Home page of Edward R. Vrscay

Edward R. Vrscay

Department of Applied Mathematics
Faculty of Mathematics
University of Waterloo
Waterloo, Ontario, Canada N2L 3G1
Tel: (519) 888 4567 x 35455
Office: MC 6326
e-mail: ervrscay "at" uwaterloo.ca

Ongoing research activities

Recent industrial research and collaboration

The ''Chrysler-Waterloo Project:'' Design of a new generation of conformable high-pressure vessels for gaseous fuels in automotive applications

This work was supported by a Natural Sciences and Engineering Research Council Collaborative Research and Development (CRD) with Chrysler Canada Inc. -- now Fiat Chrysler Automotive Canada (FCA Canada)-- as industrial sponsor during the years 2014-2018. (The heading of this section is the title of the CRD Grant.) In collaboration with FCA, we were engaged in developing a framework for the design of compressed gaseous fuel vessels that will occupy arbitrary geometries. Our goal was to develop algorithms for fitting a network of tubes with a range of diameters into an arbitrary three-dimensional region.

The following three faculty members were involved in this project:

This research was highly interdisciplinary in nature, involving various aspects of optimization, fluid mechanics, solid mechanics, software design and computing. Both theory and application played important roles.

Three M.Math. students, one M.Sc. student and one Postdoctoral Research worked on this project (see below).

I was originally approached by Chrysler Canada because of our Waterloo Fractal Coding and Analysis Group website. Our project would eventually involve very little fractal content, except for the important idea of branching. Nevertheless, the entire exercise was a very good opportunity for me, and others as well, to ``expand our horizons'' by learning new ideas and methods. For example, one of the important components of our project and subsequent algorithms was circle packing, which was used to pack tubes in regions. Here are two slide presentations on our work delivered at the AMMCS-CAIMS 2015 meeting, June 7-12, 2015, held at Wilfrid Laurier University, Waterloo, Ontario, Canada.

Here is a set of notes on an early method of circle packing for arbitrary polygonal regions which I developed a little later in the project (and for which I wrote some primitive code) in collaboration with my colleagues Sean Peterson (UW) and Franklin Mendivil:

Past research activities

Mathematical physics, in particular quantum theory. At one time, this represented a major research activity of mine. However, as time progressed and my activities in mathematical imaging were expanding, there was less and less time (and energy!) available to supervise graduate students in this area. As a result, I decided in 2007 that I would not take any new graduate students. It was a difficult decision for a number of reasons: Here is a brief list of areas of quantum mechanics in which I have worked, arranged chronologically from past to most recent:

Primary research collaborators

Recent graduate students and undergraduate research assistants

Lecture notes for courses recently taught

Here are my lecture or supplementary notes for some courses taught recently.
The "Spirit of Calculus"