Contact Information
Department of PhysicsSyracuse University
Syracuse, NY 13244
(315) 443-1010
mjeng[at]physics[dot]syr[dot]edu
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Contact InformationDepartment of PhysicsSyracuse University Syracuse, NY 13244 (315) 443-1010 mjeng[at]physics[dot]syr[dot]edu |
My field of research is soft condensed matter, with a primary focus is on glassy dynamics and jamming. My work has primarily focused on simple mathematical models, particularly cellular automata, that may yield insights into glassy behavior.
In the past I have worked on the Abelian sandpile model, conformal field theory, membranes, and a number of miscellaneous other topics.
Some of these are fields of research that I'm currently working on, or used to work in. And some are just things that I thought it would be fun to write a simulation for. Most have applets that show how the simulations work. (The applets are in most cases pared down versions of something I was using for my own personal research, so may not alway have the nicest user interfaces. Sorry!)
Normal percolation is a simple mathematical model in which sites of a lattice are randomly occupied, and the properties of the connected clusters of occupied sites are studied. While simple to describe, the model is surprisingly rich. Correlated percolation occurs when correlations are added to the site occupations by some culling condition. The pictures below are for a model of correlated percolation known as k-core percolation. Click here for the Java applet that made these pictures, as well as a more detailed description of correlated percolation. Click on the pictures for larger pictures, and the simulation parameters. This work is being done in collaboration with Jennifer Schwarz.
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I'm currently studying a dimer model that may be a good model for understanding glassy dynamics and jamming. In this model, dimers move on a densely packed (but not fully packed) two-dimensional lattice (triangular or square). Dimers can only move by translation into holes. All kinds of interesting questions can be asked about the dynamics and phase space structure of this model. The evolution of the model becomes very sluggish at high dimer densities, suggesting that it could be useful for understanding glassy behavior. This work is being done in collaboration with Sean Xing, Mark Bowick, and Jennifer Schwarz.
There are three applets associated with this model:
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When particles in two dimensions interact with almost any sort of interaction potential, numerical simulations show that they almost always form a regular triangular lattice. Only for certain very specific potentials do they form other lattices (e.g. square). The pictures below are the lattices formed by interacting charged particles in a parabolic well, and in a box. Click here for the Java applet that made these pictures. Click on the pictures for larger pictures.
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The pictures above are for particles interacting in a horizontal plane, without gravity. However, if the particles are in a tilted plane, the tendency of the particles to all want to sink to the bottom competes with the repulsion that keeps the particles apart. The result is that the lattice spacing is smaller on the bottom than at the top, so that the lattice is distorted. This has been seen experimentally, in systems of repelling magnetic dipoles, and soap bubble froths. The result is known as a conformal crystal. Belw is a picture produced by simulation of conformal crystals. (Click on it for a larger picture.) I am interested in improving our understanding these structures. This work is being done in collaboration with Mark Bowick.
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Much of my past research has been on the Abelian sandpile model. The Abelian sandpile model is a simple cellular automata. It is run on a square lattice, at which every site has a number between 1 and 4, called the grain height. Each time step, the height of a randomly chosen site is increased by one. If this gives the site a height greater than 4, it topples, decreasing its height by 4, and increasing each of its neighbors heights by one (and, if it is on an edge, sending a grain off the edge). The model was originally primarily of interest as a model for self-organized criticality, but it is now perhaps more interesting as a simple example of a logarithmic conformal field theory. Some of this work was done in collaboration with Philippe Ruelle and Geoffroy Piroux.
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The picture above shows a sample configuration of the Abelian sandpile model on a five by five lattice. It turns out that it's possible to quickly see that the configuration below is an early transient configuration; that is, the model hasn't been running for a large number of timesteps. To see why, and for a brief description of the background behind the model, go here.
Click on a picture to see an applet of bouncing balls. The balls undergo perfectly elastic collisions, so never lose energy, and never come to a rest. This has nothing to do with my research, but I wrote the applet after a talk on granular gasses (for which the simulation problem is identical), and find watching the bouncing balls to be rather mesmerizing.
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These are some Scrabble puzzle programs that I've written. You can use them to improve your Scrabble-playing skills.
A note for Scrabble enthusiasts: for all these programs I used the OSPD2, because I couldn't find a downloadable word list for OSPD4. If you know where I can get an electronic OSPD4 word list, please e-mail me at mjeng[at]physics[dot]syr[dot]edu.
The Memory Game is one of the first applets that I ever wrote, and I still enjoy it. It's basically SuperSimon, but with more options, such as having more than four colors, having longer sequences, etc. . .
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These are puzzle-like contests that I ran on the rec.puzzles and rec.games.trivia newsgroups many years ago. In these contests I asked entrants to predict the most common answers to my questions, given that all other entrants would also be attemtpting to predict the most common answers . This game was not just "Family Feud"---the self-referential nature of the contest meant that the questions could be much harder. They could thus be nonsensical:
Or ones with no obviously good answers:
Or just difficult "Family Feud"-type questions.
As you can see, for some of these questions it's very difficult to figure out what answer will be the most popular. One interesting aspect of these contests is that the best answer is not necessarily even a correct answer to the question. Complete copies of all the contests, and the answers to the contests questions, including the questions above, are here: Common Entries Contests.
These are also contests that I ran on the rec.puzzles and rec.games.trivia newsgroups many years ago. In these, entrants just had to pick one or more numbers, and the scores or winning entries were determined by both the entrant's number, and the numbers submitted by all other entrants. The rules were designed to generate interesting game-theory-type problems. Some contests were particularly interesting in that the "correct" game theory answers were easily calculable, but these game theory answers were often badly wrong. Here are some questions that I found particularly interesting from a game theory perspective:
Complete listings of the Numbers contests, and the winning answers, are here: Numbers Contests.
Here are two entries I wrote for the sci.physics FAQ:
The first one was popular enough that I later turned it into a journal article.
