Mechanics Colloquim
PROGRAM
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.