National Institute of the Republic of Serbia
ὅδε οἶκος, ὦ ἑταῖρε, μνημεῖον ἐστιν ζῴων τῶν σοφῶν ἀνδρῶν, καὶ τῶν ἔργων αὐτῶν

PROGRAM

MATEMATIČKI INSTITUT SANU
ODELJENJE ZA MEHANIKU

PROGRAM ZA NOVEMBAR 2022.

Predavanja se mogu pratiti na daljinu preko stranice:
https://miteam.mi.sanu.ac.rs/asset/YfY2cZTcN3YwGqFjc
Ukoliko želite da učestvujete u radu seminara ili da postavite pitanja na kraju predavanja, a još niste registrovani na miteam platformi Matematičkog instituta, možete se registrovati popunjavanjem forme:
https://miteam.mi.sanu.ac.rs/asset/o9cuDZYqrq7jvFxw8
Arhiva snimljenih predavanja se nalazi na stranici:
https://miteam.mi.sanu.ac.rs/asset/j9rAJJvBQHx2zgSSH

Pozivamo Vas da učestvujete u radu sednica Odeljenja i to:

Petak, 04.11.2022. u 14:15, Knez Mihailova 36, sala 301f i Online
Frol Zapolsky, University of Haifa, Israel
BIG FIBER THEOREMS
There is a general principle in mathematics which says that one annot assemble a complicated object from simple pieces. This can be formulated as follows: any map in a suitable category has a big fiber. I’ll present examples from topology, combinatorics, and symplectic geometry, which is the mathematical formalism of classical mechanics. It turns out that some of these seemingly unrelated results can be proved using very similar tools. The common approach I’ll describe is based on Gromov’s notion of ideal-valued measures and their generalization in symplectic geometry called ideal-valued quasi-measures. I’ll explain all the relevant notions. The talk is based on joint work with Adi Dickstein, Yaniv Ganor, and Leonid Polterovich.
Zajednički sastanak sa Odeljenjem za Matematiku.

Sreda, 16.11.2022. u 16:15, Knez Mihailova 36, sala 301f i Online
Emil Manoach, Institute of Mechanics-Bulgarian Academy of Sciences, Bulgaria
VIBRATIONAL METHODS FOR STRUCTURAL HEALTH MONITORING AND DAMAGE DETECTION OF STRUCTURES
The lecture is devoted to the problems in structural health monitoring (SHM) and damage detection (DD). The main goals and main stages of DD of structures are formulated. The most of the popular modal based methods for DD are presented: modal shapes, modal slopes, modal curvatures, modal strain energy methods, modal damping. Then the forced response methods are considered and some new methods based on the forced response of the structures are explained. Special attention is paid for the Poincaré map based method, the improved Poincaré map based method, Selective index method, and Shear force method. All presented methods are numerically validated and some of them are tested experimentally by using high speed camera and a scanning laser vibrometer. The advantages of the offered methods and their application in SHM are demonstrated by numerical simulations and experimental tests.
Zajednički sastanak sa seminarima Matematičke metode nehanike i Mehanika mašina i mehanizama – modeli i matematički metodi

Sreda, 16.11.2022. u 18:00, Knez Mihailova 36, sala 301f i Online
Svetoslav G. Nikolov, Institute of Mechanics-Bulgarian Academy of Sciences, Bulgaria
NONLINEAR DYNAMICS OF MECHANICAL AND BIOMECHANICAL SYSTEMS – ANALYTICAL AND NUMERICAL INVESTIGATION
It is well-known that autonomous nonlinear differential system of the form $dx/dt=f(x,\lambda)$, $x\inR^n$, where $n\ge 3$ and $\lambda$ is the vector of parameters, can display a rich diversity of periodic, multiple periodic, chaotic and hyper-chaotic flows dependent upon the specific values of one or more bifurcation (control) parameters. A principal problem toward complete understanding of nonlinear interactions is to identify where in its phase space one dynamical system is structurally stable. For example, in a small neighborhood of a structurally stable Poincare homoclinic orbit lie only periodic orbits from saddle type. On the contrary, near a structurally unstable homoclinic orbit may exist both structurally unstable and attractive periodic orbits in addition to saddle ones. Note that after Smale’s works these systems are said to be Morse-Smale systems. The structural stability (roughness) investigation of steady state and of limit cycles or other types of trajectories is a main problem in bifurcation theory. It is well-known that there is critical dependence of the stability conditions of limit cycles on the stability conditions of its steady states. Based on classical works in the literature, it was defined that by knowing the sign of Lyapunov values (called also focus values, Lyapunov quantities (coefficients)) we can efficiently study the structure of complicated nonlinear system trajectories. In other words, the type of: 1) stability loss of equilibrium and 2) winding/unwinding of system trajectories in small neighbourhoods of equilibrium depend on the sign of Lyapunov value. In this presentation, we focus our attention on the investigation of the nonlinear behavior of different mechanical and biomechanical systems.
Zajednički sastanak sa seminarima Matematičke metode nehanike i Mehanika mašina i mehanizama – modeli i matematički metodi

Sreda, 23.11.2022. u 18:00, Knez Mihailova 36, sala 301f i Online
Milan Cajić, Matematički institut SANU
TOPOLOŠKI INTERFEJS MODOVI U MEHANIČKIM METAMATERIJALIMA I FONONSKIM STRUKTURAMA SA INERTERIMA
Mehanički metamaterijali su veštački konstruisani materijali koji mogu posedovati jedinstvena mehanička svojstva koja nije moguće naći u prirodi. Istraživanja u oblasti topoloških i nelinearnih metamateriajala su u ekspaniziji poslednjih godina. Predavanje će se fokusirati na prikazu metoda i rezultata analize disperzije talasa i topoloških svojstava u linearnim metamaterijalima i fononskim strukturama sa mehaničkim inerterima. Poseban akcenat biće na analizi uticaja inertera na disperznu karakteristiku sistema, topološke invarijante i frekvenciju interfejs modova.

Sreda, 30.11.2022. u 18:00, Knez Mihailova 36, sala 301f i Online
Teodor Vrećica, Matematički institut SANU
ULOGA LOMLJENJA TALASA U REGULISANJU INTERAKCIJA IZMEDU OKEANA I ATMOSFERE
Lomljenje talasa reguliše fluksove mase, momenta, toplote i energije izmedu okeana I atmosfere. Klasične metode analize ovog fenomena se zasnivaju na parametrizaciji procenta površine vode pokrivene talasima koji se lome. Phillips 1985 predlaže drugačiji pristup zasnovan na Λ(c_b) distribuciji (prosečna dužina talasa koji se lome, po jedinici brzine talasa (c_b) i po jedinici površine). Glavna prednost ove metode je to što momenti Lambda distribucije opisuju fizički značajne procese. Na primer, razmena gasova izmedu atmosfere i okeana, kao i interakcije morskih talasa i struja se mogu istražiti pomoću ove distribucije. Slično kao što se talasi formiruju na površi izmedu vazduha i vode, oni se mogu formirati i u unutrašnjosti okeana izmedu lakše i teže vode. Unutrašnji talasi imaju značajnu ulogu u mešanju površinskih slojeva okeana i transportu energije. Potencijalna metoda za procenu gubitaka energije usled lomljenja unutrašnjih talasa, zasnovana na metodi za površinske talase, je ukratko istražena.

Obavezno je nošenje maski i održavanje distance. Broj prisutnih na predavanju ograničen na najviše 10 (uključujući i predavača).

Predavanja su namenjena širokom krugu slušalaca, uključujući studente redovnih i doktorskih studija. Održavaju se sredom sa početkom u 18 sati u sali 301f na trećem spratu zgrade Matematičkog instituta SANU, Knez Mihailova 36.

Marijana Babić
Sekretar Odeljenja za mehaniku
Matematickog instituta SANU
dr Božidar Jovanović
Upravnik odeljenja za mehaniku
Matematickog instituta SANU

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