Computer simulations in physics by using characteristic examples

Participants lectures are required primarily an elementary information on the probability and mathematical statistics as well as classical mechanics.

Remote learning
Self-reading

The main goal of this lecture is to present typical, numerical methods for simulation and visualisation of some characteristic problems in classical and quantum mechanics as well as thermodynamics and statistical mechanics.

The main goal of this lecture is to present typical, numerical methods for simulation and visualisation of some characteristic problems in classical and quantum mechanics as well as thermodynamics and statistical mechanics. For example,

1. Elements of statistical thermodynamics of small systems

2. Transport, diffusion and relaxation

3. Dynamic properties of polimers

4. Disordered systems: amorphous (glossy) and alloys

5. Phase transitions in magnetism

6. Elements of deterministic chaos

All the problems are considered by using concrete simulations (examples). The numerical metods are as follows:

A. Probabilistic methods

A1. Static "hit and miss" Monte Carlo method

A2. Dynamic Monte Carlo methods (Metropolis et al, Glauber) & Ising-Kawasaki kinetic

approach

A3. Monte Carlo renormalization group technique

A4. Quantum Monte Carlo methods

A5. Probabilistic cellular automata

B. Deterministic methods

B1. Molecular dynamics for solution of the ordinary differential equations

B2. Molecular dynamics for solution of the partial differential equations

B3. Eigenproblems in quantum mechanics

Prerequisites: Classical mechanics, quantum mechanics, thermodynamics, statistical physics

Examination: Examination

[1] D. Potter, Computational Physics, J. Wiley & Sons, London 1973 (transl. to Polish exists).

[2] T. Peng, An Introduction to Computational Physics, Cambridge Univ., Cambridge 1997 (transl. to Polish exists).

[3] S.E. Koonin, Computational Physics, Benjamin, Menlo Park 1986.

[4] D.P. Landau, K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics, Cambridge Univ. , Cambridge 2000.

[5] Monte Carlo methods in statistical physics, Topics in Current Physics, Vol.VII, red. K. Binder, Springer-Verlag, Berlin 1979.

[6] Applications of Monte Carlo methods in statistical Physics, Topics in Current Physics, Vol.36, red. K. Binder, Springer-Verlag, Berlin 1984.

[7] R.W. Hockney, J.W. Eastwood, Computer simulation using particles, McGraw-Hill, New York 1981.

[8] D. Dahlquist, A. Björck, Numerical Methods, Prentice-Hall, 1974 (tranl. to Polish exists).

[9] A. Krupowicz, Metody numeryczne zagadnień początkowych równań różniczkowych zwyczajnych, Państwowe Wydawnictwa Naukowe, Warszawa 1986.

[10] D. C. Rapaport, The art of molecular dynamics simulation, Cambridge University Press 1998.

[11] R. Kutner, Elementy mechaniki numerycznej z oprogramowaniem komputerowym, WSiP, Warszawa 1991.

[12] R. Kutner, Elementy fizyki statystycznej w programach komputerowych. Cz.I. Podstawy probabilistyczne, WSiP, Warszawa 1991.

[13] J. Ginter, R. Kutner, Komputerem w kosmos, WSiP, Warszawa 1990.

[14] Fizyka i astronomia dla liceum ogólnokształcacego, liceum profilowanego i technikum. Kształcenie ogólne w zakresie podstawowym (wraz z oprogramowanien na CD), Nowa Era, Warszawa 2005.

[14] D. C. Rapaport, The art of molecular dynamics simulation, Cambridge University Press 1998.

After completion of the course the student obtained the following results in the field of education.

KNOWLEDGE

1) He knows the most important methods of statistical computer simulation of physical systems, mainly the basic Monte Carlo method based on Markov chain and process.

2) Knows basic `ab initio' deterministic methods of molecular dynamic simulations of physical systems.

SKILLS

1) He can formulate and represent the problems posed in the form of algorithmic.

2) He can independently design and carry out simulations of the effects, physical phenomena and processes of nature static and dynamic.

3) He can analyze and visualize (up-to-date in real time) the results of the computer simulations.

ATTITUDES

1) Appreciates the importance of a thorough and comprehensive understanding of the problem in drawing conclusions and making decisions.

It all corresponds to the following effects in the field of education (see information about studying at http://www.fuw.edu.pl/ ):

1) knowledge: KW01- KW06,

2) skills: KU05 - KU09,

3) competences: K04, K05.

EXPECTED STUDENT WORKLOAD:

- participation in classes (lectures 15h + exercises 15h): 30h - 1.0 ECTS,

- preparation for classes and the dissolution of homework: 30h - 1.0 ECTS,

- exam preparation: : 25h - 1.0 ECTS.

Completion of the course may be of two methods:

1) performance (in agreement with the lecturer) own design in the form of a computer simulation of the phenomenon or physical process,

2) by the traditional method in the form of a conversation.

Both methods require class attendance and active participation in them.

It is not expected