DN2280 Computational Methods from Micro to Macro Scales 7.5 credits

• Educational level

  Second cycle

• Academic level (A-D)

  D

• Subject area

• Grade scale

  A, B, C, D, E, FX, F

• Course web page

• Course page on KTH Social

Learning outcomes

After completing this master level course the student will be able to model, analyze and compute solutions to multi-scale model problems from Schrödingers equation, for nuclei-electron systems, over molecular dynamics to Euler and Navier-Stokes equation for continuum fluids.

Course main content

Differential equations are fundamental for the modeling in Science and Engineering. As the computational power increase, it becomes feasible to use more accurate differential equation models and solve more demanding problems: for instance to determine input data from fundamental principles and to optimally reconstruct input data using measurements.The course includes lectures, computer exercises and student presentations on models, analysis and computational methods from nuclei-electron micro-systems to Euler and Navier-Stokes macro-systems for continuum fluids, using a unified mathematical method to derive and explain the coupling between the models on the different scales.
- Relation between Schrödinger-molecular dynamics-continuum partial differential equations

- Ehrenfest dynamics and surface-hopping

- the Born-Oppenheimer approximation

- electron structure calculation methods

- bridging ab initio and empirical molecular dynamics

- molecular dynamics: thermodynamics and statistical mechanics

- molecular dynamics: ensembles and simulations

- stochastic Langevin and Smolchuwski molecular dynamics

- molecular dynamics reaction paths and rates

- Euler and Navier-Stokes macroscopic equation derived from microscopic molecular dynamics

- project presentations on applications.

Eligibility

Single course students: 90 university credits including 45 university credits in Mathematics or Information Technology. English B, or equivalent.

Prerequisites

The prerequisite for the course is linear algebra, calculus, differential equations, probability and numerics corresponding to the first three years at KTH.

Literature

Lecture notes.

Examination

• LAB1 - Laboratory, 3.5 credits, grade scale: P, F
• TEN1 - Examination, 4.0 credits, grade scale: A, B, C, D, E, FX, F

In this course all the regulations of the code of honor at the School of Computer science and Communication apply, see: http://www.kth.se/csc/student/hederskodex/1.17237?l=en_UK.

Offered by

SCI/Mathematics

Contact

Anders Szepessy, e-post: szepessy@kth.se, tel: 790 6742

Examiner

Anders Szepessy <szepessy@kth.se>

Supplementary information

The course is given as a reading course.

Version

Course plan valid from: Autumn 09.
Examination information valid from: Autumn 09.