ACIT4320 Computational Methods in Modern Physics Course description

This course aims to equip the candidate with an arsenal of methods for tackling relevant problems in the scientific forefront of modern physics. Relevant examples will be taken from modern applications to physical sciences, such as astrophysics, electromagnetism, quantum physics, statistical physics and thermodynamics. The specific set of examples and the corresponding curriculum may to some extent be adjusted to the scientific interest of the candidates.

Necessary theoretical aspects related to numerical methods will be addressed only briefly. Depending on the students attending the course, the curriculum may also include an introduction to modern geometrical methods and manifold theory, and to their most important applications to physics and engineering. In any case, implementation of the relevant computational methods is essential. Problem solving and a student project will involve the use of computer programming. The candidate is free to use the programming language of his/her choice, e.g., MATLAB, Fortran, C(++) or Python.

Despite that the methods discussed in the course are applied in specific physics topics, the methods are generic and applicable to a variety of models, including models used in industry fields such as computer game engines, structural engineering and heavy industry.

While the candidate should have some experience with theoretical physics and mathematics, the main focus of this course, however, will reside on the various methods and their practical implementation. Thus, some programming experience is recommended. For those who need to refresh their programming, online resources for self-study will be made available.

No formal requirements over and above the admission requirements.

A student who has completed this course should have the following learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge

On successful completion of this course the student:

• is able to derive and implement several state-of-the-art techniques for solving relevant problems within modern physics.
• can apply integration techniques to relevant problems within physics.
• has the ability to obtain converged numerical solutions to partial differential equations such as the time dependent Schrödinger equation and the Einstein field equations in specific cases
• has knowledge of smooth structures on manifolds and is able to give examples of smooth manifolds and discuss their manifold properties
• has a thorough understanding of how computational methods in modern physics are applicable to industry, scientific computing and in general
• has knowledge of how experts from mathematical modelling and scientific computing can be useful in technologically oriented research and innovation teams in both private and public sector
• has knowledge about various computer infrastructures, such as cloud engines, as a platform for scientific computing and simulations

Skills

On successful completion of this course the student:

• can devise the solution of composite problems in modern physics from generic schemes.
• has knowledge about strengths and weaknesses of standard techniques within the relevant field and is thus able to make competent decisions as to which approach to apply to a given problem.
• can adapt, elaborate and improve on established numerical schemes in order to optimize their performance for specific examples within computational physics.
• is able to use the geometric concepts, techniques and tools associated with smooth manifolds in the analysis of mathematical problems in physics and engineering
• is able to implement and execute computational models in modern physics within the scope of applied computer and information technology

General competence

On successful completion of this course the student:

• is able to solve involved problems relevant to the forefront of research within modern theoretical and computational physics.
• can address the relevance of numerical and analytical methods within fields other than those specific to the student's background.
• can disseminate results and findings in an accessible, preferably graphical form - both through oral and written presentations
• is able to read and comprehend research articles within physics and engineering or related scientific areas which use the tools of manifold theory

• Monte Carlo techniques
• Splines (interpolation, expansion of numerical solution of PDEs)
• Diagonalization and exponentiation of matrices
• Applying certain methods for solving partial and ordinary differential equations to problems within modern physics
• Numerical problems in general relativity
• Manifolds with geometric structures central to physics and engineering
• Implementing and executing computations on cloud platforms

The main learning outcome of the course lies in the candidate's own implementation of the relevant numerical methods. Moreover, the student will evaluate, interpret and identify adequate means of presentation for the various results obtained. The lecturer will guide the student in these assignments in addition to introducing relevant theory.

The candidate is required to complete and present one individual project with a report which involves a rather extensive implementation of the numerical solution of a relevant problem from computational physics.

Practical training

Practical problem solving and implementation.

None.

One project work implementation and brief presentation of the candidate's project and oral examination. The project (report of 3000-5000 words and presentation) will count 50% of the final grade, while the remaining 50% will be based on the oral examination.

Both exams must be passed in order to pass the course. The oral exam cannot be appealed.

At the oral exam, the candidate is allowed to make use of her/his own computer for the presentation.

For the final assessment a grading scale from A to E is used, where A denotes the highest and E the lowest pass grade, and F denotes a fail.

Two internal invigilators/examiners will be present at the exam. External examiner is used periodically.