This course will analyze a wide range of computational problems in physics. We will study algorithms for problems in physics, ranging from classical mechanics, Electrostatics and Environmental Physics to Statistical Physics and Quantum Systems. Previous experience in MATLAB and programming languages such as C or C++ is considered useful, although a brief overview of basic programming commands will be given at the beginning of the course. The examples in the course will be in MATLAB.
Introduction to computational physics. The emergence of modern computers. Introduction to programming and data visualization techniques
Environmental consequences of energy production and use. Renewable energy sources and technologies. Computational Application of Renewable Energy Sources.
Calculation of the Wind Potential of a Region. Analysis of Wind Potential using the Weibull distribution. Effect of the value of the parameters (C, k) of the Weibull distribution and the study height on the determination of wind speed characteristics. Calculation of wind potential using numerical models. Average value-variations in wind speed. Effect of height on the total available potential of an area.
Calculation of solar energy in an area. Models for calculating solar radiation. Solar radiation databases.
Random systems and stochastic methods: random walks and diffusion, cluster growth, Monte Carlo integration. The Metropolis algorithm.
Quantum systems: the time-dependent and independent Schrödinger equation, the variation method, and tables.
Computational methods for motion equations. Principles and use of the Molecular Dynamics method. Effect of physical properties of matter (temperature, pressure) on atomistic calculations. Effect of stress, strain.
Atomic interaction potentials. Atomic interaction potentials in relation to different types of atomic bonds. Metallic interaction potentials. Potentials for semiconductor compounds. Molecular and hydrocarbon interaction potentials. Ionic crystal dynamics.
Ab initio calculations. Hartree Fock (HF), Linear Augmented Plane Wave (LAPW), Density Functional Theory (DFT), Linear combination of atomic orbitals (LCAO), Tight Binding (TB).