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Full-Text Articles in Physical Sciences and Mathematics
Geometry, Growth And Pattern Formation In Thin Elastic Structures, Salem Al-Mosleh
Geometry, Growth And Pattern Formation In Thin Elastic Structures, Salem Al-Mosleh
Doctoral Dissertations
Thin shells are abundant in nature and industry, from atomic to planetary scales. The mechanical behavior of a thin shell depends crucially on its geometry and embedding in 3 dimensions (3D). In fact, the behavior of extremely thin shells becomes scale independent and only depends on geometry. That is why the crumpling of graphene will have similarities to the crumpling of paper. In this thesis, we start by discussing the static behavior of thin shells, highlighting the role of asymptotic curves (curves with zero normal curvature) in determining the possible deformations and in controlling the folding patterns. In particular, we …
Open Books On Contact Three Orbifolds, Daniel Herr
Open Books On Contact Three Orbifolds, Daniel Herr
Open Access Dissertations
In 2002, Giroux showed that every contact structure had a corresponding open book decomposition. This was the converse to a previous construction of Thurston and Winkelnkemper, and made open books a vital tool in the study of contact three-manifolds. We extend these results to contact orbifolds, i.e. spaces that are locally diffeomorphic to the quotient of a contact manifold and a compatible finite group action. This involves adapting some of the main concepts and constructions of three dimensional contact geometry to the orbifold setting.
Swelling And Folding As Mechanisms Of 3d Shape Formation In Thin Elastic Sheets, Marcelo A. Dias
Swelling And Folding As Mechanisms Of 3d Shape Formation In Thin Elastic Sheets, Marcelo A. Dias
Open Access Dissertations
We work with two different mechanisms to generate geometric frustration on thin elastic sheets; isotropic differential growth and folding. We describe how controlled growth and prescribing folding patterns are useful tools for designing three-dimensional objects from information printed in two dimensions. The first mechanism is inspired by the possibility to control shapes by swelling polymer films, where we propose a solution for the problem of shape formation by asking the question, ``what 2D metric should be prescribed to achieve a given 3D shape?'', namely the reverse problem. We choose two different types of initial configurations of sheets, disk-like with one …
Problems In Generic Combinatorial Rigidity: Sparsity, Sliders, And Emergence Of Components, Louis Simon Theran
Problems In Generic Combinatorial Rigidity: Sparsity, Sliders, And Emergence Of Components, Louis Simon Theran
Open Access Dissertations
Rigidity theory deals in problems of the following form: given a structure defined by geometric constraints on a set of objects, what information about its geometric behavior is implied by the underlying combinatorial structure. The most well-studied class of structures is the bar-joint framework, which is made of fixed-length bars connected by universal joints with full rotational degrees of freedom; the allowed motions preserve the lengths and connectivity of the bars, and a framework is rigid if the only allowed motions are trivial motions of Euclidean space. A remarkable theorem of Maxwell-Laman says that rigidity of generic bar-joint frameworks depends …