We propose a new approach to the study of diffusion dynamics in vibrated granular systems. The dynamic of a granular material is mainly defined by dry friction interactions. This type of interaction is difficult to model for a large quantity of particles. ...
This thesis is a study of wave maps from a curved background to the standard two dimensional sphere S2. The target is always assumed to be embedded in R3 in the standard way. The do- main manifold (the "curved background") will be diffeomorphic to S2 × R, ...
We consider the variational problem of finding the longest closed curves of given minimal thickness on the unit sphere. After establishing the existence of solutions for any given thickness between 0 and 1, we explicitly construct for each given thickness ...
This thesis concerns optimal packing problems of tubes, or thick curves, where thickness is defined as follows. Three points on a closed space curve define a circle. Taking the infimum over all radii of pairwise-distinct point triples defines the thickness ...
Given a two-dimensional smooth manifold M and a bijective pro jection p from M on a fixed plane (or a subset of that plane), we explore systematically how a wavelet transform (WT) on M may be generated from a plane WT by the inverse projection. Examples whe ...
What is the longest rope on the unit sphere? Intuition tells us that the answer to this packing problem depends on the rope's thickness. For a countably infinite number of prescribed thickness values we construct and classify all solution curves. The simpl ...
We investigate numerical simulations and visualizations of the problem of tying a knot in a piece of rope. The goal is to use the least possible rope of a fixed, prescribed radius to tie a particular knot, e.g. a trefoil, a figure eight, and so on. The rop ...
