Computational Techniques in
Theoretical Physics

• Three main methods for scientific investigation and problem solving:

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• 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.
• Insight.
• Ability to deal with complex systems.
• Cost decreasing, wider use.
• 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.
• Insight.
• Restricted to simplified models.
• Experimental methods:
• Scientific test on real objects.
• Almost any system.
• Few insight.
• Increasing cost.
• Computational methods become

• 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.