Czech

doc. Ing. Roman Gröger, Ph.D. et Ph.D.

Institute of Materials Science and Engineering

Knowledge of mathematics at the level of the 2nd year of FME (differentiations of the functions of many variables, basic probability theory, numerical methods), and basic knowledge of programming.

At the end of the semester, each student will be assigned a problem that will be tightly linked to some of the methods explained in the lectures and more deeply studied in the exercises. The output of each such assignment will be the formulation (or modification of already existing) simulation code, its application to study the given problem and writing a report that summarizes these developments and the principal results. The exam will then consist of an oral defense of this report.
The attendance at exercises is mandatory and each absence must be propertly justified. The absence will be accepted upon the student submitting a written report from the missed exercise which proves that the student understood the method explained.

This course will provide a broad overview of the most frequently used methods for computational simulations of materials from the atomic level, via a range of mesoscopic descriptions to the continuum simulations of macroscopic bodies. In the series of exercises, the students will get acquianted with computer implementations of the individual algorithms, which will make it possible to understand the inputs into, methods used and results obtained from standard commercial and open-source packages for computer simulations of materials.
Within this course, the students will acquire knowledge of a broad range of computational methods used to study the relationships between microstructure and physical properties of materials. It will provide basic theoretical and practical skills for the studies of nanostructures, interacting many-body systems and for simulations of mesoscopic and macroscopic systems based on their continuum descriptions.

Programme D-MAT-P: Materials Sciences, Doctoral, recommended course

20 hours, optionally

The objective of the lectures is to introduce fundamental theoretical descriptions of individual methods, their analyses, and in some cases also analytical solutions.
Topics of the lectures:
1. Modelling of relationships between microstructure and physical properties, history and presence.
2. Equilibrium statistical mechanics, spin models and their mean field solutions.
3. Phase space, phase trajectory, ergodic theorem, entropy.
4. Numerical methods for the minimizations of functions of N variables.
5. Crystallography and symmetry in the real and reciprocal spaces.
6. Molecular statics, atomic-level forces, energies and stresses in many-body systems.
7. Molecular dynamics, stability of numerically integrated equations of motions, thermostats, barostats.
8. More advanced interaction potentials and their physical origins.
9. Mesoscopic phase field models.
10. Phase field crystal model.
11. Methods for finding the minimum energy paths of systems.
12. Finite Element Method, shape functions and elasticity.
13. Modern trends in computational studies of materials.