George W. Hart

Selected Recent Publications

Some Past Research Topics

My recent work is centered on computational algorithms and computer technology in the design of geometric sculpture,.  I am also very interested in puzzle design and the history of geometry in art.  Some areas of my past research that people still contact me about are briefly summarized below, with pointers to further information.

1. Multidimensional Analysis

The study of ``dimensioned quantities," such as 1 volt, and 2 meters, and their possible interrelationships, forms an interesting branch of applied mathematics (or physics or engineering) called dimensional analysis. Traditionally this field only concerns scalar quantities (not vectors and matrices).

The linear algebra which results when one considers vectors and matrices which contain dimensioned quantities as their components is surprisingly interesting and rich. Although it is implicit in all branches of modern engineering, it has not been carefully studied before.

For an introduction to dimensioned linear algebra and the dimensional analysis of matrix relationships, be sure to check out my Multidimensional Analysis page, and check out my book, which assumes an undergraduate background in linear algebra:

George W. Hart, Multidimensional Analysis: Algebras and Systems for Science and Engineering, Springer Verlag, 1995.

Software for Scalars:

A very useful computer program (which I have written and placed in the public domain) for manipulating, converting, and calculating with dimensioned scalars is available, DimCalc, runs under Windows 3.1 or higher software. The file to get is which is a compressed package of the software and extensive on-line help information. Expand the directory someplace and double click the dimcalc.exe file within it to run the program.

2. Nonintrusive Appliance Load Monitoring

A Nonintrusive Appliance Load Monitor determines the energy consumption of individual appliances turning on and off in an electric load, based on detailed analysis of the current and voltage of the total load, as measured at the interface to the power source. The approach has been developed to simplify the collection of residential energy consumption data by utilities, but also has other applications. It is called nonintrusive to contrast it with previous techniques for gathering appliance load data, which require placing sensors on individual appliances, and hence an intrusion onto the energy consumer's property.

An interesting aspect of this research is the interdisciplinary manner in which it combines power systems theory and communications theory---power consumption is decoded as an act of information transfer. The theory and current practice of Nonintrusive Appliance Load Monitoring, including goals, applications, load models, appliance signatures, algorithms, prototypes, field-test results, current research directions, and the advantages and disadvantages of this approach relative to intrusive monitoring are described in the following tutorial survey article:

G. Hart, ``Nonintrusive Appliance Load Monitoring," IEEE Proceedings, December 1992, pp. 1870-1891.

For additional on-line information, be sure to explore my Nonintrusive Appliance Load Monitoring Page.