Classification of integrable two-component Hamiltonian systems of hydrodynamic type in 2+1 dimensions

Hamiltonian systems of hydrodynamic type occur in a wide range of applications including fluid dynamics, the Whitham averaging procedure and the theory of Frobenius manifolds. In 1+1 dimensions, the requirement of the integrability of such systems by the generalised hodograph transform implies that integrable Hamiltonians depend on a certain number of arbitrary functions of two variables. On the contrary, in 2+1 dimensions the requirement of the integrability by the method of hydrodynamic reductions, which is a natural analogue of the generalised hodograph transform in higher dimensions, leads to finite-dimensional moduli spaces of integrable Hamiltonians. In this paper we classify integrable two-component Hamiltonian systems of hydrodynamic type for all existing classes of differential-geometric Poisson brackets in 2D, establishing a parametrisation of integrable Hamiltonians via elliptic/hypergeometric functions. Our approach is based on the Godunov-type representation of Hamiltonian systems, and utilises a novel construction of Godunov's systems in terms of generalised hypergeometric functions.Comment: Latex, 34 page

Staeckel systems generating coupled KdV hierarchies and their finite-gap and rational solutions

We show how to generate coupled KdV hierarchies from Staeckel separable systems of Benenti type. We further show that solutions of these Staeckel systems generate a large class of finite-gap and rational solutions of cKdV hierarchies. Most of these solutions are new.Comment: 15 page

Implementation of Zero Liquid Discharge Systems in Russian Industry

The article focuses on the implementation of zero liquid discharge (ZLD) systems precluding the pollutant release to the environment at metallurgical, machine-building and metalworking enterprises. The need to change over to such systems is due to two main factors: 1. Significant savings in fresh water used in production; 2. A decrease in the number of all kinds of pollutants reaching the environment with various discharges (purified, insufficiently purified and completely untreated). The main feature of ZLD systems at industrial enterprises is the presence of tailing management facilities, e. g. concentrated wastewater treatment facilities; industrial wastewater sludge treatment facilities; non-recyclable oily wastewater and sludge incineration facilities; reclaimed (recycled) industrial wastewater treatment facilities etc. The development stages of ZLD systems in Russia are presented. In 1973, for the first time in the world's practice, in the Verkh-Isetsky Metallurgical Plant in the city of Sverdlovsk (now Yekaterinburg), the ZLD developed by Prof. V. I. Aksenov and his colleagues was launched and has successfully operated in the cold rolled transformer steel workshop. As an example of wastewater treatment facility as part of a ZLD system, some technical installation solutions are described in order to treat chemically contaminated acid ferrous-containing wastewater generated in pickling carbon steel. The focus is on the feasibility of implementing local ZLD systems instead of central ZLD systems. The advantages of such local systems are: possible regenerating exhausted process solutions at the place of their formation, obtaining demineralized water, the local treatment of chemically polluted wastewater, lower investment and operating costs. © Published under licence by IOP Publishing Ltd

Identification method based on Zadeh filter models

Mathematical modeling which provides the description of objects and proper organization of control operations in future is an integral stage in the automation of production. One of the approaches to build a mathematical model of an object is to represent nonlinear systems as combinations of inertial and nonlinear inertialess elements. The models thus obtained are called block-oriented. In this paper, we consider nonlinear dynamic objects represented as the models of the Zadeh filter class. In the process of the method development the identification equations were derived for the case when the test signal is a single sinusoid. Then the case of two sinusoids was considered. Such investigations allowed us to identify the patterns and describe the general case for several test components in the signal. The results of digital modeling using the sum of harmonic signals confirm the feasibility and validity of the proposed approach for identifying nonlinear models of the Zadeh filter class

Invariant description of solutions of hydrodynamic type systems in hodograph space: hydrodynamic surfaces

Hydrodynamic surfaces are solutions of hydrodynamic type systems viewed as non-parametrized submanifolds of the hodograph space. We propose an invariant differential-geometric characterization of hydrodynamic surfaces by expressing the curvature form of the characteristic web in terms of the reciprocal invariants.Comment: 12 page

Zero Liquid Discharge (ZLD) Industrial Wastewater Treatment Systems as Sustainable Development Basic Ecological Components

The problems in processing the acid ferrous-containing rinsing water and spent pickling solutions are considered. The first-ever in metallurgy zero liquid discharge (ZLD) industrial wastewater treatment systems of a transformer cold rolling plant at the Verkh-Isetsky steelworks in Sverdlovsk (now - LLC VIZ Steel is a part of Novolipetsk Steel Group of Companies) is described. The experience of the VIZ Steel, particularly in relation to industrial wastewater treatment and sludge processing, is useful for designing ZLD industrial wastewater treatment systems of metallurgical, machine-building and metalworking enterprises. The recommendations for organizing the ZLD industrial wastewater treatment systems in the pickling plants with the repeated use of the treated rinsing water and processing the spent pickling solutions and the sludges are presented. For practical calculations of clarifiers the empirical formulas are offered. Process flow diagram of acid ferrous-containing rinsing water treatment is suggested. Acid ferrous-containing rinsing water treatment includes the following processes: rinsing water neutralization to pH 9-10,5 by 5 % calcium hydroxide and partial ferrous oxidation by air; addition of anionic flocculant and active gypsum priming to the neutralized rinsing water; settling of rinsing water conditioned by reagents in clarifiers; treatment of clarified water on deep bed sand filters; reclaimed water treatment. © Published under licence by IOP Publishing Ltd

Analytic model for a frictional shallow-water undular bore

We use the integrable Kaup-Boussinesq shallow water system, modified by a small viscous term, to model the formation of an undular bore with a steady profile. The description is made in terms of the corresponding integrable Whitham system, also appropriately modified by friction. This is derived in Riemann variables using a modified finite-gap integration technique for the AKNS scheme. The Whitham system is then reduced to a simple first-order differential equation which is integrated numerically to obtain an asymptotic profile of the undular bore, with the local oscillatory structure described by the periodic solution of the unperturbed Kaup-Boussinesq system. This solution of the Whitham equations is shown to be consistent with certain jump conditions following directly from conservation laws for the original system. A comparison is made with the recently studied dissipationless case for the same system, where the undular bore is unsteady.Comment: 24 page

Laplace transformations of hydrodynamic type systems in Riemann invariants: periodic sequences

The conserved densities of hydrodynamic type system in Riemann invariants satisfy a system of linear second order partial differential equations. For linear systems of this type Darboux introduced Laplace transformations, generalising the classical transformations in the scalar case. It is demonstrated that Laplace transformations can be pulled back to the transformations of the corresponding hydrodynamic type systems. We discuss periodic Laplace sequences of with the emphasize on the simplest nontrivial case of period 2. For 3-component systems in Riemann invariants a complete discription of closed quadruples is proposed. They turn to be related to a special quadratic reduction of the (2+1)-dimensional 3-wave system which can be reduced to a triple of pairwize commuting Monge-Ampere equations. In terms of the Lame and rotation coefficients Laplace transformations have a natural interpretation as the symmetries of the Dirac operator, associated with the (2+1)-dimensional n-wave system. The 2-component Laplace transformations can be interpreted also as the symmetries of the (2+1)-dimensional integrable equations of Davey-Stewartson type. Laplace transformations of hydrodynamic type systems originate from a canonical geometric correspondence between systems of conservation laws and line congruences in projective space.Comment: 22 pages, Late

Bacteria of genus <i>Filifactor</i> in patients with periodontitis and type 2 diabetes in accordance with metagenomic analysis of the periodontal microbiome

Introduction. Periodontal diseases are a common pathology with chronic periodontitis (CP) being the most severe form. This polymicrobial disease has become a problem of great importance in recent years due to the possibility of development of systemic effects associated with this condition. CP is often combined with type 2 diabetes (T2D). The main cause of the occurrence and development of periodontal pathology is played by the bacteria Filifactor alocis, the least studied and most recently discovered periodontal pathogen. The objective of this study was to identify bacteria of genus Filifactor as part of the periodontal microbiome associated with CP and T2D and to clarify the mechanisms of their possible influence on associated metabolic processes according to comparative metagenomic analysis. Materials and methods. A metagenomic study of the microbiome of periodontal pocket samples from 28 patients with CP associated with T2D and 22 patients with CP, as well as the microbiome of dental gingival sulcus samples from 19 clinically healthy individuals was performed. 16S-sequencing of the ribosomal RNA gene was used to determine the taxonomic composition of the microbiome. Prediction of metabolic pathways involving the microbiome was performed with the help of the shotgun method. Results. Filifactor bacteria were the one of the most frequent microorganisms only in patients with CP associated with T2D. The rate of identification of these bacteria was correlated with low predicted metagenomic levels of fatty acid biosynthesis and pyrimidine metabolism in the affected area. Conclusion. The detection frequency of Filifactor bacteria in patients associated with CP and T2D is negatively correlated with the selected features of putative metabolic pathways of the microbiome, which include fatty acid biosynthesis and pyrimidine metabolism