Research projects

can choose the same project, but then you must work independently,

have independent results and make an independent project summary.
 
 

1. The M’memba effect.

2. Getting lost on a cubic lattice.

3. Building and calibrating a thermometer.

4. Simulating the movement of molecules in an ideal gas.

5. Computer simulation study of the self-avoiding random walk.

Many more to come …..

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1. The M’memba effect

This is a very strange phenomenon discovered by an undergraduate student from Kenya. The phenomenon contradicts all what common sense would give for a process of freezing. If we take two identical cup and put warm water in one of it and hot one in the second (temperature much higher than the first one) we would expect that after putting them in the ice-box of the refrigerator the one with hot water would freeze much slower. However sometimes one can observe that the hot one freeze much quicker than the other one in which the waters initial temperature was lower. How can this be? Can this be true? You have to find it out by making experiments on your own. You need to repeat this experiment several times; you need to have many pair of identical cups from different materials and different sizes, and a good refrigerator. You have to consider many initial temperatures of the two cups and have to consider also many positions inside the icebox. A thermometer working from 10C-100C would also be necessary to measure the initial water temperature. Usually a bath thermometer would do this work. This project seems to be a great fun, take care only of the refrigerator!

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2. Getting lost on a 3D cubic lattice.

Prove (by computer simulations or analytically if you can…) that 3d is the lowest dimensional space where somebody can get completely lost...I.e. the probability that the random walk path crosses the starting point is going to zero, when the number of steps is going to infinity….What will happen in 1d and 2d?

(use square and cubic lattice sites in 2d and 3d, respectively)

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This is a more "experimental-like" project. This aim is to build and calibrate by yourself (no help and materials will be provided) a thermometer which will work with a 2⁰C accuracy on the [+10, +80] temperature interval.  

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4. Simulating the movement of molecules in an ideal gas.

This project is for students who like and master computer simulation methods is physics. The aim is to make a computer code which will visualize the movement of billiard ball-like molecules in a 2D space.  

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5. Computer simulation of a self-avoiding random walk.

The self-avoiding random walk is one of the basic models in stochastic phenomena. It is a random walk, where the walker cannot go back to a previously visited lattice site (or the track cannot cross itself). The basic quantity we are interested in is the scaling properties for the mean square displacement as a function of the number of steps. This scaling has to be investigated both for 2D and 3D walks. One should also study the fractal nature of the generated paths, calculating their fractal dimension.

http://www.yu.edu/faculty/cwilich/stat/saw.pdf

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