SubjectsSubjects(version: 953)
Course, academic year 2023/2024
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Numerical simulations in Matlab: applications in condensed matter physics and optics - NOOE137
Title: Numerické simulace v Matlabu: aplikace ve fyzice pevných látek a optice
Guaranteed by: Institute of Physics of Charles University (32-FUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022
Semester: summer
E-Credits: 4
Hours per week, examination: summer s.:0/3, MC [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: English
Teaching methods: full-time
Teaching methods: full-time
Guarantor: doc. RNDr. Jan Kunc, Ph.D.
Classification: Physics > Physics, Astronomy and Astrophysics, Biophysics and Chemical Physics, Ecology and Environmentalism, External Subjects, General Subjects, Geophysics, Mathematics for Physicists, Meteorology and Climatology, Mathematical and Computing Modelling in Physics, Nuclear and Subnuclear Physics, Optics and Optoelectronics, Solid State Physics, Surface Physics and P. of Ion.M., Teaching, Theoretical and Math. Physics
Annotation -
The main objective of the course is to provide fundamental concepts of a high-level programming in Matlab. The course is intended for students who want to gain hands-on experience with advanced numerical simulations. The numerical methods are demonstrated on several practical examples during the lecture. The hands-on experience will ease understanding several concepts taught in Solid State Physics courses. The modern methods employing machine learning algorithms will be beneficial for all students who want to perform in-depth analysis of their experimental data.
Last update: Heřman Petr, prof. RNDr., CSc. (18.03.2019)
Aim of the course -

The main objective of the course is to provide fundamental concepts of a high-level programming in Matlab. The course is intended for students who want to gain hands-on experience with advanced numerical simulations. The numerical methods are demonstrated on several practical examples during the lecture. The hands-on experience will ease understanding several concepts taught in Solid State Physics courses. The modern methods employing machine learning algorithms will be beneficial for all students who want to perform in-depth analysis of their experimental data.

Last update: Heřman Petr, prof. RNDr., CSc. (18.03.2019)
Course completion requirements -

The successful completion requires a numerical implementation of a given problem of the solid state physics or optics. The numerical implementation will be done in Matlab, the source code will be well documented and the student will be able to answer several questions concerning the source code.

Last update: Kunc Jan, doc. RNDr., Ph.D. (30.10.2019)
Literature - Czech

[1] D. Vasileska, S. M. Goodnick, G. Klimeck, Computational Electronics, Semiclassical and Quantum Device Modeling and Simulation, CRC Press 2010.

[2] Computational Electromagnetics with Matlab, Matthew N. O. Sadiku, CRC Press 2019

[3] Electromagnetic Waves, Materials, and Computation with Matlab, Dikshitulu K. Kalluri, CRC Press 2012

Last update: Heřman Petr, prof. RNDr., CSc. (18.03.2019)
Requirements to the exam -

The successful completion requires a numerical implementation of a given problem of the solid state physics or optics. The numerical implementation is given as a homework. The numerical implementation will be done in Matlab, the source code will be well documented and the student will be able to answer several questions concerning the source code.

Last update: Kunc Jan, doc. RNDr., Ph.D. (30.10.2019)
Syllabus -

(1) Introduction

Matlab basics, global and local functions, function handles, scripts, live scripts, basic mathematical operations, the numerical representation of matrices, linear indexing, matrix inversion, numerical integration, interpolation, extrapolation, data smoothing by polynomial function or by median

(2) Graphical tools in Matlab

Plotting function of one and two variables, drawing 2D and 3D graphs, plot labels, shading, lighting, curves in 3D, creating dynamical animations

(3) Non-linear algebraic equations

Fermi level in a doped semiconductor with impurities. Chemical potential temperature dependence.

(4) Non-linear curve fitting

Curve fitting, including the estimation of the fitted parameters' errors.

(5) Ordinary differential equations

Explicitly and implicitly defined ordinary differential equations, sets of ODEs

(6) Partial differential equations in 1D

Solving PDE in one spatial coordinate and time

(7) Partial differential equations in 2D

Definition of problems, eigenvalue problem, geometry specification, triangulation, mesh refining, drawing edges and domains, boundary conditions of the Dirichlet, Neumann and Robin type. Evaluating the solution, drawing the solution, gradient calculation, vector field

(8) Partial differential equations in 3D

Major differences with 2D, defining geometry (AutoCAD, Blender), drawing the solution, solution cross-sections, flows, surface solution

(9) Tight-binding method

Band structure of the graphene nanoribbons.

(10) Selected methods of machine learning

Non-negative matrix factorization, spectral clustering, K-means, K-medoids, Singular value decomposition, etc. are used for advanced experimental data analysis.

Last update: Kunc Jan, doc. RNDr., Ph.D. (07.06.2023)
 
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