Computational Methods in Modern Physics

Course Description

Different computing methods used for simulations in contemporary physics problems are presented through four topics. 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.

Learning Outcomes

  1. Describe the curved spacetime and light trajectories in the curved spacetime.
  2. Apply ray tracing technique to optics problems.
  3. Describe the crystal lattice and interatomic forces.
  4. Apply the concept of force and energy to finding the optimum configuration of a system.
  5. Explain the concept of short and long range interactions.
  6. Identify quantitatively abrupt structural change in a system.
  7. Apply a machine learning algorithm to a classification problem.

Forms of Teaching

Lectures

Exercises

Independent assignments

Week by Week Schedule

  1. High-energy physics events
  2. High-energy physics events, Application of machine learning to event classification
  3. Application of machine learning to event classification
  4. Metric in curved spacetime
  5. Geodesic equation, Metric in curved spacetime
  6. Geodesic equation, Tracing photon trajectories
  7. Tracing photon trajectories
  8. Midterm exam
  9. Van der Waals force interactions
  10. Van der Waals force interactions, Graphene layers
  11. Graphene layers
  12. Percolation concepts; Abrupt transitions in behavior; Long range connectivity
  13. Percolation concepts; Abrupt transitions in behavior; Long range connectivity
  14. Electrical conductivity in composite materials
  15. Final exam

Study Programmes

University undergraduate
Computing (study)
Elective Courses (6. semester)
Electrical Engineering and Information Technology (study)
Elective Courses (6. semester)
University graduate
Audio Technologies and Electroacoustics (profile)
Free Elective Courses (2. semester)
Communication and Space Technologies (profile)
Free Elective Courses (2. semester)
Computational Modelling in Engineering (profile)
Free Elective Courses (2. semester)
Computer Engineering (profile)
Free Elective Courses (2. semester)
Computer Science (profile)
Free Elective Courses (2. semester)
Control Systems and Robotics (profile)
Free Elective Courses (2. semester)
Data Science (profile)
Free Elective Courses (2. semester)
Electrical Power Engineering (profile)
Free Elective Courses (2. semester)
Electric Machines, Drives and Automation (profile)
Free Elective Courses (2. semester)
Electronic and Computer Engineering (profile)
Free Elective Courses (2. semester)
Electronics (profile)
Free Elective Courses (2. semester)
Information and Communication Engineering (profile)
Free Elective Courses (2. semester)
Network Science (profile)
Free Elective Courses (2. semester)
Software Engineering and Information Systems (profile)
Free Elective Courses (2. semester)

Literature

(.), V. Šips, I. Rendulić: Uvod u fiziku čvrstog stanja,
(.), General Relativity, MIT OpenCourseWare https://ocw.mit.edu/ans15436/ZipForEndUsers/8/8-962-spring-2006/8-962-spring-2006.zip,
(.), Modelling Environmental Complexity, Percolation Theory chapter, MIT OpenCourseWare https://ocw.mit.edu/courses/earth-atmospheric-and-planetary-sciences/12-086-modeling-environmental-complexity-fall-2014/lecture-notes/MIT12_086F14_percolation.pdf,
(.), Albert, J., et al. (2008). Implementation of the random forest method for the imaging atmospheric Cherenkov telescope MAGIC. Nuclear Instruments and Methods in Physics Research A, 588, 424,

For students

General

ID 183467
  Summer semester
5 ECTS
L3 English Level
L1 e-Learning
45 Lectures
13 Laboratory exercises