Computational Methods in Modern Physics

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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

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

Forms of Teaching

Lectures

Exercises

Independent assignments

Week by Week Schedule

High-energy physics events
High-energy physics events, Application of machine learning to event classification
Application of machine learning to event classification
Metric in curved spacetime
Geodesic equation, Metric in curved spacetime
Geodesic equation, Tracing photon trajectories
Tracing photon trajectories
Midterm exam
Van der Waals force interactions
Van der Waals force interactions, Graphene layers
Graphene layers
Percolation concepts; Abrupt transitions in behavior; Long range connectivity
Percolation concepts; Abrupt transitions in behavior; Long range connectivity
Electrical conductivity in composite materials
Final exam

Study Programmes

University undergraduate

Computing (study)

Elective Courses (6. semester)

Electrical Engineering and Information Technology (study)

Elective Courses (6. semester)