Theoretical solid-state physics and nanoscience with Professor Phil Allen I have a small group (right now, one graduate student; most often, two students). Sometimes I work with a high school student during the summer. I interact with solid state physicists both at Stony Brook and at Brookhaven. My research interests are evolving into the area of nanoscale crystals and molecular devices. I have time for one, or possibly two undergraduate students, if they are sufficiently resourceful that they don't need continuous help. For an undergraduate research project, I suggest problems which require writing a computer code to answer a question which is a little too hard to solve by paper and pencil. Here are two examples: 1.  Suppose you have a rigid cluster of molecules, each of which has a permanent dipole moment, and which can each orient in an arbitary direction. They interact with each other through the dipole-dipole interaction. What is the orientation which minimizes the total energy? For example, consider a cluster of 7 such dipoles, one located at the origin, and one each at the positions +a or -a along the x, y, and z axes. Larger clusters than 7 can be examined. It's a nice problem in linear algebra. The results will need to be analyzed for symmetry using some methods from group theory. This question may shed light on the unknown nature of ferroelectric order in nanocrystals. Nanotechnology will be a thriving field for the next half century, spawning new fields of nanoengineering, so its a great field for a young person to get involved with. 2.  How does a pulse, propagating in a one-dimensional crystal, approach thermal equilibrium? Suppose the crystal consists of point masses each separated by distance a from their neighbors. Suppose the atoms interact only with their two nearest neighbors. If the force is harmonic (potential S(k/2)(xn+1 -xn -a)2), the answer is that the pulse propagates at the "group velocity", slowly spreading, but never reaching thermal equilibrium. It is necessary to add anharmonic forces. When this is done, you can solve the problem numerically on a computer, and if you ask the right questions, you may be able to shed light on this question which has bothered physicists for more than 50 years. The question has to do with the crossover to chaos, and how this changes as a system gets bigger. October 2003