ὅδε οἶκος, ὦ ἑταῖρε, μνημεῖον ἐστιν ζῴων τῶν σοφῶν ἀνδρῶν, καὶ τῶν ἔργων αὐτῶν

**Mechanics Colloquim **

** PROGRAM**

MATEMATIČKI INSTITUT SANU

ODELJENJE ZA MEHANIKU

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PROGRAM ZA SEPTEMBAR 2011. English Serbian
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Pozivamo Vas da učestvujete u radu sednica Odeljenja i to:

__Sreda, 14. septembar 2011. u 18 sati:__

Lecture No 1161

* Prof. dr Livija Cveticanin, Full Professor of Faculty of Technical Sciences University of Novi Sad, (Project ON174000) *

** Dynamics of the non-ideal mechanical systems: A review **

A review on the literature dealing with the main properties of non-ideal vibrating systems would be presented. The analytical and numerical methods applied for analyzing such systems would be shown. The practical examples of non-ideal systems would be considered. The most common phenomenon for the systems would be discussed. The specific properties for various models would be also discussed. Special attention would be given to the Sommerfeld effect and steady-state deterministic chaos in this system. Methods for controlling chaos and its elimination would be presented, too. The direction of the future investigation would be given.

__SREDA, 21. septembar 2011. u 18 sati:__

Prof. dr Dragomir Zekovic i prof dr Zoran Stokic, Masinski fakultet Univerziteta u Beogradu

Secanje na prof. dr Vukmana Covica, redovnog profesora Masinskog fakulteta Univerziteta u Beogradu i clana Seminara mehanike

Lecture No 1162

* Trifce Sandev Radiation Safety Directorate, Skopje, Republic of Macedonia *

Abstract: We consider generalized stochastic and kinetic equations to model anomalous diffusion processes. The generalized Langevin equation with frictional memory kernels of the Mittag-Leffler type for a free particle and a harmonic oscillator is investigated through velocity and displacement correlation functions. The Laplace transform method and the properties and asymptotic behavior of the Mittag-Leffler type functions are applied to find the relaxation functions, which are in close connection with the correlation functions. The asymptotic behavior of the particle in the short and long time limit is obtained from the analytical results and by using the Tauberian theorems. It is shown that for various values of the parameters of the frictional memory kernels anomalous diffusion occurs. We distinguish cases of subdiffusion and superdiffusion. The proposed models may be used to model anomalous diffusive processes in complex media. From the other side, we investigate generalized fractional diffusion and fractional Fokker-Planck equations. These equations with Caputo or Riemann-Liouville time fractional derivatives are introduced in the context of the continuous time random walk theory. Instead of ordinary time derivative, we use composite or so-called Hilfer time fractional derivative, which was originally introduced by Hilfer, based on fractional time evolutions. This composite derivative arises in context of relaxation models, and it is shown to provide an excellent description of experimental data over more than ten orders of magnitude, with less parameters than traditional fit functions such as Havriliak-Negami. The solutions are obtained in terms of the Mittag-Leffler type functions and Foxs H-function by application of the Fourier-Laplace transform methods. The asymptotic behaviors of the solutions are derived and the moments of fundamental solutions obtained. The obtained results may be helpful for the evaluation of data from complex systems, in particular, in the context of relaxation dynamics in glassy systems or aquifer problems.

References:

[1] R. Hilfer, Application of Fractional Calculus in Physics (Singapore: World Scientific Publishing Company, 2000).

[2] R. Metzler and J. Klafter, Phys. Rep. 339 (2000) 1; R. Metzler and J. Klafter, J. Phys. A: Math. Gen. 37 (2004) R161.

[3] T. Sandev and Z. Tomovski, Phys. Scr. 82 (2010) 065001.

[4] T. Sandev, Z. Tomovski and J.L.A. Dubbeldam, Physica A 390 (2011) 3627.

[5] T. Sandev, R. Metzler and Z. Tomovski, J. Phys. A: Math. Theor. 44 (2011) 255203.

[6] T. Sandev and Z. Tomovski, The General Time Fractional Fokker-Planck Equation with a Constant External Force (to be presented: Symposium on Fractional Signals and Systems, Coimbra, Portugal, 4 5 November 2011).

[7] H.M. Srivastava and Z. Tomovski, Appl. Math. Comput. 211 (2009) 198.

[8] Z. Tomovski, R. Hilfer and H.M. Srivastava, Integral Transform. Spec. Func. 21 (2010) 797.

__SREDA, 28.septembar 2011. u 18 sati:__

Lecture No 1163

* Prof. Dr Marinko Ugricic PhD (Eng), Economical institute, Belgrade, (Project OI174001)*

** NUMERICAL SIMULATION OF PROCESSES IN PHYSICS OF EXPLOSION **

Abstract: Physics of explosion deals with different and complex processes, followed by the shock wave in the materials and extremely high parameter of state (density, pressure, temperature, stress and strain rate, etc.), so that they belong naturally to the class of mechanics problem of nonlinear continuum. The examples of explosive propulsive systems used in military and civil purposes are very large and all of them consist of two basic components: explosive charge as a source of energy and inert layer (with or without confinement) as an executive part that after acceleration and eventual deformation must produce expected effect. The requirements for qualitative description and evaluation of the processes of explosive propulsion, provided entirely by experiments, were exceeded a long time ago. The modern design requests more complex analyses of quantitative type that shortens significantly time and reduce costs of development of new systems of explosive propulsion. Further, numerical simulation of processes of explosive propulsion represents powerful and effective method in the analysis of singular and summary influence of the significant factors on the course of process and in solving of optimization assignments of explosive propulsive systems, as well. Numerical simulation of the above mentioned systems functioning may be realized by the use: empirical (quasi-analytical), analytical, numerical and coupled methods of the mathematical modeling of processes. Each of given methods, besides the determined systems of equation, require some number of enter data to be known, related to the physical and chemical characteristics of explosive charge and inert materials (layer, confinement) for considered system. For the inert component of system the values of material density, dynamic pressure resistance, hardiness, and tensile strength and so on are involved in calculation. For a finer and more complex analysis that takes into account the shock wave on the process of explosive propulsion we need to know the equation of state of materials (i.e. shock adiabate) and sound velocity in the material. On the other hand, the input data related to the explosive charge lake the density of explosive, thermodynamic and kinematic parameters of detonation, isentropic exponent of gaseous product of detonation; and for more detailed analysis the dynamic shock adiabate of explosive and equation of state of products of detonation, must be entered in the calculation. Today, the numerical simulation of processes in the physics of explosion, that considers appropriate mathematical modeling and analysis based on the finite elements method, is preferable. The illustration of possibilities of the AUTODYN solver based on this method is shown by some examples of simulation of functioning of the explosive propulsive systems such as the shaped charge, high explosive projectile, explosive reactive armour, concrete penetrating warhead, etc.

Reference:

1. WALTERS, W. P., ZUKAS, J. A.: Foundamentals of shaped charges, A Wiley-Interscience Publication, John Wiley and sons, New York, 1989.

2. Orlenko L.P. (readaktor): Fizika vzriva, izdanie trete dopolnenoe i prerabotanoe pod redakcie izdatelstvo "Nauka", Glavnaja redakcija fiziko-matematiceskoj literaturi, Moskva 2004.

3. UGRCIC, M.: Numerical simulation and optimisation of the shaped charge function, Scientific Technical Review, Vol. XLVIII, Num. 4, pp. 30-41, 1998.

4. www.century-dynamics.com and www.ansys.com Theory manual, Century Dynamics, Solutions through Software, Huston, USA.

5. EMAM, R., MIRANVILLE, A.: Mathematical modeling in continuum mechanics, Second edition, Cambridge University Press The Edinburgh Building, Cambridge UK, Published in the United States of America by Cambridge University Press, New York, 2005.

6. UGRCIC, M.: Warheads and rocket engines of aircraft missiles, COFIS Export-Import Co. Ltd., Malta, 2010.

7. UGRCIC, M.: Projektili bojne glave kumulativnog dejstva, VIZ, Beograd, 2010. (u pripremi za tampu)

8. UGRCIC, M.: Modeling and Simulation of Interaction Process of Shaped Charge Jet and Explosive Reactive Armour, International Conference EXPLOMET'95, El Paso - USA, pp. 511-518, 1995.

9. Ugrcic, M, Ugrcic, D.: FEM Techniques in Shaped Charge Simulation, Scientific Technical Review, Vol. LVIX, No.1, pp. 26-34, 2009.

Predavanja ce se odrzavati sredom sa pocetkom u 18.00 casova, u sali 301 F na trecem spratu zgrade Matematickog instituta SANU, Knez Mihailova 36/III, (zgrada preko puta glavne zgrade SANU).

Poziv naucnicima i istrazivacima da prijave svoja predavanja:

Prijava potencijalnog predavaca treba da sadrzi apstrakt predavanja do jedne stranice na srpskom jeziku cirilicom i prevod na engleski jezik, kao i CV obima do dve stranice. Prijavu poslati na adresu upravnika Odelenja za mehaniku u vidu Word DOC na adresu: khedrih@eunet.rs

Start of each lecture is at each Wednesday at 18,00 h in room 301 F at Mathematical Institute SANU, street Knez Mihailova 36/III.

Announcement and Invitation:

All scientists and researchers in area of Mechanics are invited to contribute to the Program of Mechanics Colloquium of Mathematical Institute of Serbian Academy of Sciences and Arts. One page Abstract of proposed Lecture with short CV is necessary to submit in world doc to Head of Department of Mechanics (address: khedrih@eunet.rs), one month before first day in the next month.

Sekretar Odeljenja

dr Srdjan V. Jovic

sekretar Odelenja za mehaniku

Matematickog instituta SANU, Beograd

e-mail: jovic003@yahoo.com

dr Srdjan V. Jovic

sekretar Odelenja za mehaniku

Matematickog instituta SANU, Beograd

e-mail: jovic003@yahoo.com

Upravnik Odeljenja

Prof. Dr. Katica R. (Stevanovic) Hedrih

Prof. Dr. Katica R. (Stevanovic) Hedrih