Computational Physics

Code:

F316

Acronym:

F316

Keywords
Classification	Keyword
OFICIAL	Physics

Instance: 2015/2016 - 2S

Active?	Yes
Responsible unit:	Department of Physics and Astronomy
Course/CS Responsible:	Bachelor in Physics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:F	10	Plano de estudos a partir de 2008	3	-	7,5	70	202,5

Teaching language

Portuguese

Objectives

We'll consider problems from several areas of physics that were studied
in previuos courses or are being studied in parallel this semester,
from the point of view of their numerical solution. We'll describe
and apply several basic numerical techniques. The use of standard
numerical libraries in writting programs will be taught and encouraged.
Introduction to scientific numerical simulation.

Learning outcomes and competences

Address problems of Physics and obtain the relevant equations to be solved. Identify  appropriate algorithms to solve those equations. Implement them in a programming language. Analize critically the results obtained, in particular by comparing them with limit scenarioswhose results are known and/or analytically obtainable.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Working knowledge of a programming language (Python) in the solution of general problems. Linear algebra. Differential equations. Mechanics.

Program

1- Presentation of some Physics problems as examples of the need to use numerical techniques to be implemented in the computer. Solution of equations: separation of roots; iterative processes; succesive bisections; false position; Newton method.

Systems of linear equations: Gauss and Gauss-Jordan; triangular LU-factorization; Gauss-Seidel and convergence conditions. Systems of nonlinear equations: linearization by Newton's method.

2.-  Analytic approximation of experimental data. Example ofr the calibration of a sensor. Interpolation techniques. Interpolating polynomials of Newton and Lagrange. Aitken-Neville formula. Spline interpolation. Linear and polynomial regression by the least-squares method. Basis of orthogonal functions: Legendre and Tchebychev polynomials.

3- Quadrature. Integration by Newton-Cotes formulas. Romberg integration and gaussian quadrature.  Improper integrals. Study of a pendulum's period as a function of its amplitude.

4- Dynamical systems and nonlinear systems. Solution of ODE. Initial and boundary conditions.  Runge-Kutta methods. Adaptive-step.Integration of Newton's equation of motion in 3D space. Harmonic oscillator. Forced, damped regime. resonance spectra. 

5- Cahotic solutions of deterministic systems. Study of Lorentz model, linear forced pendulum and double pendulum.  Graphical representation in phase space, Poincaré sections and bifurcation diagrams. Determination of  Lyapunov's exponents.

6-  Molecular Diynamics simulations. Verlet's formulas. Diluted gas properties. Velocity distribution. Melting transition.

7- General methods for boundary value problems. Eigenvalues. Shooting and finite differences methods. Time independent Schrodinger equation's solution in 1D for a Lennard-Jones potential. System of coupled oscillators.

Mandatory literature

Landau Rubin H.; Computational physics. ISBN: 0-471-11590-8
Chapra Steven C.; Numerical methods for engineers. ISBN: 0-07-100412-2
DeVries Paul L.; A first course in computational physics. ISBN: 0-471-59963-8

Complementary Bibliography

Koonin Steven E.; Computational physics. ISBN: 0-8053-5430-1
Gould Harvey; An introduction to computer simulation methods. ISBN: 0-201-50604-1
Press W.H. Flannery B.P. Teukolsky S.A. Vetterling W.T.; Numerical Recipes The Art Of Scientific Computing

Teaching methods and learning activities

Lectures and computing lab classes for hands-on solution of problems to be solved with the numerical methods taught in class.

Software

Pacotes Python: sciPy, matplotlib,...
Python interpreter

keywords

Physical sciences > Mathematics > Computational mathematics > Computational models
Physical sciences > Physics > Computational physics

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	35,00
Teste	30,00
Trabalho escrito	35,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	100,00
Frequência das aulas	42,00
Trabalho laboratorial	20,00
Total:	162,00

Eligibility for exams

Students must attend 3/4 of scheduled lab classes. They must also turn in the computing projects and in class tests in the deadlines.

Calculation formula of final grade

-3 mini-quizzes with 1 or 2 problems to be done in the lab classes (at set dates) (10% each);

-final exam (35%, regardeless of being normal exame or replacement exam)

-computational project (35%)

Examinations or Special Assignments

computational project, in which a physics problem is solved, using computational methods learned in the UC.

Classification improvement

Retaking  the "final exam" component (35% weight)