Seminář katedry matematiky

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Seminář katedry matematiky

Zde najdete stručný popis již proběhnuvších přednášek.

Název přednášky: Metóda riedkej siete a inverzná kvantifikácia neistoty
(Sparse Grid Collocation Method and Inverse Uncertainty Quantification)

Přednášející: Eva Vidličková,

Matematicko-fyzikální fakulta, Univerzita Karlova v Praze 

Abstrakt: Mnoho fyzických javov sa dá popísať parciálnymi diferenciálnymi rovnicami. Tie typicky vyžadujú adekvátnu znalosť vstupných dát, ktoré su v praxi získané rôznymi meraniami. Potrebné dáta sú len zriedka dostatočne presné. Chyby v meraní totiž sposobujú šum dát, ktorý vedie k neistotám vo vstupných hodnotách. Kvantifikácia neistoty sa snaží popísať efekt týchto neistôt na riešení rovníc. Jedným zo spôsobov je vyjadriť aproximáciu riešenia ako rozvoj v polynomiálny chaos, z ktorého už vieme získať všetky potrebné výsledky. Metóda riedkej siete je efektívny nástroj na vybudovanie rozvoja v polynomiálny chaos.

Název přednášky: On the lubrication problem in a rough thin domain filled with micropolar fluid

Přednášející: Igor Pažanin, Ph.D.,

Department of Mathematics, Faculty of Science, University of Zagreb, Croatia

Abstrakt: The classical lubrication problem is mainly concerned with the situation in which two solid surfaces being in relative motion are separated by a thin layer of fluid acting as a lubricant. Such situation appears naturally in applications consisting of moving machine parts e.g. in journal bearings. If the gap between the moving surfaces becomes very small, the experimental results from the tribology literature suggest that the fluid’s internal structure should be taken into account as well. A possible way to acknowledge that is to employ the micropolar fluid model. Engineering practice also indicates that it is of interest to combine the lubrication phenomena with the analysis of the roughness effects. In view of that, in this talk a micropolar fluid flow through a rough thin domain is addressed. The domain's thickness is considered as the small parameter ε, while the roughness is defined by a periodical function with period of order ε². Starting from three-dimensional micropolar equations and using asymptotic analysis with respect to ε, we derive the macroscopic model clearly detecting the effects of the specific rugosity profile and fluid microstructure. Rigorous justification of the formally obtained asymptotic model is provided by obtaining the effective system via two-scale convergence. The setting with non-standard boundary conditions for microrotation will also be addressed.

This is a joint work with Francisco Javier Suarez-Grau (Universidad de Sevilla).

References
[1] D. Bresch, C. Choquet, L. Chupin, T. Colin, M. Gisclon: Roughnessinduced effect at main order on the Reynolds approximation, SIAM Multiscale Model. Simul. 8 (2010), 997-1017.
[2] I. Pažanin, F. J. Suárez-Grau: Effects of rough boundary on the heat transfer in a thin-film flow, C. R. Mecanique 341 (2013), 646–652.
[3] I. Pažanin, F. J. Suárez-Grau: Analysis of the thin film flow in a rough domain filled with micropolar fluid, Comput. Math. Appl. 68 (2014), 1915–1932.

Poslední úprava: 2. 12. 2015

Design stránek: Stanislav Olivík, 2013