National Institute of the Republic of Serbia
ὅδε οἶκος, ὦ ἑταῖρε, μνημεῖον ἐστιν ζωῶν τῶν σοφῶν ἀνδρῶν, καὶ τῶν ἔργων αὐτῶν
PROGRAM
PROGRAM ZA NOVEMBAR 2007.
Pozivamo Vas da učestvujete u radu sednica Odeljenja i to:
SREDA, 7. novembar 2007. u 18 sati:
Sinisa DJ. Mesarovic, School of Mechanical Engineering and Materials Engineering, Washington State University, Pullman, WA 99164-2920
Thermodynamic Coarse-graining of Dislocation Mechanics and the Size-dependent Continuum Crystal Plasticity
Classical crystal plasticity is size-invariant. Yet, numerous experiments on crystalline materials indicate that in small volumes (<100mm), the size effects are appreciable. This is the result of piling-up of geometrically necessary dislocations (GNDs) against the boundaries ~V a high-energy configuration. In contrast to the existing phenomenological gradient theories, we derive a micromechanical theory from dislocation mechanics by thermodynamic coarse-graining.
The microstructural energy is the elastic strain energy associated with the presence of geometrically necessary dislocations. The integral formulation of Kroner~Rs continuum theory of dislocations, recently developed by the author, provides an efficient method of calculating this energy. It also brings to light the apparently irreducible non-locality of the problem, which arises as a consequence of long-range interactions between dislocations. We consider strain energies computed from different descriptions of dislocations on solids: (i) Discrete representation; (ii) Semi-discrete representation, with continuous slip distribution within discrete slip plane; and; (iii) Continuous representation, whereby dislocations are represented by a continuous tensor field. The portion of energy that is missing from the classical crystal plasticity is the error in microstructural energy arising from replacing the actual, discrete representation with the continuous field. The theory features multiple evolving characteristic lengths, associated with an active slip system and representing average spacing between discrete slip planes. In addition to the higher order terms, the theory also contains boundary energy dependent on the state in the bulk.
SREDA, 14. novembar 2007. u 18 sati:
Livija Cveticanin, Fakultet tehnickih nauka Novi Sad
Oscilator sa nelinearnim prigusenjem
Uobicajeno je da se kod oscilatora razmatra prigusenje koje potice od sile suvog trenja ili linearnog viskoznog trenja. Medjutim, eksperimenti su pokazali da sila prigusenja obicno nije linearna funkcija brzine. Cilj ovih istrazivanja je da prouci uticaj nelinearnog prigusenja na oscilatorno kretanje sistema sa jednim stepenom slobode. Matematicki model sistema je strogo nelinearna diferencijalna jednacina drugog reda. Priblizno analiticko resenje nadjeno je primenom modifikovane homotopijske perturbacione metode i metode eliptickog harmonijskog balansa. Analiticka resenja su poredjena sa numerickim i pokazala su veliku tacnost. Izvedeni su zakljucci o uticaju nelinearnog prigusenja na oscilacije sistema.
SREDA, 21. novembar 2007. u 18 sati:
Camelia Frigioiu, University Dunarea de Jos, Faculty of Sciences, Department of Mathematics, Galati, Romania
The Dynamical Systems of Rheonomic Finslerian Mechanical Systems
In this paper it will be studied the dynamical system of a rheonomic Finslerian mechanical system, whose evolution curves are given, on the phase space $TM\times R$, by Lagrange equations of the form: \[ \frac{d}{dt}\left( \frac{\partial L}{\partial y^{i}}\right) -\frac{\partial L% }{\partial x^{i}}=\sigma_{i}(x,\dot{x},t);\,y^{i}=\frac{dx^{i}}{dt}=\dot{% x^{i}}, \] where $L(x,\dot{x},t)=F^{2}(x,\dot{x},t)$ is a regular time dependent Lagrangian, $F(x,y,t)$ is the fundamental function of a rheonomic space and $% \sigma_{i}(x,\dot{x},t)$ are the components of a external force defined as $% d-$covector field on $TM\times R$. Then one can associate to the considered mechanical system a vector field $S$ on $TM\times R$, which is a canonical semispray. All geometric objects of the rheonomic Finslerian mechanical system one can be derived from $S$. So we have the fundamental notion as the nonlinear connection $N$, the metrical $N$-linear connection, etc. \end{abstract} \begin{thebibliography}{99} \bibitem{1} Abraham,M.,Marsden,J, Foundation of Mechanics, Benjamin, New-York, 1978; \bibitem{2} Anastasiei,M.,On the geometry of time-dependent Lagrangians, Mathematical and Computing Modelling,20, no4/5,Pergamon Press,1994; \bibitem{3} Anastasiei,M.,Kawaguchi,H.,Geometry of time dependent Lagrangians. Non-linear connections, Tensor, N.S., 48(1989), 273-282; \bibitem{4} Frigioiu,C, Metode geometrice in Mecanica Analitica de ordin superior, Ph.D.Thesis, Univ.Al.I. Cuza Iasi, 2003; \bibitem{5} De Leon M.,Rodriguez, P.R.,Methods of Differential Geometry in Analitical Mechanics, North-Holland, (1989), 73-124; \bibitem{6} Miron,R.,Anastasiei, M.,The Geometry of Lagrange Spaces:Theory and Applications, Kluwer Academic Publishers,FTPH, no 59,1994; \bibitem{7} Miron,R.,Anastasiei M., Bucataru, I.,Handbook of Finsler Geometry, (edited by P.L.Antonelli), Kluwer Acad. Publ., 2003; \bibitem{8} Miron,R.,Frigioiu, C.,Finslerian Mechanical Systems, Algebras, Groups and Geometries, 21, (2004); \bibitem{9} Miron,R.,Hrimiuc, D.,Shimada,H.,Sabau,V., The Geometry of Hamilton and Lagrange Spaces, Kluwer Academic Publishers,FTPH, no 118, 2000; \end{thebibliography} author's address: "University "Dunarea de Jos" Faculty of Sciences,Department of Mathematics Domneasca 47, Galati,Romania e-mail: cfrigioiu@ugal.ro
SREDA, 28. novembar 2007. u 18 sati:
Aleksandar Baksa, Matematicki fakultet Beograd, Vladimir Dragovic, Matematicki institut Beograd
Leonard Ojler (1707. - 1783.) - zivot i delo
Saopstenje je posveceno obelezavanju 300. godisnjice Ojlerovog rodjenja. Pored biografskih podataka velikog naucnika bice reci i o njegovom naucnom doprinosu. Iz inpozantnog opusa, koji sadrzi radove iz gotovo svih oblasti matematike, mehanike, astronomije i primene tih nauka, prikazacemo neka Ojlerova interesantna otkrica.
Sednice se održavaju u zgradi SANU, Knez Mihailova 35, u sali 2 na prvom spratu.