DIFFERENTIAL GEOMETRY, CONTINUUM MECHANICS AND MATHEMATICAL PHYSICS Seminar

 

PROGRAM

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Predavanja možete pratiti i online putem MITEAM stranice seminara Diferencijalna geometrija, mehanika kontinuuma i matematička fizika: https://miteam.mi.sanu.ac.rs/asset/YNvstaSeP9v2tgqTP

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Plan rada seminara Diferencijalna geometrija, mehanika kontinuuma i matematička fizika za DECEMBAR 2025.

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Petak, 12.12.2025. u 12:15, Pariske Komune bb, Niš i Live stream
Srđan Jakovljević, Matematički institut SANU
FINITE VOLUME METHODS FOR SOLVING CONSERVATION LAWS – SOME APPLICATIONS
Partial differential equations have not only a huge importance for mathematicians, but also for scientists of other fields, like physicists, chemists and biologists, for instance. The first ones focus mostly on their theoretical side, while the minds mentioned in the second place try to find some real-life applications for them. In this work, we examined their application in continuum physics, more precisely fluid dynamics. On the mathematical side of view, we began the examination of the first-order finite volume methods, continued with their natural extensions to a higher, yet still discrete, level and ended with some quite abstract and continuous leaning counterparts. Still, here is the focus on the description of some natural phenomena. Finite volume methods were used to describe the behavior of large masses of matheria that can be considered as a fluid. The results obtained in this field of continuum mechanics helped us greatly in understanding phenomena relevant to industry, ecology and meteorology, just to mention some areas. Still, this is just a small step on the long and unending cycle of scientific research. The methods mentioned above are answers to particular criteria formulated for a certain problem situation. There is a lot of room for improvement, further optimisation and "fixing".

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Petak, 26.12.2025. u 12:15, Pariske Komune bb, Niš i Live stream
Milan Cajić, Matematički institut SANU
ANISOTROPIC DIELECTRIC ELASTOMERS WITH FRACTIONAL VISCOELASTICITY
Dielectric elastomers with fiber reinforcement are studied as anisotropic soft electro-active materials with time-dependent behavior. A unified fractional viscoelastic electro-mechanical model is introduced, based on an anisotropic nearly-incompressible hyperelastic formulation with multiplicative decomposition. The weak form is derived for efficient implementation in FEniCSx, and corresponding simulations performed (bending and electro-mechanical instability) to illustrate the role of anisotropy and the effect of fractional viscoelasticity. The framework sets the stage for further extensions toward thermo- and magneto-coupled soft materials. The presentation is based on joint works with Danilo Karličić and Stepa Paunović.

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