Институт математики и математического моделирования

Очный семинар (с трансляцией в Zoom) - в 413 каб. КазНУ - «Дифференциальные операторы и их приложения», 22.08.2024

Городской научный семинар

«Дифференциальные операторы и их приложения»

КазНУ, каб. 413

15:00, 22 августа 2024 г

Трансляция семинара в Zoom

https://us02web.zoom.us/j/6678270445?pwd=SFNmQUIvT0tRaHlDaVYrN3l5bzJVQT09

Идентификатор конференции: 667 827 0445, Код доступа: 1

Руководители семинара:

академик НАН РК М. Отелбаев, академик НАН РК Т.Ш. Кальменов,

профессор Б.Е. Кангужин, член-корр. НАН РК М.А. Садыбеков

Докладчик: Prof. Vladimir Mityushev

Cracow University of Technology, Kraków, Poland

Тема доклада: "Riemann-Hilbert problem and random composites"

Abstract: The study of structurally disordered dispersed patterns and the hidden relationships between the geometric random characteristics of composites and their physical properties is a common focus in various branches of mechanics, mathematics, and physics. Our objective is to address the challenge of providing a constructive quantitative description of the chaos/regularity exhibited by composites. We specifically investigate the macroscopic properties of dispersed regular and random composites with a qualitative analysis of the degree of randomness, anisotropy, and clustering. Our analytical theory of Representative Volume Element (RVE) based on the Riemann-Hilbert problem for a multiply connected domain enables us to investigate random media precisely. The notion of dispersed random composites is frequently oversimplified in engineering studies. Some engineers take a picture of a “random composite” from their mind, perform computations with the prescribed physical constants and say that the deal is done. However, various random structures need advanced analysis based on the vast number of observations and computational experiments. We propose the computationally effective method of structural sums coinciding with the lattice sums for regular composites. In particular, the results yield new high-order analytical exact and asymptotic justified formulas for the effective conductivity and elasticity tensors of dispersed composites with isotropic phases. We introduce and justify quantitative characteristics of randomness, clustering, degree of anisotropy for random composites, degree of interaction of two different components, etc.

Kazakh Mathematical Journal

Очный семинар (с трансляцией в Zoom) - в 413 каб. КазНУ - «Дифференциальные операторы и их приложения», 22.08.2024

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