TFNPF0002 Numerical Modeling in Physics I

Institute of physics in Opava
summer 2025
Extent and Intensity
4/2/0. 8 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Jan Schee, Ph.D. (lecturer)
doc. RNDr. Jan Schee, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Jan Schee, Ph.D.
Institute of physics in Opava
Prerequisites (in Czech)
(FAKULTA(FU) && TYP_STUDIA(N))
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course introduces to the students fundamentals of numerical modeling of physical processes. The general theory is illustrated on specific, mostly astrophysical applications.
Learning outcomes
Passing the course a student acquires following skills:
- independently mathematically formulate physical problem,
- discretization of the problemu,
- choice of suitable numerical metod and solve problem along with and error estimate,
- results presentation in form of tables and plots of suitably chosen physical quantities describing the state of problem solution
Syllabus
  • The key topics of the course:
    • Physical quantities representation - scalars, vectors and matrices as arrays. Discretization of a problem. Integer numbers, Floating point numbers. Errors: roundoff, truncation. Finite precision arithmetic and error propagation.
    • Kinematics: tables and plots generation, state of particles – positions and velocities.
    • Kinematics: particle confined in a box(reflection from the walls), mutually interacting particles in the box (Brown motion), evolution of particles, velocity distribution.
    • Dynamics: equations of motion and their numerical integration, Euler and Runge-Kutta methods.
    • Dynamics: Particle on splring (1-D motion), planet motion and Rutherford scattering.
    • Dynamics: multi-particle systems, planar(2D) and spatial(3D) motion
    • Dynamics: system of non-interacting particles moving in central fields.
    • Dynamics: spherical cluster model, system of mutually, gravitationally, interacting particles.
    • Dynamics: Adaptive step Runge-Kutta methods, test particles motion in electromagnetic field, relativistic motion.
    • Gravitational lens:light escape cones and silhouette construction, Carter's equations, boundary conditions.
Literature
    recommended literature
  • PRESS, William H. Numerical recipes: the art of scientific computing. 3rd ed. New York: Cambridge University Press, 2007. ISBN 978-0-521-88068-8. info
  • Misner, C. W., Thorne, K. S., Wheeler, J. A. Gravitation, Freeman, San Francisco, 1973 (2017)
  • P. Schneider, J. Ehlers and E. E. Falco. Gravitational lenses. Springer, 1999. info
  • RYBICKI G. B., LIGHTMAN A. P. Radiative Processes in Astrophysics. Wiley-VCH, Weinheim, 2004. ISBN 978-0-471-82759-7. info
Teaching methods
Lectures. Exercises. Working out given project.
Assessment methods
oral exam, defense of final project
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms summer 2021, summer 2022, summer 2023, summer 2024.
  • Enrolment Statistics (summer 2025, recent)
  • Permalink: https://is.slu.cz/course/fu/summer2025/TFNPF0002