Detail předmětu

Multilevel Modelling of Materials

CEITEC VUT-DS136AAk. rok: 2024/2025

Multiscale modeling of materials is an essential approach to understanding the properties between microstructure and macroscopic physical properties of materials. Atomistic methods based on empirical and semi-empirical potentials and Monte Carlo methods represent effective and commonly used tools for computer simulations of nanostructures (thin fibers, nanotubes, epitaxial layers, graphene), studies of radiation damage, moving dislocations under tension, solid solutions, phase transformations in multiferroics, and the like. In this course, the students will gain knowledge about the methods of computer modeling of materials from atomic level to macroscopic studies based on the finite element method. The individual methods will be demonstrated on simple examples that either allow analytical solution or can be studied using a simple program. In a series of individual assignments, students will gain practical experience with the implementation of these algorithms using Python and with methods of data visualization. Personal experience with the implementation of these approaches is a prerequisite for the systematic use of commonly available simulation programs and for the independent solution of research projects.  

Jazyk výuky

angličtina

Vstupní znalosti

The knowledge of mathematics at the 2nd year of FME (differentiation of functions of several variables, probability theory, numerical methods) and basic knowledge of programming is expected. Basics of programming in Matlab, Python, eventually. C or Fortran are an advantage, but not a requirement. 

Pravidla hodnocení a ukončení předmětu

Each student will be assigned an individual work, which will be related to some of the discussed methods. The output of these assignments will be the creation or modification of an existing simulation program, its use for solving the given problem and a written report summarizing the problem formulation, solution and main results of these simulations. The exam will consist of an oral defense of this work. 

Učební cíle

The aim of the exercises is to get acquainted with computer implementations of individual models, which will allow detailed understanding of inputs, methods and results obtained from commonly used commercial and open-source programs for simulating microstructure and physical properties of materials. 


Základní literatura

D. Frenkel, B. Smith: Understanding molecular simulation. Academic Press (2002). (EN)
E. H. Stanley: Introduction to phase transitions and critical phenomena. Oxford Science Publications (1987) (EN)
J. P. Sethna: Statistical mechanics: Entropy, order parameters, and complexity. Oxford University Press (EN)
K. G. Wilson: Problems in physics with many scales of length. Scientific American 241 (1979) 140–157. (EN)
M. P. Allen, D. J. Tildesley: Computer simulation of liquids. Clarendon Press (1987). (EN)