Welcome to Peter Scott's home page…
This page, which is the start of a new home page that I hope to add to, describes a few of the projects I am currently working on, some related to physics and some related to other topics. Of course, everything is related to physics. The photo of me was taken in 2012.
The last time I taught a course for the Physics Board (now the Physics Department) was in 2003. I still miss the experience.
Here is a link to the text of an oral history, originally recorded in 1994 when I officially retired, and edited (with additions) in 2004. In it are descriptive words about the wonderfully yeasty early years of the UCSC campus, along with descriptions of the development of the research here on chaos and nonlinear dynamics.
Upper Division Physics Lab Courses
In 2014 I took on what is turning out to be a rather lengthy project, involving the updating of three sections of the lab manual—sections that I first wrote ages ago (in the 1980s and 90s), when I was the instructor for Physics 133 (Intermediate Lab) and Physics 134 (Advanced Lab). Surprisingly, those sections are still in use in those courses, pretty much in their original versions. But they need work.
A current draft (August, 2015) containing the revised sections is here.
Associated with those sections, there were a few computer programs, written in C++, that no longer compiled or ran, so I started with the task of updating those programs. At the moment there are four programs, each of which accepts a datafile as its argument. Here are the descriptions:
meanvar: Given a datafile with a single column of (usually more-or-less equal) x-values, this program calculates the sample mean (along with its uncertainty) and sample variance (along with its square root, the standard deviation) for the collection of x-values. The datafile may have a second column of numbers, which will be interpreted either as weights or as standard errors for the associated x-values. If the standard errors are independently estimated, the program will also calculate a value of chi-square.
plotdata: Given a datafile with two columns of numbers (the x-values and associated y-values), this program will create a graph that displays a plot of the y-values vs. the x-values. If the datafile contains a third column of numbers that are independent estimates of the standard errors of the associated y-values, the relevant error bars will be shown on the graph.
fitline: Given a datafile with two or three columns of numbers—the x-values, the y-values, and optionally, the associated uncertainties in the y-values—this program will provide a best (least-squares) fit of a straight line to the data and provide values for the slope and intecept of the straight line, along with their associated uncertainties (standard errors). If the uncertainties in the y-values are independently estimated, the value of chi-square will also be provided as a test of “goodness of fit”. The program will also produce a good graph of the results.
fit: This program is similar to the fitline program, except that it will fit a (typically nonlinear) function to the data contained in the datafile.
The user of the program must provide the C++ code that describes the hypothesized function to be fit to the data—a function that will typically include a number of parameters in its description. The program will adjust the values of those parameters, using the “Marquardt” (or “Marquardt-Levenberg”) algorithm, to achieve a least-squares fit of the function to the data. The user must also provide initial estimates for the values of the parameters.
The program will provide final values, along with uncertainties, for each of the parameters, and display a good graph of the results.
The latest versions of the source code (contained in “tar files” or “tarballs”) for each of the above programs may be found here. This source code may be compiled and run on a variety of operating systems. It has been tested on Linux and Windows 7, and will probably also compile and run on Mac OS X as well. Detailed instructions are provided with each program.
In 1972, Bill Burke, a Professor of Physics and Astrophysics here, whose primary research interest was in the field of General Relativity, had some ideas for simplifying and clarifying the presentation of the Special Theory of Relativity in our introductory courses. He wrote up a set of notes, which he called a Special Relativity Primer. In subsequent years I collaborated with Bill in expanding his initial draft and making some figures for it, and several of us who were involved in teaching introductory physics courses then used the Primer as a text. It turned out to be an effective way to introduce special relativity, not only to beginning physics students, but to more advanced students as well. Bill unfortunately died in an auto accident in Utah in the summer of 1996.
Subsequently I decided to make the Special Relativity Primer available to a broader audience, since those notes were never published. I am now working on making an updated version of the complete Primer. This project has been on the back burner for much too long. If you would like to be notified when additional sections are completed, let me know.
The Lorenz Equations
Many years ago, when I became interested in the mysteries of nonlinear dynamics and deterministic chaos, I decided to write a program to display the Lorenz Attractor. The brown image shows a typical plot produced by the program. Click on the image to enlarge it, and to learn more about the Lorenz Attractor and to download the program that displays it.
In 1963, Ed Lorenz wrote what is believed to be the most often cited paper in the chaos literature. It is entitled Deterministic Nonperiodic Flow. In it, he solves a set of three first-order coupled nonlinear differential equations—a simplification of the Navier-Stokes equations. These equations describe the flow patterns in a layer of fluid of uniform depth that is heated from below and cooled at the top, with a constant temperature difference between the bottom and the top of the layer.
Lorenz was a meteorologist, thinking that such a layer might be a simple model for a layer of the Earth's atmosphere, so the behavior of the solutions might shed some light on how predictable the weather might be.
NOVA: The Strange New Science of Chaos
In 1988, at a UCSC conference, we described some experiments that Rob Shaw and I had done, and invited conferees to visit our lab, where we had set up our apparatus. Several people came to visit, among whom were two associated with NOVA. Subsequently these NOVA folks arranged to come and film our setup, and we were honored to discover that we had become part of a NOVA program, which was first aired on January 31, 1989.
This show is now available on YouTube, and may be viewed here. Our experimental setup is displayed in two sections of this video, one starting at approximately 19:15 (showing the Lorenz equations being solved on an analog computer) and the other starting at approximately 29:08 (showing our experiments with a dripping faucet).
A Review of Composting Toilets
I have recently (November, 2016) updated a review of composting toilet installations in public venues in the U.S. (We do not discuss residential installations.) If you would like to read it, click on this link.
A Start of a Song Collection
Here is a start of what will eventually be a collection of songs, including It's Gravity with a Capital G (now with a new video), along with Dancing on the Brink of the World (also known as The River Song), and one version of a song we often produce as a birthday gift.
If you have comments or questions about anything on this website, feel free to write to me by clicking here.