[institut] Plan rada za maj 2015. godine

Thu Apr 30 17:50:46 CEST 2015

Postovane kolege,

saljemo vam plan predavanja u okviru Odeljenja za mehaniku Matematickog
instituta SANU za maj 2015. godine. Molimo vas da, ukoliko ste u
mogucnosti, prilozeni plan odstampate i okacite na oglasnim tablama vasih
institucija.

S postovanjem,
Katarina Kukic
Sekretar Odeljenja za mehaniku

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PLAN RADA ZA MAJ 2015. GODINE

Petak 8.5.2015. 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 13.5.2015. 18 casova, sala 301f
Bozidar Jovanovic, Matematicki institut SANU

INTEGRALI KRETANjA BALANSIRANOG SIMETRICNOG KRUTOG TELA OKO NEPOKRETNE TACKE

Rezime: Posmatramo Ojlerove jednačine 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 slučaju 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 20.5.2015. 18 casova, sala 301f
Nenad Filipovic, Fakultet inzenjerskih nauka, Univerzitet u Kragujevcu

Naslov i rezime predavanja bice naknadno dostavljeni.

Sreda 27.5.2015. 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.

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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

http://www.mi.sanu.ac.rs/colloquiums/mechcoll.htm
mehanika at mi.sanu.ac.rs

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