution, pristine crystals, or solution-cast polymer films. A crystallographic study provides a link between the spatial proximity of the aromatic rings of the ligands (ranging from 3.349 to 3.731 A) and the enhancement of emission efficiency, which increases dramatically from 0.02 to 0.78 at 296 K as the ring spacing contracts. Photophysical and theoretical analyses confirm the involvement of intramolecular interactions in the formation of the emissive state and describe the observed phenomena at the molecular level

On a class of second-order PDEs admitting partner symmetries

Recently we have demonstrated how to use partner symmetries for obtaining noninvariant solutions of heavenly equations of Plebanski that govern heavenly gravitational metrics. In this paper, we present a class of scalar second-order PDEs with four variables, that possess partner symmetries and contain only second derivatives of the unknown. We present a general form of such a PDE together with recursion relations between partner symmetries. This general PDE is transformed to several simplest canonical forms containing the two heavenly equations of Plebanski among them and two other nonlinear equations which we call mixed heavenly equation and asymmetric heavenly equation. On an example of the mixed heavenly equation, we show how to use partner symmetries for obtaining noninvariant solutions of PDEs by a lift from invariant solutions. Finally, we present Ricci-flat self-dual metrics governed by solutions of the mixed heavenly equation and its Legendre transform.Comment: LaTeX2e, 26 pages. The contents change: Exact noninvariant solutions of the Legendre transformed mixed heavenly equation and Ricci-flat metrics governed by solutions of this equation are added. Eq. (6.10) on p. 14 is correcte

Instability of two interacting, quasi-monochromatic waves in shallow water

We study the nonlinear interactions of waves with a doubled-peaked power spectrum in shallow water. The starting point is the prototypical equation for nonlinear uni-directional waves in shallow water, i.e. the Korteweg de Vries equation. Using a multiple-scale technique two defocusing coupled Nonlinear Schr\"odinger equations are derived. We show analytically that plane wave solutions of such a system can be unstable to small perturbations. This surprising result suggests the existence of a new energy exchange mechanism which could influence the behaviour of ocean waves in shallow water.Comment: 4 pages, 2 figure

Nonlinear Longitudinal Bulk Strain Waves in Layered Elastic Wavegudes

We consider long longitudinal bulk strain waves in layered waveguides using Boussinesq-type equations. The equations are developed using lattice models, and this is viewed as an extension of the Fermi-Pasta-Ulam problem. We describe semi-analytical approaches to the solution of scattering problems in delaminated waveguides, and to the construction of the solution of an initial-value problem in the class of periodic functions, motivated by the scattering problems.Comment: 24 pages, 11 figure

S-functions, reductions and hodograph solutions of the r-th dispersionless modified KP and Dym hierarchies

We introduce an S-function formulation for the recently found r-th dispersionless modified KP and r-th dispersionless Dym hierarchies, giving also a connection of these $S$-functions with the Orlov functions of the hierarchies. Then, we discuss a reduction scheme for the hierarchies that together with the $S$-function formulation leads to hodograph systems for the associated solutions. We consider also the connection of these reductions with those of the dispersionless KP hierarchy and with hydrodynamic type systems. In particular, for the 1-component and 2-component reduction we derive, for both hierarchies, ample sets of examples of explicit solutions.Comment: 35 pages, uses AMS-Latex, Hyperref, Geometry, Array and Babel package

Second harmonic generation: Goursat problem on the semi-strip and explicit solutions

A rigorous and complete solution of the initial-boundary-value (Goursat) problem for second harmonic generation (and its matrix analog) on the semi-strip is given in terms of the Weyl functions. A wide class of the explicit solutions and their Weyl functions is obtained also.Comment: 20 page

Concerted reductive coupling of an alkyl chloride at Pt(IV)

Oxidation of a doubly cyclometallated platinum(II) complex results in two isomeric platinum(IV) complexes. Whereas the trans isomer is robust, being manipulable in air at room temperature, the cis isomer decomposes at −20 °C and above. Reductive coupling of an alkyl chloride at the cis isomer gives a new species which can be reoxidised. The independence of this coupling on additional halide rules out the reverse of an SN2 reaction, leaving a concerted process as the only sensible reaction pathway