- Course subjects and program (Download)
- A good text for commands in Fortran, C++ and matlab (Download)
- Some necessary things for programming skills (Download)
Extra news:
The date of final exam has been changed to Thursday (91/03/25) at 8:30 am in the seminar room of physics department.
Exercises
1) Using the underlying data (Download), compute the mean, variance and probability density function of each sets. (Deadline 90/12/15)
2) Using previous data sets, compute PDF for each sets with error-bars, joint PDF and Conditional PDFfor various values of $\tau$. Finally by using various kernels try to smooth computed PDFs. (Deadline 90/12/25)
3) Using previous data sets, compute auto-correlation and cross-correlation functions error-bars, Pearson's correlation and variance as a function of window. In the next task, compute the probability distribution function for computer random generator. Finally make a gaussian distribution function with size N=100000 in the interval [-10,10]. (Deadline 91/1/15)
4) Using BOX MULLER method make a set of random data with Gaussian PDF, investigate the Gaussianity of the generated data. Base on Two-Point correlation function, calculate two-point correlation of a 1D data for Zero,+2\sigma and -2\sigma features. Repeat the same tasks but for 2D data sets (set1 & set2). (Deadline 91/1/25)
5) Calculate the most important properties of random-walk in 1D and 2D networks. Choose different values for forward jump and backward jump probabilities and recompute mentioned properties. (Deadline 91/2/05)
6) Simulate the evolution of a brownian particle based on 1D Langevin equation. Compute the statistical averaging of relevant quantities such as velocity, position, autocorrelation and PDF of velocity for stationary situation. By determining the Kramers-Moyal's coefficient for simulated particle calculate the evolution of various order of moments (m=4 , m=5). (Deadline 91/02/15)
7) Plot the bifurcation and phase diagrams for three kinds of chaotic phenomena mentioned in the class. Using one of data file that you have, and determine the discrete differential using 4 and 8 neighbors. Using RKF45 method compute the position of a typical negative charge as a function of time, putting on the vertical axes of a ring charged by constant charge linear density with radius R. (Deadline 91/02/20)
8) Using self-consistence method, plot magnetization as a function of temperature for spin 1/2. According to thermal conduction equation mentioned in the class, compute $T(x,t)$. Using the Laplace's equation in 2D, and by generating random number determine the electric potential in the space by means of boundary conditions. Plot the electric field and equipotential surface for a typical 2D space containing 3 arbitrary point charges. (Deadline 91/03/01)
9) Compute power spectrum of sunspot data set (download), using correlation function and directly based on data. Superimpose 0.8.txt data set with some arbitrary periodic functions and then compute spectral density. Make a data set which has gaussian pdf for a given correlation function. (Deadline 91/03/10)
10) Using butterfly diagram, write Fast Fourier Transform and check it by public numerical libraries subroutine. Using FFT method compute the time evolution of typical wave-packet based on Schrodinger equation with time independent potential. (Deadline 91/03/15)
11) Using wavelet transform, analysis two set data produced by two arbitrary frequencies for which, in one set these frequencies take place simultaneously but for other one, these frequencies appear in successive pattern. Using sunspot date, make low and high-pass filters and plot your results. Apply SVD and EMD methods on sunspot data. (Deadline 91/03/25) (lecture for wavelet (Download))
12) Using the basic concept of Monte Carlo simulation, compute the value of $\pi$. In addition, calculate the definite integration of an arbitrary function using two following approaches: 1) make random data with the uniform distribution and 2) make random data with a function same as integrand function. (Deadline 91/03/25)
Preliminary marks (Download) or you can find it in this link (Download)
