FOREWORD TO THE SPECIAL ISSUE

devoted to 70th Anniversary of Prof. Stefan Radev,

Corresponding Member of the Bulgarian Academy of Sciences



On 20th of November 2012 a scientific session on the occasion of the 70th Anniversary of prof. Stefan Radev has been held at the Institute of Mechanics of the Bulgarian Academy of Science. In this issue selected and reviewed contributions from this session are presented.
Prof. Nikolay K. Vitanov, D. Sc., Dr.rer.nat, Ph. D.
Chairman of the Scientific session devoted to
the 70th Anniversary of Prof. Stefan Radev



CITATION OF FIVE TECHNICAL PAPERS PUBLISHED

IN JOURNAL OF THEORETICAL AND APPLIED

MECHANICS, Vol. 42, No. 1 AND 2 PUBLISHED WITH

THE FINANCIAL SUPPORT OF PROJECT

BG051PO001–3.3.05.–0001 “SCIENCE AND BUSINESS”,

FUNDED ON OPERATIONAL PROGRAM

DEVELOPMENT OF HUMAN RESOURCES” AT THE

EUROPEAN SOCIAL FUND”



The cited below five technical papers are published in Journal of Theoretical and Applied Mechanics,Vol. 42, No. 1 and 2 with the financial support of project BG051PO001–3.3.05.–0001 “Science and business”, funded on Operational program “Development of human resources” at the “European social fund”:
The five technical papers cited below are published in the following
sites:
http://versitaopen.com/jtam
http://versita.com/jtam
http://www.degruyter.com/view/j/jtam
http://www.imbm.bas.bg/tm/jtam/index.html
[1] Kazakoff, Al. B. Advances in Engineering Software for Lift Transporta-
tion Systems. Journal of Theoretical and Applied Mechanics, 42 (2012),
No. 1, 3–22.
[2] Rizov, V. I. Fracture in Composites – An Overview (Part I). Journal of
Theoretical and Applied Mechanics, 42 (2012), No. 2, 3–42.
[3] Parvanova, S. Calculation of Stress Intensity Factors Based on Force-
displacement Curve Using Element Free Galerkin Method. Journal of The-
oretical and Applied Mechanics, 42 (2012), No. 1, 23–40.
[4] Mladensky, A. S., V. I. Rizov. Application of J-Integral in the Case
of a Single Crack in Cantelever Beam. Journal of Theoretical and Applied
Mechanics, 42 (2012), No. 1, 41–54.
[5] Stoilov, G., V. Kavardzhikov, D. Pashkouleva. A Comparative
Study of Random Patterns for Digital Image Corelation. Journal of Theo-
retical and Applied Mechanics, 42 (2012), No. 2, 55–66.





St. Radev

Institute of Mechanics, Bulgarian Academy of Sciences,

Acad. G. Bonchev St., Bl. 4, 1113 Sofia, Bulgaria,

e-mail: stradev@imbm.bas.bg

F. R. A. Onofri, A. Lenoble, L. Tadrist

IUSTI UMR 7343 CNRS/Aix-Marseille University,

5 r. E. Fermi, Technopˆole de Chˆateau Gombert, Marseille 13453, France,

e-mails: Fabrice.Onofri@polytech.univ-mr.fr, Anne.lenoble@laposte.net,

Lounes.Tadrist@polytech.univ-mr.fr


REVIEW ON THE INSTABILITY AND OPTICS

OF CAPILLARY JETS AND GLASS FIBRES:

A FRUITFULL COLLABORATION BETWEEN

INSTITUTE OF MECHANICS AND IUSTI


Abstract. The paper review key results [1-14] of the joint researches conducted by IMech and IUSTI. In the First part, we review models and experimental results on the linear and nonlinear instability of a capillary jet including both axisymmetric and nonaxisymmetric disturbances. In the Second part, results on draw resonances, occurring during a glass fibre process are reviewed, as well as the unique optical models and methods developed to perform these studies.

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Zlatinka I. Dimitrova

G. Nadjakov” Institute of Solid State Physics, Bulgarian Academy of Sciences,

71, Tzarigradsko Chaussee Blvd, 1784 Sofia, Bulgaria,

e-mail: zdim@phys.bas.bg

Kaloyan N. Vitanov

Faculty of Mathematics and Informatics, “St. Kliment Ohridski” University of Sofia,

5, J. Bourchier Blvd, 1164 Sofia, Bulgaria,


INTEGRABILITY OF DIFFERENTIAL EQUATIONS WITH

FLUID MECHANICS APPLICATION: FROM PAINLEVE

PROPERTY TO THE METHOD OF SIMPLEST

EQUATION


Abstract. We present a brief overview of integrability of nonlinear ordinary and partial differential equations with a focus on the Painleve property: an ODE of second order possesses the Painleve property if the only movable singularities connected to this equation are single poles.

The importance of this property can be seen from the Ablowitz-Ramani- Segur conhecture that states that a non-linear PDE is solvable by inverse scattering transformation only if each nonlinear ODE obtained by ex- act reduction of this PDE possesses the Painleve property. The Painleve property motivated much research on obtaining exact solutions on non-linear PDEs and leaded in particular to the method of simplest equation. A version of this method called modified method of simplest equation is discussed below.

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Nikolay K. Vitanov

Institute of Mechanics, Bulgarian Academy of Sciences,

Acad. G. Bonchev St., Bl. 4, 1113 Sofia, Bulgaria,

e-mail: vitanov@imbm.bas.bg

Amin Chabchoub, Norbert Hoffmann

Institute of Mechanics and Ocean Engineering,

Hamburg University of Technology, 21073 Hamburg, Germany,

e-mails: amin.chabchoub@tuhh.de, norbert.hoffmann@tuhh.de


DEEP-WATER WAVES: ON THE NONLINEAR

SCHR¨ ODINGER EQUATION AND ITS SOLUTIONS


Abstract. We present a brief discussion on the nonlinear Schr¨odinger equation for modelling the propagation of the deep-water wavetrains and a discussion on its doubly-localized breather solutions, that can be connected to the sudden formation of extreme waves, also known as rogue waves or freak waves.

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Baljeet Singh

Department of Mathematics, Post Graduate Government College,

Sector 11, Chandigarh-160 011, India,

e-mail: bsinghgc11@gmail.com

Ranbir Singh

Department of Mathematics, Modern Institute of Engineering and Technology,

Ambala, Haryana, India,

e-mail: ranbirdhull84@gmail.com


RAYLEIGH WAVE IN A ROTATING INITIALLY

STRESSED PIEZOELECTRIC HALF-SPACE


Abstract. The governing equations of an initially stressed rotating piezoelectric medium are solved for surface wave solutions. The appropriate solutions in the half-space of the medium satisfy the required boundary conditions to obtain the frequency equation of Rayleigh wave for

charge free as well as electrically shorted cases. The non-dimensional speed of the Rayleigh wave is computed numerically for particular examples of Lithium niobate and PZT-5H ceramics. The effects of rotation and initial stress are observed graphically on the non-dimensional speed of the Rayleigh wave.

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Ivan Jordanov, Elena Nikolova

Institute of Mechanics, Bulgarian Academy of Sciences,

Acad. G. Bonchev St., Bl. 4, 1113 Sofia, Bulgaria,

e-mails: i_jordanov@email.bg, elena@imbm.bas.bg


ON NONLINEAR WAVES IN THE SPATIO-TEMPORAL

DYNAMICS OF INTERACTING POPULATIONS


Abstract. In this paper the spatial-temporal dynamics of the members of interacting populations is described by means of nonlinear partial differential equations. We consider the migration as a diffusion process influenced by the changing values of the birth rates and the coefficients of interaction between the populations. The general model is reduced to analytically tractable partial differential equations (PDE) with polynomial nonlinearity up to third order for the particular case of one population and one spatial dimension. We obtain an analytical solution which describes nonlinear kink and solitary waves in the population dynamics by applying the modified method of simplest equation to the described model.

Key words: Population dynamics, migration, partial differential equations (PDEs), modified method of the simplest equation, kinks.

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P. Dobreva

Institute of Mechanics, Bulgarian Academy of Sciences,

Acad. G. Bonchev St., Bl. 4, 1113 Sofia, Bulgaria,

e-mail: polya2006@yahoo.com


OPTIMIZATION OF THE CODE OF THE NUMERICAL

MAGNETOSHEATH-MAGNETOSPHERE MODEL


Abstract. The proposed three dimensional model contains two earlier developed 3D regional numerical models: a grid-characteristic model of the magnetosheath and a finite element model of the magnetosphere. The model output is the distribution of gas-dynamic parameters in the magnetosheath and of magnetic field inside the magnetosphere. The efforts are focused on the modernization of the existing software, written in Fortran, using several techniques for parallel programming such as OpenMP extensions. After analyzing the numerical performance of the model a possible scenario for the code optimization is shown. First results with the improved variant of the model are presented.

Key words: Magnetosheath, magnetosphere, parallel algorithms.

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Cristian Puscasu, Mihaela Grigorescu, Axene Ghita, Raluca

Voicu, Mariana Stefanescu, Victoria Teleaba

National Research & Development Institute for Gas Turbines COMOTI,

I220D, Iuliu Maniu Avenue, sector 6,

Code 061126, OP76, CP 174, Bucharest, Romania,

e-mail: cristian.puscasu@comoti.ro

Ivanka Zheleva,

Ruse University “Angel Kanichev”,

8, Studentska Street, 7017, Russe, Bulgaria,

e-mail: izheleva@uni-ruse.bg


SIMULATION OF FLUID FLOW IN CENTRIFUGAL

TRICANTER


Abstract. An ANSYS simulation of the multiphase complex fluid flow motion in a centrifugal device (tricanter) is presented in the paper. This centrifugal device is designed for one step efficient solution for contaminated river water processing with oil and oil products. The proposed tricanter is one of the main objectives of the project named “Common strategy to prevent the Danube’s pollution technological risks with oil and oil products CLEANDANUBE” financed by European Commission within the frame of Romania-Bulgaria Trans-Border Cooperation Program 2007 – 2013 (grant MIS-ETC code 653). Results for liquid phases (water and oil products) and for solid particles motion are presented graphically and are commented.

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S. Slavtchev, P. Kalitzova-Kurteva

Institute of Mechanics, Bulgarian Academy of Sciences,

Acad. G. Bonchev St., Bl. 4, 1113 Sofia, Bulgaria,

e-mails: slavcho@imbm.bas.bg, penka@imbm.bas.bg

A. Oron

Department of Mechanical Engineering, Technion-Israel Institute of Technology,

Haifa 32000, Israel,

e-mail: meroron@technion.ac.il


EVOLUTION EQUATION FOR NONLINEAR

LONG-WAVELENGTH MONOTONIC MARANGONI

INSTABILITY IN A BINARY LIQUID LAYER WITH

NONLINEAR SORET EFFECT

Abstract. The Soret effect in binary systems is called nonlinear when the thermo-diffusive flux is proportional to the temperature gradient with a coefficient being linear function of the concentration of one of the solute components. This effect is significant in highly dilute solutions. The long- wavelength Marangoni instability in a thin layer of binary liquid, in the presence of the nonlinear Soret effect, is considered. The nonlinear dynamic behaviour of the liquid system is studied in the case of monotonic instability. The solution of the dimensionless equations of mass and momentum balances, heat transfer and mass diffusion is searched near the linear instability threshold, in the form of series in a small parameter that measures the supercriticality. An equation for spatiotemporal evolution of the liquid system is derived based on the first two approximations.

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PROF. STEFAN RADEV,

CORRESPONDING MEMBER OF THE BULGARIAN

ACADEMY OF SCIENCES AND HIS CONTRIBUTIONS

TO FLUID MECHANICS