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

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. C 2014 AIP Publishing LLC

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

Blow-up and global existence for a general class of nonlocal nonlinear coupled wave equations

We study the initial-value problem for a general class of nonlinear nonlocal coupled wave equations. The problem involves convolution operators with kernel functions whose Fourier transforms are nonnegative. Some well-known examples of nonlinear wave equations, such as coupled Boussinesq-type equations arising in elasticity and in quasi-continuum approximation of dense lattices, follow from the present model for suitable choices of the kernel functions. We establish local existence and sufficient conditions for finite time blow-up and as well as global existence of solutions of the problem.Comment: 11 pages. Minor changes and added reference

Dynamic Phosphorescent Probe for Facile and Reversible Stress Sensing

Dynamic phosphorescent copper complex incorporated into the main chain of polyurethanes produces a facile and reversible response to tensile stress. In contrast to common deformation sensors, the applied stress does not lead to bond scission, or alters the phosphor structure. The suppression of dynamics responsible for the nonradiative relaxation is found to be the major pathway governing stress response. As a result, the response of dynamic phosphor described in this work is stress specific. Compared to initial unloaded state, a nearly twofold increase of photoluminescence intensity occurs in response to a 5–35 MPa stress applied to pristine metalated polymers or their blends with various polyurethanes. Finally, the dynamic sensor proves useful for mapping stress distribution patterns and tracking dynamic phenomena in polyurethanes using simple optical imaging techniques

MEDICO-SOCIAL AND INDIVIDUAL PSYCHOLOGICAL CHARACTERISTICS OF DRUG ADDICTED TEENAGERS AND THEIR HEALTHY RELATIVES

We conducted the research for detection of premorbid medico-social and personal features of related teenagers, using and not using psychoactive agents. Comparative analysis of 90 teenagers with drug addiction and their 90 healthy relatives (control group) was realized. Research was conducted by the method of anonymous questioning with use of specially developed questionnaire consisting of 88 questions, and also psychological methods -16 personal factors Kettell test, SMIL, and Zung depression test. Dispersive analysis was used to determine factors of medico-social character which can be considered informative for diagnostics of addiction deviations. Method of experimental psychology allowed to reveal individual and psychological features of teenagers leading to formation of addictive behavior. Teenagers suffering from drug addiction are much less socially successful than their healthy relatives. As compared to their healthy relatives, drug addicts' anamneses had more medico-social and premorbid factors of addictive risk: various neurotic episodes during childhood, craniocereberal traumas. They were exposed to actions of sexual violence more often. Their typical characteristics include tendency to internal aggression, parasuicide thoughts, suicide attempts and a paracriminal circle of contacts. Results of research at this stage gave the grounds to assume that under identical family conditions of education some teenagers are getting drug addiction, while others don't. This can be explained by the existence of individual and personal features which can already be induced by factors outside of the family. Experimental and psychological method revealed the individual and psychological features of teenagers promoting formation of dependent behavior. Unlike their healthy relatives teenage addicts have peculiar features such as aggressive tendencies, explosive nature of reaction, uneasiness and nervousness reflecting a condition of the extreme stress, hyper compensatory involvement of various protective mechanisms, hyperactivity in their search of an exit to their difficult situation, lower background of mood and narrow zone of contacts. Thus, in comparison with healthy relatives, anamnesis of teenagers addicts more often contain medico-social, behavioral and premorbid predictors of addictive behavior, and a number of specific features. All this needs to be considered while setting up individual programs of rehabilitation, and during development of primary prevention programs of psychoactive substances use in the youth environment

Comparative Analysis of Thermohydraulic Performance of Enhanced Viscous Oil and Oil Product Heaters

© Published under licence by IOP Publishing Ltd. This paper covers the analysis of positive and negative effects produced when enhanced helical hollow beams are installed into oil and oil product heaters if compared to the baseline designs. Special attention is given to the consideration of effect on the complex rheology of high-paraffin oils

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

Ways to Transfer Oil and Oil Products in Heating Conditions and Methods for Their Enhancement

© Published under licence by IOP Publishing Ltd. This paper discusses the methods of oil transportation through pipelines. Particular attention is paid to the processes of complex rheological behavior of high-paraffin crude oils. Optimal methods applicable for transportation of heavy oil with the help of intensifiers are revealed