Metamaterials, Morphometrics, Morphogenesis, and Mappings

applied mathematics;computational geometry;mathematical modelling;metamaterials;kirigami;origami;quantitative biology;morphometrics;morphogenesis;medical imaging;geometry processing;scientific computing

Choi, Pui Tung ; Mahadevan, L.,Rycroft, Chris H.

University:Havard University

Department:Engineering and Applied Sciences - Applied Math

关键词: applied mathematics;    computational geometry;    mathematical modelling;    metamaterials;    kirigami;    origami;    quantitative biology;    morphometrics;    morphogenesis;    medical imaging;    geometry processing;    scientific computing;   

Others  :  https://dash.harvard.edu/bitstream/handle/1/37365874/CHOI-DISSERTATION-2020.pdf?sequence=1&isAllowed=n

美国|英语

来源: Digital Access to Scholarship at Harvard

【 摘 要 】

In this thesis, we develop mathematical tools to tackle important problems in metamaterials, morphometrics, morphogenesis, and mappings. Specifically, we propose novel methods with a solid theoretical foundation to control the geometry and topology of kirigami and origami metamaterials. We also analyze the growth and form of biological shapes including insect wing and ferret brain using computational geometry. We further propose physically-based methods for producing mappings and deformations of two- and three-dimensional objects and explore their applications to geometry processing, medical imaging and data visualization. Altogether, this thesis brings in new mathematical insights and techniques for advancing our understanding of the physical world, the biological world, and the digital world.