Thesis supervisor: András Árpád Sipos
Location of studies (in Hungarian): BUTE Abbreviation of location of studies: BME
Description of the research topic:
In mathematics, minimal surfaces provided one of the first examples of the effectiveness of the theory, which later became known as the calculus of variations. Minimizing the surface area functional not only produces beautiful curved surfaces but also provides the shape of the membrane shell under eigenstresses. For loadings exiting the tangent plane of the surface, the equilibrium surface is a so-called Weingarten surface, where at each point of the surface, the mean curvature H and the Gaussian curvature K satisfy the same algebraic relation. However, it is well-known that the calculation of Weingarten surfaces is a highly nonlinear problem due to the presence of the Gaussian curvature K. This PhD research aims to investigate the properties of Weingarten surfaces analytically. Considering that the classical minimal surface can be generated as a stationary solution of the mean curvature flow, i.e., a geometric partial differential equation (gPDE), we aim to construct an algorithm for computing Weingarten surfaces using the so-called Bloore flow. A distinguished focus is the study of the flows’s convergence properties and the estimation of the transient time. Considering that the Bloore flow is the gPDE associated with collisional abrasion, in addition to the rigorous analysis and the development of numerical methods, we also aim to explore the similarities and differences between the abraded forms in nature and the shape of membrane shells under various loadings. A téma meghatározó irodal
Deadline for application: 2024-05-24
2024. IV. 17. ODT ülés Az ODT következő ülésére 2024. június 14-én, pénteken 10.00 órakor kerül sor a Semmelweis Egyetem Szenátusi termében (Bp. Üllői út 26. I. emelet).
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