Students practice using this important vocabulary and scientific terminology.Teacher Tips Consider choosing four students to read aloud the four parts.Please sign-up for the email list of the class, to receive homework assignments, last minute announcements, class cancellations etc. Contact and office hour information for the two graders for the class: Purba Chatterjee ([email protected]).
Please note that they will not respond to any email that is not an @email address, so do not use gmail etc for course matters.
The Fermi-Pasta-Ulam-Tsingou problem is still a topic of interest, and a recent review can be found in this article.
You may wish to ask students what Olivia says about the objects in the drawing. Q asks the class to look at five images of the hillside (part of their homework).
(Note that Olivia mentions that it is a “weird energy system” that “is storing up energy.”) These are key concepts that will be explored throughout the unit. She tells the members of each table group to compare answers and to discuss their thinking.
In class we talked briefly about the problems of equilibration and the notion that glass is a solid that flows on a long enough timescale.
In fact, it does not seem to be true that cathedrals in Europe have windows that are thicker at the bottom than the top due to this effect.Here is a recent article that reviews briefly analytic solutions of the two-dimensional Ising model, and in particular the mapping to a system of free fermions which is what enables the analytic solutions. Link to recent papers on the statistical mechanics section of the condensed matter preprint archive at Los Alamos.The article has references in it to much earlier work, especially the seminal review article of Schultz, Mattis and Lieb, Rev. Note that many, many papers relevant to statistical mechanics and phase transition physics are not listed here, but appear in the condensed matter section.These include the following links: Some of the modern applications of phase transition and RG ideas are to complex dynamical systems in economics, sociology, computer networks etc.A good resource is the Santa Fe Institute and the New England Complex Systems Institute.Let’s look at the last part of your homework with that hillside problem. When things are easy you’re not really learning, you’re just performing. Think through how the energy would move through this system.Remember that these exercises were supposed to help you begin thinking about energy. Then cut out the the images and tape them on another piece of paper in the correct order.There are several computer simulations of the Ising model and other simple statistical mechanics model available on the WWW.With these you can visualise equilibrium behaviour of correlations, dynamic critical behaviour and even the kinetics of the approach to equilibrium.My extra credit starter challenge for you all today is to look at the last problem of your homework, the one with the hillside, and to add a caption that describes what’s happening in the sequence.But try to use the terms I’ve written on the whiteboard correctly as you write.