DEPARTAMENTO DE FÍSICA

 

Física Computacional - F

Ano letivo: 2011-2012
Specification sheet

Specific details
course codecycle os studiesacademic semestercredits ECTSteaching language
1002874126.0pt


Learning goals

Main importance: Ability to solve problems.

General Culture in Physics.

Mathematical competences to solve problems.

 

Secondary competences:

Ability to search and use bibliography.

Theoretical understanding of the physical phenomena.

Thorough general culture in Physics, namely computational algorithms that are used in the different fields of Physics.

Syllabus

Numeric interpolation: Spline and Lagrange interpolation.

Numeric differentiation: rules of 2, 3 and 5 points and Richardson method. Numeric integration: Trapezoid Rule, Simpson’s rule, Romberg and Gaussian Quadrature.

Zeros and extrema of the function of a variable: bisection, secant, regula falsi and the newton-raphson methods.

Linear systems of equations: Gauss-Jordan elimination, LU factorization, Cholesky factorization and QR factorization.

Extrema of the function of various variables: maximum decrease method and conjugated gradients method, genetic algorithms, simulated annealing and search methods in a pattern.

Applications in Physics (molecular geometry, etc.).

Monte Carlo method: integration, radioactive decay, diffusion. Random walks and Metropolis algorithm. Ising Model.

Problems of intrinsic values: diagnolization of Schrödinger equation.

Differential equations: Euler’s method, Runge-Kutta methods and predictor-corrector methods.

The cushioned and forced pendulum.  Chaos.

Resolution of the Schrödinger equation by means of the integration of the differential equation: the Numerov’s method.

Laplace and Poisson’s equations.

Fourier transforms.

Molecular Dynamics.

Quantum Monte Carlo methods: the hydrogen and helium atoms and H2 and H2+ Molecules.

Prerequisites

Mathematical Analysis I, II, III.

Linear Algebra and Analytical Geometry.

Computers and Programming.

Quantum Mechanics I.

Generic skills to reach
. Computer Skills for the scope of the study;
. Competence to solve problems;
. Competence in autonomous learning;
. Adaptability to new situations;
. Competence in applying theoretical knowledge in practice;
. Competence in oral and written communication;
. Critical thinking;
. Creativity;
. Initiative and entrepreneurial spirit;
. Quality concerns;
(by decreasing order of importance)
Teaching hours per semester
lectures30
laboratory classes30
total of teaching hours60

Assessment
Problem solving100 %
assessment implementation in 20112012
Resolution of problems : 100.0%

Bibliography of reference

PRESS, William [et.al.]. Numerical Recipes in F77/F90/C/C++: The Art of Scientific Computing, Cambridge: Cambridge University Press.

HJORTH-JENSEN, M. Computational Physics. http://www.uio.no/studier/emner/matnat/fys/FYS3150/h11/undervisningsmateriale/Lecture%20Notes/lectures2011.pdf

PANG, Tao (2006). An Introduction to Computational Physics. Cambridge: Cambridge University Press. ISBN: 978-0521825696.

ALLEN, M. P. and TILDESLEY, D. J. (1989). Computer Simulation of Liquids. Oxford: Clarendon Press. ISBN: 978-0198556459.

FRENKEL, Daan and SMIT, Berend (2001). Understanding Molecular Simulation: From Algorithms to Applications. New York: Academic Press. ISBN: 978-0122673511 .

Teaching method

The essential objectives of this curricular unit are those marked with the number1 in the Dublin descriptors mentioned above. Especially, students are expected to be able to identify, implement and critically analyse a numeric method (or a set of methods) in order to solve an essential problem of Physics. The adopted strategy comprises the brief theoretical lecturing of a wide number of methods and an assessment system based on the accomplishment of small project assignments and their reports. Students will be advised to carry out 4 assignments: the first two should be done during two weeks (the time given to students to accomplish the assignment, which is counted from the day on which the assignment is delivered by the teacher); the last two should be done during 4 weeks.

These assignments allow students to develop their ability to do research and their ability to work alone in the resolution of advanced problems.

Resources used
Laboratório de Computação Avançada