Mathematics and Computer Science Department

Dan Alexander

I am an historian of mathematics. My initial research was in the history of complex dynamics which is an important subfield of the study of chaotic dynamical systems.? Complex dynamics provides the means to study such objects as the Mandelbrot Set and Newton's method. I have published a book, A History of Complex Dynamics: From Schroder to Fatou and Julia, and several other related articles.

Currently I am working on two projects:
The first involves World War II experiences of the famous Polish ma hematician Stefan Banach who survived the war in occupied Poland working in the Weigl Institute under the protection of a Schindler-esque figure, Rudolph Weigl, who has been honored by Israel for his efforts in saving Jews from the Nazi's in occupied Poland. I have spoken on this subject at national and international meetings in the US and Germany. I published a short review of a book about Banach that presented my initial findings in Historia Mathematica.

 

My second project involves and second history of complex dynamics that depicts the wider context from which the Complex Dynamics emerged in the late 1800's and early 1900's. I working with two collaborators in Italy on this and hope to have a manuscript ready in the next year or two.

 

Michael Rieck

Working with Professor Subhankar Dhar at San Jose State University, and others, my scholarly research at Drake has been primarily focused on the area of "ad hoc wireless communications network," and in particular, the development and testing of new routing protocols. We concocted a new type of router set which we call a k-SPR set, and have published a number of articles related to this, and have presented our work at conferences in India and the United States. Two of these articles appear in  Journal of Microprocessors and Microsystems (v. 28, n. 8, p. 427-437) and Computer Networks (v. 47, n. 6, p. 785-799).
During the 2001-2002 academic year, I employed three of our majors (R. Huele, A. Whitehead, G. Timms) to assist me with research into ad hoc wireless networks. I taught them about a number of routing protocols, including the ones I was developing with Dhar at the time. They helped me gather and analyze preliminary data, and were acknowledged in our first conference paper (HPC Asia 2002).
In December 2002, while attending HPC Asia 2002, I learned about a popular software system that researchers had been using to study ad hoc networks. This system, known as “NS-2,” is substantial, yet free, including source code that could be adapted to meet many of our needs. Upon returning to Drake, I immediately installed NS-2 in our computer lab. One of my research assistants (Huele) became quite interested in NS-2, and ended up using it as the focus for his senior capstone.
Two additional computer science majors (J. Ehrlich and T. Meredith) won an award from the Computer Research Association (CRA) in order work as my research assistants for the 2004-2005 academic year. This was for the purpose of gaining a better understanding of NS-2, and ultimately altering its source code, so as to explore our new routing protocols. We developed a routing protocol that we called “AODV / k-SPR,” which blended a popular protocol (AODV) with a protocol developed by Dhar and me. The students submitted a paper in connection with their work, and presented a slide show at the 38th Annual Midwest Instruction and Computing Symposium (MICS). They also presented their work in poster form at the DUCURS 2005 (first photo). Yet two more computer science majors (S. Nesheim and M. Smith) have received funding through a Maytag Innovation Award, during the 2004-2005 academic year, for the purpose of continuing the work done the previous year. (See second photo.)

 

Timothy Urness

Research interests: Scientific Visualization, Computer Graphics, Virtual Reality

I am interested in using computer graphics to help scientists better understand physical phenomena. Visualizing data using computer graphics enables researchers to obtain a succinct, meaningful visual summary of the contents of a dataset. This allows the key physical structures from multiple distributions to be understood both independently and in the context of other distributions, and can result in new scientific discoveries.

 

Experimentally acquired variables from a turbulent flow dataset can be analyzed using a "color weaving" technique that allows multiple variables to be visualized simultaneously.

 

A visualization technique, based on embossing, encodes the out-of-plane component of a 3D vector field over a 2D domain

 

In this image, velocity and vorticity vector fields can simultaneously be analyzed to detect the orientation of a vortex.

 

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