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Sreda, 07. mart 2012. u 18 sati:
Lecture No 1181
Teaching Assistant dr med. Andjelka Hedrih, Department for biomedical science, State University of Novi Pazar, Novi Pazar, Serbia. (Projekat ON174001)
Modeling oscillations of a zona pelucida before and after fertilization - ENOC Young Scientist Prize 2011EuroMech Society
Zona pellucida (ZP), acellular mantel of mammalian oocite, changes its thickness and elastic properties before and after fertilization. To describe changes in mechanical properties of ZP, we use the method of discreet continuum and model ZP as a discreet spherical net with non-linear elastic and visco-elastic connections. Elements in this discreet spherical net correspond to ZP proteins. Oscillatory spherical net Model of mouse ZP could explain its' non-linear oscillatory behaviour. A mathematical model of non-linear free and forced vibrations is presented. Before fertilisation discreet ZP net consists of elements that have ideally non-linear-elastic properties and ZP net has ideally non-linear-elastic properties. After fertilisation this model is modified in the following way: material particles (ZP proteins) are interconnected with standard light hereditary elements with visco-non-linear-elastic properties. Ideally non-linear-elastic spherical ZP net that envelops a non-fertilised oocite has oscillatory properties. It oscillates as a system with 3n degrees of freedom and with 3n eigen circular frequencies. On a distortion caused by spermatozoa, material particles, in general case, each oscillates in a 3n-frequency regime. Mechanical impact of spermatozoa causes distortion of equilibrium state of the ZP elastic network and it starts to oscillate. It can be considered that spermatozoa transfer a part of its kinetic energy to the ZP network that is used for changing its initial state. To describe oscilatory behaviour of ZP under free and force regime we made three independent sets of coupled non-linear differential equations. First set of the non-linear differential equations contains independent non-linear differential equations of Georg Duffing type. For solving three independent subsystems of non-linear differential equations we use two methods, Lagranges method of variation constants as well as asymptotic method of Krilov Bogolyubov-Mitropolyskiy for obtaining system of the first approximation for corresponding number of amplitudes and phases. Material particles in the net move in three orthogonal directions and in each of directions are multifrequency vibrations asynchronous, and resultant of nonlinear dynamics are space trajectory in the form of the generalized Lissajus curves. Model could explain oscillations of the ZP network in the fertilization process- diameter and consistency change. It is possible that in ZP before fertilization appears different type of multifrequency regime of oscillations: from pure periodic to pure chaotic-like regimes. Synchronized regimes of the knots mass particle motion in the sphere ZP net are favorable kinetic states for possible successful penetration of spermatozoid trough ZP and fertilization. Chaotic-like motion of ZP glycoproteins is an unfavorable kinetic state for spermatozoids penetration of ZP.
 Papi M, Sylla L, Parasassi T, Brunelli R, Monaci M, Maulucci G, Missori M, Arcovito G, Ursini F, and De Spirito M. (2009) Evidence of elastic to plastic transition in the zona pellucida of oocytes using atomic force spectroscopy. App Phy Lett 94: 153902.
 Khalilian M, Navidbakhsh M, Valojerdi MR, Chizari M, Yazdi PE. (2010) Estimating Young's modulus of zona pellucida by micropipette aspiration in combination with theoretical models of ovum. ?.R. Soc. Interface. 7(45):687-94.
 Papi M, Brunelli R, Sylla L, Parasassi T Monaci M, Maulucci G, Missori M, Arcovito G, Ursini F, De Spirito M. (2010) Mechanical properties of zona pellucida hardening. Eur Biophys J 39:987992.
 Familiari G, Relucenti M, Heyn R, Micara G, and Correr S. (2006) Three-Dimensional Structure of the Zona Pellucida at Ovulation. Microscopy research and technique 69:415426.
 Sun Y, Nelson BJ, Greminger MA. (2005) Investigating Protein Structure Change in the Zona Pellucida with a Microrobotic System. The International Journal of Robotics Research 24 ( 23): 211-218.
 Hedrih (Stevanovic) K., (2006), Modes of the Homogeneous Chain Dynamics, Signal Processing, Elsevier, 86(2006), 2678-2702.. ISSN: 0165-1684 www.sciencedirect.com/science/journal/01651684
 Hedtrih (Stevanovic) K., (2008), Dynamics of coupled systems, Nonlinear Analysis: Hybrid Systems, Volume 2, Issue 2, June 2008, Pages 310-334.
SREDA, 14. mart 2012. u 18 sati:
Lecture No 1182
Mr eljko R. Đuriic assistant, Electrotechnical Faculty, University of Belgrade and ptof. dr Duan Mikicic (retired person) Electrotechnical Faculty, University of Belgrade and Mathematical Institute SANU (Project ON174001)
Analysis of wind characteristics in the south Bamat Region and conductions associated with wind power integration in powersystem of Serbia
The paper analyses typical generation profiles of the perspective wind plants in South Banat region obtained on the basis of multiannual dedicated wind speed measurements in the target region and realistic wind turbine characteristics. In addition to this, it analyses the correlation level between the average EPS daily load profile and the wind plant generation diagrams. It also consider the energy balancing conditions within the system under abrupt wind speed changes in the target region. On the basis of the statistic analysis of wind speed data, it examines the wind plant outage probability within the target region due to strong wind. Executed analyses will provide for the consideration of the technical issues occurring during wind plant integration into the Serbian power system and aid the assessment of realistic wind plant capacities acceptable by the system.
SREDA, 21. mart 2012. u 18 sati:
Lecture No 1183
Prof. dr Veljko A. Vujicic, (retired person), Natural-mathematical Faculty University of Belgrade and Mathematical Institute SANU (Project ON 174020)
A contribution to MOND Theory Modification of Newtonian Dynamics.
SREDA, 28. mart 2012. u 18 sati:
Lecture No 1184
Mr Julijana Simonovic, dipl.mas.ing, asistent, Faculty of Mechanical Engineering, University of Nis, Serbia (Projekat ON174001)
Models of hybrid dynamical system and its analogy
Series of models of the hybrid multi- plates, beams or belts system dynamics will be presented. Structure of such a systems contain a number of thin deformable plates, beams or belts all with the same boundary conditions and coupled by layers containing continually distributed discrete standard elements. The layers are homogeneous and different type. The layer type differs with the properties of discrete elements structure. The standard light linear and nonlinear ideally elastic, visco-elastic hereditary, fractional order, standard rolling visco-elastic and standard Amontons-Coulombs type friction elements will be used to modeled homogeneous layers in the presented models of the hybrid multi system dynamics. Constitutive relations of the corresponding listed standard element will be presented. By analysis kinetic and material properties of the subsystems of the hybrid multi-plates, beams or belts systems it is possible to form series of the systems (partial differential or partial integro-differential or partial fractional order differential) equations describing the dynamical equilibrium of system dynamics. This will be presented in one chosen example of the plates system. The phenomenological mapping and mathematical analogy between the systems of different type could be discussed and mathematical modeled. Based on presented results and analogy some main properties of different hybrid multi system dynamics will be described and pointed out in the concluding comets.
Key words: multi-plates, beams or belts systems, standard rolling visco-elastic elements, standard light linear and nonlinear ideally elastic element.
Acknowledgment. I extend all my special and sincerely thanks Professor Katica (Stevanovic) Hedrih supervisor of my Doctoral thesis, where the presented models are consisting part, for all her comments and motivation that she gave to me. Parts of this research were supported by the Ministry of Sciences and Environmental Protection of Republic of Serbia through Mathematical Institute SANU Belgrade Grant OI174001 - Dynamics of hybrid systems with complex structures. Mechanics of materials.
 Goroko O. A. i Hedrih (Stevanovic) K., Analiticka dinamika (mehanika) diskretnih naslednih sistema, (Analytical Dynamics (Mechanics) of Discrete Hereditary Systems), University of Ni, 2001, Monograph, p. 426, YU ISBN 86-7181-054-2.
 Hedrih (Stevanovic), K., (2007), Energy analysis in the nonlinear hybrid system containing linear and nonlinear subsystem coupled by hereditary element, Nonlinear Dynamics, Springer, 30.01.2007, vol. 51, no. 1, pp. 127-140.
 Hedrih (Stevanovic) K., (2005), Partial Fractional Order Differential Equations of Transversal Vibrations of Creep-connected Double Plate Systems, in Monograph - Fractional Differentiation and its Applications, Edited by Alain Le Mahaute, J. A. Tenreiro Machado, Jean Claude Trigeassou and Jocelyn Sabatier, U-Book, pp. 289-302.
 Hedrih (Stevanovic) K., (2006), Transversal Vibrations of Double-Plate Systems, Acta Mechanica Sinica, Springer, (2006) 22, pp. 487-501
 Hedrih (Stevanovic) K., (2010), Vibrations of a Heavy Mass Particle Moving along a Rough Line with Friction of Coulomb Type, International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 11, No.3 March 2010, pp. 203-210.
 Hedrih (Stevanovic) K. and Simonovic J.,(2008), Transversal Vibrations of a Double Circular Plate System with Visco-elastic Layer Excited by a Random Temperature Field, Int. J. Non-linear Sciences and Numerical Simulation, 2008, Vol. 9, No.1, pp.47-50.
 Hedrih (Stevanivic) K. and Simonovic J., (2007), Transversal Vibrations of a non-conservative double circular plate system, FACTA UNIVERSITATIS Series: Mechanics, Automatic Control and Robotics, VOL. 6, NO 1, 2007, PP. 3 - 64.
 Hedrih (Stevanovic) K. & Simonovic J.,(2010),: Models of Hybrid Multi-Plates Systems Dynamics, The International Conference-Mechanical Engineering in XXI Century, Ni, Serbia, 25-26 September 2010, Proceedings, pp.17-20, 2010.
 Hedrih (Stevanovic) K., Simonovic J. D., (2010), Non-linear dynamics of the sandwich double circular plate system, International Journal of Non-Linear Mechanics, Volume 45, Issue 9, November 2010, Pages 902-918, 2010.
 Hedrih (Stevanovic) K. and Simonovic J., (2012), Multi-frequency analysis of the double circular plate system non-linear dynamics, Nonlinear Dynamics: Volume 67, Issue 3,pp. 2299-2315, Springer, 2012.
 Simonovic J., (2008), Dinamika mehanickih sistema sloenih struktura (Dynamics of Complex Structure Mecnanical Systems), Magistar of Sciences Degree Thesis, Faculty of Mechanical Engineeringin University of Ni, 2008 (in Serbian).
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