intro

Computational Techniques in
Theoretical Physics

Three main methods for scientific investigation and problem solving:

Theoretical
Eperimental
Computational.

The computational aspect becomes more and more important:

Need to study complex systems (astronomy, ecosystems, chemistry and life-science).
Improved computational algorithms.
Advances in computer technology (availability of higher speed computers at lower cost).

Comparison with Other Scientific Methods:

Computational methods:

Scientific understanding through analysis of mathematical models on computers.

Advantage:

Insight.
Ability to deal with complex systems.
Cost decreasing, wider use.

Disadvantage:

Computer resource.
Difficulty in programming.

Theoretical methods:

Derivation of mathematical models logically from more fundamental models or laws of nature.
Interpretation of a phenomenon by analytical study of mathematical models.

Advange:

Insight.

Disadvantage:

Restricted to simplified models.

Experimental methods:

Scientific test on real objects.

Advantage:

Almost any system.

Disadvantage:

Few insight.
Increasing cost.

Computational methods become

advantageous when:

The problem at hand is too difficult to do analytically.
An approximate theoretical result may not be reliable, and it is necessary to check with a different method.
An experiment is not feasible or expensive.

Computational method has the flavors of both theoretical and experimental methods.

Good understanding of theoretical background of the subject to be investigated by computational method.

Analyses of results similar to analyzing experimental data.

Examples of simulations:

Chaos and fractals in dynamical systems.

Planetary motions.

Atomic motions in a chemical compound => Computer aided drug design.

Ibuprofen

Protein interaction with a drug

A protein complexed with a compound from Chinese natural product:

Computational science is a very large field

Any calculations of any systems using computers extensively and using algorithms based on scientific principles could be called computational science.

Simulation:

Computer analysis of the behavior of a system.

Classical Systems:

Systems obeying Newton's laws.

This module focuses on:

A few well established simulation methods
Illustration of methods by a few well studied examples
Familiarize with concepts by tutorials and homeworks, learn computer programming by lab assignments

These are outlined in Module Outline.