This course is devoted to most novel methods in statistical mechanics and stochastic processes.

• Course subjects and program (Download)
• A good text for commands in Fortran, C++ and matlab (Download)
• Some necessary things for programming skills (Download)
• Midterm exam will be on 92/02/21

References:

1. arXiv:physics/0406120
2. Data analysis: A Bayesian Tutorial, by D.S. Sivia & J. Skilling, Oxford science Publication,  2010
3. Data reduction and error analysis for the physical sciences, P. R. Bevington & D. K. Robinson, McGrawHill, 2003
4. Error of Observations and their Treatment, J. Topping, 1972.
5. Practical Physics, G. L. Squires, 1985.
6. درسنامه دکتر محمدرضا اجتهادی http://sharif.edu/~ejtehadi/lectures/Lectures.htm
7. درسنامه دکتر محمدرضا رحيمی تبار http://sharif.edu/~rahimitabar/course.htm
8. درسنامه خودم (Download)

Exercises:

1) Using the underlying data (Download), compute the mean, variance and probability density function of each sets. (Deadline 91/12/10)

2) Find different kernels used in calculating probability distribution function and report one of them. Base on kernel you found for previous question to recalculate probability distribution function for the given data. (Deadline 91/12/15)

3) Calculate JPDF, p(x;y), for few specific points. Plot $\Delta(\tau_n) = \sum_{x_1,x_2}|p(x_1(t);x_2(t+\tau_n)) - p(x(t)) p(x(t+\tau_n))|$ as a function of $\tau_n$. (Deadline 91/12/15)

4) Suppose in a box there is an harmonic oscillator. In the random time intervals, we open the door of this box. Derive the probability distribution function of position of mass by using PDF transformation method. (Deadline 91/12/15)

5) Prove that a multi-variant PDF in the general form is normalized. (Deadline 91/12/15)

6) For three data sets available in the first question calculate $\sigma_w$ and if possible find $\tau_x$ in each set. (Deadline 91/12/15)

7) Base on Two-Point correlation function, calculate two-point correlation of a 1D data set available in first question for Zero,+2\sigma and -2\sigma features. Repeat the same tasks but for 2D data sets (2D-Data). (Deadline 91/12/20)

8) Compute the PDF of computer random generator. Make a Gaussian random series using simple and Box Muller methods. Derive analytically Three-point correlation function of T(\theta,\phi). (Deadline 91/12/25)

9) Calculate the power spectrum of the sun spot data (Download). (Deadline 92/01/20)

10) Using about 10000 no. of each data sets given in question 1 and compute the power spectrum for them. Also superimpose each data with some sinusoidal data and recompute  power spectrum, in your plot show each frequencies embedded in your data. (Deadline 92/01/20)

11) Calculate PDF for computer random generator , show the error bars in PDF in your plot. (Deadline 92/01/20)

12) Generate a set of Gaussian random numbers with method thought in the class and by calculating the PDF of your data show that it is consistent with Gaussian distribution. (Deadline 92/01/20)

13) Generate Non-Gaussian data set with given correlation function (e.g. the shape of correlation function follows a scale invariant behavior $C~ \tau ^ {-\gamma}$) and show that three point correlation function of your data is not zero. (Deadline 92/01/20)

14) Prove analytically that the real part of Fourier Transform is enough to calculate correlation function. (Deadline 92/01/20)

15) For a langevin equation without drag coefficient, find a relation between temperature and intensity of noise force. (Deadline 92/01/30)

16) Show the equivalence of forward and backward Kramers-Moyal expansion. (Deadline 92/01/30)

Final exam marks (Download)

Preliminary marks+all questions (Download)