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Mathematical Sciences Analysis and PDE Seminar: "Patterns around us: a calculus of variations prospective". Oleksandr Misiats, (Virginia Commonwealth University)

Tuesday, December 14, 2021
11:00 am to 11:50 am

Zoom Meeting ID: 980 0579 2992

Speaker: Oleksandr Misiats (Virginia Commonwealth University)

Title: Patterns around us: a calculus of variations prospective

Abstract: Crumples in a sheet of paper, wrinkles on curtains, cracks in metallic alloys, and defects in superconductors are examples of patterns in materials. A thorough understanding of the underlying phenomenon behind the pattern formation provides a different prospective on the properties of the existing materials and contributes to the development of new ones. In my talk I will address the issue of modelling pattern formation via nonconvex energy minimization problems, regularized by higher order terms. Two particular examples of such models will be described in greater details: formation of vortices in Ginzburg-Landau model of superconductors, as well as emergence of patterns in phase transitions in shape-memory alloys. I will discuss the issue of well-posedness of such modelling, which reduces to the question of the existence of minimizers in certain functional classes. I will also provide some examples qualitative properties of minimizers via sharp energy bounds.