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

Mechanics Colloquim

 

PROGRAM


MATEMATIČKI INSTITUT SANU
ODELJENJE ZA MEHANIKU

PROGRAM ZA MAJ 2015.

Pozivamo Vas da učestvujete u radu sednica Odeljenja i to:

Sreda, 6. maj 2015. u 18 casova, sala 301f:
Nenad Filipovic, Faculty of Mechanical Engineering, Center for Bioengineering, University of Kragujevac, Sestre Janjica 6, 34000 Kragujevac, Serbia
COMPUTER MODEL OF SEMI-CIRCULAR CANAL AND SIMULATION OF BALANCE DISORDER

Abstract: Biomechanical model of the semi-circular canals (SCC) for balance disorder is presented. It is part of FP7 EMBalance project. A model of the SCC with parametric defined dimension and fully 3D three SCC with fluid-structure interaction from patient specific 3D reconstruction is investigated. All the models can be used for correlation with the same experimental protocols with head moving and nystagmus eye motion. Three SCC give more details and understanding of the pathology of the specific patient gives more insight in this standard clinical diagnostic procedure. The hot caloric test with real patient geometry is computed simulated and compared with experimental data. The temperature distribution of the horizontal canal duct is more dominant and a longer period of irrigation time is required in order to stimulate the two other vertical canals. Computer results also show shear stress and force distribution from endolymph flow during natural convection. Future studies are necessary for validation of the presented computer model with clinical diagnostic and therapy measurements.

Petak, 8. maj 2015. u 14 casova, sala 301f:
Zajednicka sednica Odeljenja za matematiku, Odeljenja za mehaniku, Odeljenja za racunarstvo i primenjenu matematiku i Seminara za istoriju i filozofiju matematike
Katica R. (Stevanovic) Hedrih, Matematicki institut SANU
PETROVIC'S ELEMENTS OF MATHEMATICAL PHENOMENOLOGY AND PHENOMENOLOGICAL MAPPINGS: THEORY AND APPLICATIONS

Abstract: Lecture starts with short description of Element of Mathematical Phenomenology and Phenomenological Mappings published in Petrovic's theory. The biographical data of Mihailo Petrovic (1868-1943) is presented. Petrovic was a famous Serbian mathematician, one of three Henrei Poincare's doctoral students. Next it is a description of abstraction of real system to the physical, chemical or biological and mathematical model.

Some of basic elements of mathematical phenomenology are elements of non-linear-functional transformations of coordinates from one to other functional curvilinear coordinate system. Some of these elements, as it is basic vectors of tangent space of kinetic point vector position and their changes (velocity of their magnitude extensions and component angular velocities of rotations), are presented in different functional coordinate systems.

Mihailo Petrovic's theory contains two types of analogies: mathematical and qualitative, and in this lecture third type - structural analogy is described. Taking into account large possibility for applications of all three types of analogies, numerous original examples are presented using, between other, fractional system dynamics with one degree of freedom, finite number of degrees of freedom as well as multi-body discrete continuum hybrid fractional order system dynamics.

Mathematical analogies between vector models in local area of stress state, strain stare of the point in stressed and deformed deformable body as well as with vector model of the mass inertia moment state at point of rigid body, used mass inertia moment vectors coupled for pole and axis, are presented, also.

Using discrete continuum method, fractional order mode analysis in hybrid system dynamics is presented. For a class of fractional order system dynamics with finite number of degrees of freedom, independent eigen main fractional order modes are determined with corresponding eigen main coordinates of the system and presented by Tables. A number of theorems of energy fractional order dissipation presented in corresponding Tables, also. It is shown that applications of qualitative, structural and mathematical analogies in analysis of fractional order modes appear in analogous mechanical, electrical and biological fractional order chains, and that is very power, suitable and useful tools to reduce research models to corresponding minimal numbers, and, in same time, develop power of analysis use phenomenological mappings between local and global phenomena and properties.

An analogy between kinetic parameters of collision of two rigid body in translator motions and collision of two rolling billiards' balls is presented and corresponding new theorems are defined.

Phenomenological approximate mappings on nonlinear phenomena, in local area around stationary points or stationary states, are presented. Corresponding kinetic parameters of model of nonlinear dynamics of real system behavior are presented, also. For obtaining approximate differential equations and approximate solutions in local area around singular points, linear and non-liner approximations are used. Method of local analysis based on phenomenological approximate mappings between local linear as well as nonlinear phenomena is power to obtain information of all local nonlinear phenomena in the nonlinear dynamics of the system for completing kinetic elements for global analysis of the system nonlinear dynamics and stability and to use different analogies.

Sreda, 13. maj 2015. u 18 casova, sala 301f:
Bozidar Jovanovic, Matematicki institut SANU
INTEGRALI KRETANjA BALANSIRANOG SIMETRICNOG KRUTOG TELA OKO NEPOKRETNE TACKE

Rezime: Posmatramo Ojlerove jedna.ine kretanja krutog tela u R^n. Dajemo novi dokaz poznate teoreme Miscenka i Fomenka [2] da su Manakovljevi integrali, u slucaju nesimetricnog krutog tela, poptpuni komutativni skup polinoma na Lijevoj algebri so(n) [1]. Takodje, u slucaju simetricnog krutog tela, pokazujemo potpunost Mankovljevih integrala u klasi SO(n) invarijantih integrala na familiji homogenih prostora grupe SO(n) [1].

U drugom delu predavanja posmatramo Ojlerove jednacine kretanja simetricnog krutog tela, restrikovane na invarijantni podprostor definisan nula vrednostima odgovarajucih Neterinih integrala. U slucaju SO(n-2) simetrije pokazujemo da su skoro sve trajektorije periodicne i da se mogu izraziti preko eliptickih funkcija, dok u slu.aju SO(n-3) simetrije pokazujemo da je sistem raslojen na cetvorodimenzione invarijantne povrsi i da se moze integraliti na osnovu nedavnog Kozlovljevog rezultata [3].

Rezultati su dobijeni u saradnji sa Vladimirom Dragovicem i Borislavom Gajicem.

Reference
[1] Dragovic, V., Gajic B. and Jovanovic, B.: On the completeness of the Manakov integrals, to appear in Fundametalnaya i prikldnaya matematika.
[2] Mishchenko, A. S. and Fomenko, A. T.: Euler equations on finite-dimensional Lie groups. Izv. Acad. Nauk SSSR, Ser. matem. vol 42 (1978), no. 2, 396--415.
[3] Kozlov, V.V.: The Euler.Jacobi.Lie Integrability Theorem, Regul. Chaotic Dyn., 2013, vol. 18, no. 4, pp. 329-.343.

Sreda, 27. maj 2015. u 18 casova, sala 301f:
Nevena Stevanovic, Masinski fakultet, Univerzitet u Beogradu
NEKA TACNA RESENjA ZA STRUJANjE RAZREDjENIH GASOVA

Rezime: Od 80-tih godina proslog veka doslo je do revolucionarnog napretka u nauci sto je omogucilo pravljenje izuzetno malih uredjaja . mikro-elektro-mehanickih sistema, a kasnije i jos manjih . nano-elektro-mehanickih sistema. S obzirom na to da je u ovim uredjajima prisutno strujanje fluida, zajedno sa razvojem ovih uredjaja intenzivno se razvija i mikrofluidika i nanofluidika. Polazeci od jednacina kontinuuma uz granicne uslove klizanja na zidu dobijena su i prikazana neka tacna analiticka resenja za strujanje gasa u mikrokanalima, mikrocevima i mikrolezajima. Pri izboru prikazanih modela kriterijum je relativna jednostavnost u njihovom odredjivanju, bez koriscenja numerike ili nekih posebnih matematickih metoda. Analizirano je stacionarno izotermsko dozvucno strujanje gasa pri malim vrednostima Rejnoldsovog broja u mikrokanalima i mikrocevima koje se desava usled razlike pritiska na ulazu i izlazu, kao i u mikrolezajima gde se strujanje desava zahvaljujuci kretanja jednog zida.




Predavanja su namenjena sirokom krugu slusalaca, ukljucujuci studente redovnih i doktorskih studija. Odrzavaju se sredom sa pocetkom u 18 casova u sali 301f na trecem spratu zgrade Matematickog instituta SANU, Knez Mihailova 36.

dr Katarina Kukic
Sekretar Odeljenja za mehaniku
Matematickog instituta SANU
dr Vladimir Dragovic
Upravnik odeljenja za mehaniku
Matematickog instituta SANU