Computing Methods of Modern Physics

Course Description

Ray tracing in curved spacetime: Spacetime. Curved spacetime. Metric. Path length. Riemannov tensor. Einstein s equation and spherically symmetric solutions. Light propagation in curved spacetime. Numerical solutions of differential equation. Ray-tracing. Gravitational lens. Application of machine learning to event classification in high energy physics: Introduction to ground-based gamma-astronomy: observed objects and instruments. Data acquisition and analysis chain. Event reconstruction. Problem of signal separation in the presence of high levels of noise. Application of random forest algorithm to the gamma-hadron separation problem in high energy physics. Material surface adsorption: Chemisorption and physisorption. Van der Waals force. Crystal lattice. Van der Waals material layers (graphen as an example). Simulating Van der Waals material adsorption onto a surface. Finding optimal orientation of adsorbed material with respect to the substrate layer. Percolation, application to material properties: Percolation concepts. Abrupt transitions in material behavior. Long range connectivity. Electrical conductivity in composite materials. Tunneling effects. Monte Carlo simulations of materials, comparison with measured properties.

General Competencies

Students will learn how to apply computational methods (numerical and analytic) by studying modern physics problems i.e. 20th and 21st century physics topics: quantum mechanics, quantum solid state physics and classical and quantum solitons. Special attention will be given to situations where standard analytic methods are not applicable. Students will simulate motion of quantum particle in different quantum potentials. They will acquire and develop computational skills by solving problems in gravitational theory and cosmology as well.

Learning Outcomes

  1. Explain the gravitational lens effect.
  2. Apply appropriate numerical methods for solving differential equations to the problem of finding light trajectories in curved spacetime.
  3. Explain the process of atmospheric particle shower creation initiated by high energy photons.
  4. Apply machine learning methods to event classification.
  5. Describe the origin and properties of van der Waals forces.
  6. Apply computer modelling to the problem of finding energy minimum of a given system configuration.
  7. Apply computer modelling to the percolation phenomena.

Forms of Teaching

Lectures

Lectures with the AV support and a computer package "IQ" for QM simulations.

Exams

Midterm exam, homework assignments with problems, final exam.

Exercises

Within lectures problems will be solved. Also examples will be discussed by using a progam package for QM simulation.

Laboratory Work

Simulation of quantum mechanical processes on a computer. Simple problems solved on a computer.

Consultations

Consultations will be organized in a direct contact with students.

Seminars

Each of the students will be assigned a special topic which will be shortly presented during lectures.

Grading Method

Continuous Assessment Exam
Type Threshold Percent of Grade Comment: Percent of Grade
Laboratory Exercises 0 % 10 % 0 % 10 %
Homeworks 0 % 10 % 0 % 10 %
Seminar/Project 0 % 10 % 0 % 10 %
2. Mid Term Exam: Written 0 % 20 % 0 %
Final Exam: Written 0 % 50 %
Exam: Written 0 % 30 %
Exam: Oral 40 %

Week by Week Schedule

  1. Spacetime. Curved spacetime. Metric. Path length.
  2. Riemannov tensor. (možda sljedeći tjedan) Einstein’s equation and spherically symmetric solutions.
  3. Light propagation in curved spacetime. Numerical solutions of differential equation.
  4. Ray-tracing. Gravitational lens.
  5. Introduction to ground-based gamma-astronomy: observed objects and instruments. Data acquisition and analysis chain.
  6. Event reconstruction. Problem of signal separation in the presence of high levels of noise.
  7. Application of random forest algorithm to the gamma-hadron separation problem in high enery physics.
  8. Midterm exam
  9. Chemisorption and physisorption. Van der Waals force.
  10. Crystal lattice. Van der Waals material layers (example graphen).
  11. Simulating Van der Waals material adsorption onto a surface. Finding optimal orientation of adsorbed material with respect to the substrate layer.
  12. Percolation concepts. Abrupt transitions in material behavior. Long range connectivity.
  13. Electrical conductivity in composite materials. Tunneling effects.
  14. Monte Carlo simulations of materials, comparison with measured properties.
  15. Final exam

Study Programmes

Electrical Power Engineering -> Electrical Engineering and Information Technology (Module)

Software Engineering and Information Systems -> Computing (Module)

Literature

Valeri P. Frolov, Andrei Zelnikov (2011.), Introduction to Black Hole Physics, Oxford University Press
H. Kasai, P. Lazić (2016.), Physics Of Surface, Interface And Cluster Catalysis, Ch.2, IOP Publishing Ltd
Myra Spiliopoulou, Lars Schmidt-Thieme, Ruth Janning (2013.), Data Analysis, Machine Learning and Knowledge Discovery, Springer Science & Business Media
Zheng et al. (2011.), Characteristics of the Electrical Percolation in Carbon Nanotubes/Polymer Nanocomposites, American Chemical Society

Lecturers in Charge

Grading System

4 ECTS
L3 English Level
L1 e-Learning
30 Lecturers
0 Exercises
15 Laboratory exercises

Grading

90 Excellent
80 Very Good
70 Good
60 Acceptable