Practical Assignment 1: Simulation of Gas Dynamics
This practical assignment focuses on the study of gas dynamics in a system of particles in motion within a box. The system models particles in a box in the plane that repel each other and collide with the walls.
A repulsive potential is employed, which varies based on the distance between the particles and an interaction constant. The calculation of forces between particles is described, and the manner in which they act in accordance with the proposed potential is established.
Click here to open the notebook (spanish only)
Practical Assignment 2: Image Compression (jpeg)
In this practical assignment, we will implement a simplified version of the .jpg file compression algorithm, based on the observation that real signal transforms are typically dominated by low frequencies with a limited contribution from high frequencies.
The strategy involves performing a signal transform, discarding frequencies above a threshold, and storing only a reduced set of frequencies, achieving compression. Signal recovery entails completing the transformed vector with zeros and applying the inverse transform. While the jpg algorithm adheres to this principle, it also employs the cosine transform instead of the Fourier transform due to its ability to work with real numbers and its greater concentration of information in low frequencies.
The cosine transform is implemented using the dct command in the FFTW library.
Click here to open the notebook (only in spanish).
Practical Assignment 3: Diffusion Simulation in a Cup
This assignment revolves around solving an equation that models the diffusion of a substance in a liquid within a circular domain. The method of lines is employed, and polar coordinates are used for discretization and problem-solving. Neumann boundary conditions are imposed on the domain edges, taking into account the circular geometry’s peculiarities. The aim is to numerically find the solution of the equation within a rectangle in the polar domain.