Геометрија, образовање и визуализација са применама, 20. јун 2019.

Наредни састанак Семинара биће одржан у четвртак, 20 јуна 2019. у сали 301ф Математичког института САНУ. У оквиру овог састанка, планирана су два предавања.

Прво предавање, 20. јун 2019, 16:00

Предавач: Ilja Gogić, Department of Mathematics, Faculty of Science, University of Zagreb

Наслов предавања: CENTRАLLY STABLE ALGEBRAS

Апстракт:
We define an algebra A to be centrally stable if, for every epimorphism F from A to another algebra B, the center Z(B) of B is equal to F(Z(A)), the image of the center of A. After providing some examples and basic observations, we consider in somewhat greater detail central stability in tensor products of algebras, and finally establish our main result which states that a finite-dimensional unital algebra A over a perfect field F is centrally stable if and only if A is isomorphic to a finite direct product of algebras A_i, where each A_i is a tensor product of a commutative algebra and a central simple algebra over some finite field extension of F.
This is a joint work with Matej Bresar (University of Ljubljana and University of Maribor).

Прво предавање, 20. јун 2019, 17:15

Предавач: Igor Pažanin, Department of Mathematics Faculty of Science, University of Zagreb

Наслов предавања: MATHEMATICAL ANALYSIS OF MICROPOLAR FLUID FLOW IN THIN DOMAINS: RIGOROUS DERIVATION OF NEW MODELS

Апстракт:
The  micropolar  fluid  model  represents  an  essential  generalization of  the  well-established Navier-Stokes model which takes into account the microstructure of the fluid. It describes the behavior of numerous real fluids (e.g. liquid crystals,blood, muddy fluids, certain polymeric fluids, even water in models with small scales)  better  than  the classical  model.  The  aim  of  this  talk  is  to  present  some of our results on the asymptotic approximation of the micropolar fluid flow in thin pipe-like domains. We begin by considering an incompressible micropolar fluid flowing through an undeformed straight pipe and find the effective behavior of the flow via rigorous asymptotic analysis with respect to the pipe’s thickness. Since the engineering practice requires extensive knowledge of curved-pipe flows, we extend our analysis to the case of general curved pipe with an arbitrary central curve. Using differential geometry tools and two-scale asymptotic technique,  we construct  the approximation  explicitly  acknowledging  the  effects  of fluid microstructure and pipe’s distortion. We provide the rigorous justification of the obtained effective model by proving the corresponding error estimate. Finally, we also investigate the micropolar fluid flowing through a thin pipe with specific helical shape not entering in the above framework.


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