Applications of knot theory in fluid mechanics

Knot Theory and its applications

Fluid Mechanics: Fundamentals and Applications

Symbolic-Numeric Applications in Fluid Mechanics

Although symbolic computing can be considered to have started in the 1960s (with the invention of the language LISP), it was not until the marketing of the computer algebra system Mathematica in the late 1980s that acceptance amongst scientists “took off”. Many systems beside Mathematica experienced increases in sales as a result of Mathematica’s marketing expertise. These days there are two ma...

Engineering Applications of Computational Fluid Mechanics

Turbulences in liquids caused by jets can be of interest for numerous applications. For one, it concerns flood spillway structures within civil engineering but also is key in any area where turbulent mixing is present. The numerical simulations of jets that impinge into plunge pools are still in an early phase of their development. This paper verifies the accuracy of the Flow-3D software packag...

Applications of statistical mechanics in number theory

The links between statistical physics and number theory are discussed. First the attempts to prove the Riemann Hypothesis by means of the suitable spin model and the Lee–Yang theorem about zeros of the partition function are shortly reviewed. Next, the analogies between random walks and prime numbers are mentioned. In the last section the partition function of the system whose energies are de n...