MM837: Computational Physics (10 ECTS)

STADS: 13016101

Level
Master's level course

Teaching period
The course is offered in the autumn semester.

Teacher responsible
Email: bulava@imada.sdu.dk

Additional teachers
dellamor@cp3.dias.sdu.dk
pica@cp3.dias.sdu.dk

Timetable
Show entire timetable
Show personal time table for this course.

Comment:
Ubegrænset deltagerantal. Fælles undervisning med MM553 Beregningsmæssig fysik

Prerequisites:
None.

Academic preconditions:
Students taking the course are expected to have knowledge of:

• Differentiation and integration of functions of one and several variables
• Basic concepts of linear algebra (vector spaces, matrices, eigenvalues ...)
• Ordinary Differential Equations
• Basic programming.

Course introduction
The aim of the course is to enable the student to apply computational methods in order to solve non-trivial problems in nonetheless practical and efficient way. Computational methods have become a standard approach in many areas of science, especially in condensed matter, particle physics, hydrodynamics,  plasma-dynamics, biophysics and chemistry.   The course provides tools to address problems which typically cannot be solved by analytical methods.

The course builds on the knowledge acquired in the courses DM550
(Introduction to Programming) , MM547 (Ordinary Differential Equations: Theory, Modelling and Simulation ), MM536 (Calculus for Mathematics) and MM538 (Algebra and Linear Algebra) .

The course is of high multidisciplinary value and gives an academic basis for a Master thesis project in several core areas of Natural Sciences.

In relation to the competence profile of the degree it is the explicit focus of the course to:

• Give the competence to :
1. handle complex and development-oriented situations in study and work contexts.
2. to independently engage in disciplinary and interdisciplinary collaboration with a professional approach based on group -based project.
• Give skills to:
1. analyze practical and theoretical problems with the help of numerical simulation based on a suitable mathematical model.
2. analyze a mathematical model qualitative and quantitative traits.
3. describe and evaluate sources of error for the modeling and calculation for a given problem.
• Give knowledge and understanding of:
1. mathematical modeling and numerical analysis of problems in science and technology.
2. how scientific knowledge is achieved by an interplay between theory, modeling and simulation.

Expected learning outcome
The learning objectives of the course are that the student demonstrates the ability to:

• Reflect on the numerical and algorithmic principles presented during the course and connect them with other numerical/computational techniques from other courses in the curriculum.  
• Reflect on the most appropriate solution techniques for the problem at hand, based on the knowledge acquired in the curriculum.
• Present and reflect on the scientific results achieved in a scientifically correct way.

Subject overview
The following main topics are contained in the course:

• Numerical methods for classical Hamiltonian systems
• The N-body problem
• Integration schemes
• Numerical methods for Schroedinger equation in one dimension
• Monte Carlo Simulations of Spin Systems:
• Markov chains and Metropolis algorithm
• Cluster algorithm
• Wang-Landau algorithm
• Simulation of two-dimensional models
• Numerical Simulation in Quantum Field Theories
• Heatbath algorithm for Yang-Mills theories
• Hybrid Monte Carlo algorithm for matter fields

Literature

Meddeles ved kursets start.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
Mandatory assignments. Evaluated by the Danish 7-mark scale, internal marking.

Expected working hours
The teaching method is based on three phase model.
Intro phase: 56 hours
Skills training phase: 28 hours, hereof:
 - Tutorials: 28 hours

Educational activities

Educational form
Activities during the study phase:

• preparation of exercises in study groups
• preparation of projects

Language
This course is taught in Danish or English, depending on the lecturer. However, if international students participate, the teaching language will always be English.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.