Modular Design of Micropattern Geometry Achieves Combinatorial Enhancements in Cell Motility

Combinatorial optimization in geometry

In this paper we extend and unify the results of [20] and [19]. As a consequence, the results of [20] are generalized from the framework of ideal polyhedra in H to that of singular Euclidean structures on surfaces, possibly with an infinite number of singularities (by contrast, the results of [20] can be viewed as applying to the case of non-singular structures on the disk, with a finite number...

Combinatorial Geometry

Combinatorial geometry is the study of combinatorial properties of fundamental geometric objects, whose origins go back to antiquity. It has come into maturity in the last century through the seminal works of O. Helly, K. Borsuk, P. Erdős, H. Hadwidger, L. Fejes Tóth, B. Grübaum and many other excellent mathematicians who initiated new combinatorial approaches to classical questions studied by ...

Selection of Suitable Geometry in Compact Heat Exchanger Design

Selection of Suitable Geometry in Compact Heat Exchanger Design

Combinatorial Problems in Computational Geometry

In this thesis we study a variety of problems in combinatorial and computational geometry, which deal with various aspects of arrangements of geometric objects, in the plane and in higher dimensions. Some of these problems have algorithmic applications, while others provide combinatorial bounds for various structures in such arrangements. The thesis involves two main themes: (i) Counting Crossi...