University of Twente

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Advanced Fluid Mechanics

Fluid mechanics is a subject with a long and rich history. Advanced Fluid Mechanics is a graduate-level fluid mechanics course where you will learn about several fluid dynamics processes using established mathematical analyses. A plethora of topics, from conservation laws and Stokes flows to waves, instabilities, and geophysical flows, will help you appreciate the richness of the field. Although the course is of particular interest for students from Applied Physics and Mechanical Engineering, the topics would be of interest to Biomedical and Chemical Engineering students as well.

Utrecht University

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Turbulence in Fluids

taught by Anna von der Heydt and Aarnout van Delden

It outlines that the student is capable of distinguishing between laminar and turbulent flows while characterizing their fundamental properties. They are proficient in performing linear stability analysis on basic fluid flow examples and analyzing instabilities and turbulence using key mathematical techniques such as bifurcations, chaos theory, stochastic events, and probabilistic descriptions of turbulent flows.

The student also understands the physical mechanisms driving fluid instabilities, including phenomena like the Kelvin-Helmholtz instability and Rayleigh-Bénard convection, which lead to transitions to turbulence. They have a solid grasp of foundational theories on turbulent flows, encompassing dimensional and scaling arguments, conserved quantities, the turbulent energy cascade, and Kolmogorov theory. These principles can be applied to geometrically simple flow conditions.

Additionally, the student possesses foundational knowledge of intermittency and corrections to basic turbulence theories and is familiar with numerical modeling approaches for these phenomena. Lastly, they are capable of calculating the transport properties of fundamental turbulent flows.

Statistical Physics

taught by Peter van Capel

After completing this course, you will be familiar with the elementary principles of thermodynamics and statistical physics. You will be able to apply these principles to theoretically calculate the behavior of relatively simple (mostly ideal, non-interacting) classical many-body systems in thermodynamic equilibrium. You will also be able to integrate this theoretical knowledge in the execution of an experimental investigation and a numerical simulation, to use it in quantitative analysis and interpretation of results, and to report your research in writing in the form customary in the exact sciences. Example research topics: the relations between thermodynamic quantities such as pressure, temperature and volume in a gas, phase transitions, Brownian motion.

Subatomic Physics

taught by Panos Christakoglou

This text outlines a set of learning objectives related to relativistic mechanics, quantum field theory, and the Standard Model of particle physics. The student is capable of working with covariant and contravariant vectors and performing transformations between different inertial systems. They can apply relativistic mechanics to calculate particle decays and collisions.

The student is proficient in deriving equations of motion for classical systems as well as relativistic field equations and performing calculations for various types of relativistic fields. They can identify the building blocks of the Standard Model, including leptons, quarks, gauge bosons, and their quantum numbers. Additionally, they can distinguish between the three fundamental interactions of the Standard Model—electromagnetic, weak, and strong—along with their corresponding force carriers, and understand the conservation laws associated with each interaction.

The student is adept at using Fermi’s golden rule to calculate scattering cross-sections and decay processes. They can compose and interpret Feynman diagrams to represent basic interactions between subatomic particles. Furthermore, the student can explain the origins of the terms in the QED and QCD Lagrangians and derive these terms using appropriate gauge transformations.

Finally, the student can apply the Feynman rules for QED and QCD to formulate the matrix elements of basic processes and effectively connect theoretical predictions with experimental results.