Taylor-Green vortex sheet, reduced units

The Taylor-Green vortex sheet is a solution to the 2D Navier-Stokes equations for an incompressible Newtonian fluid:

\frac{d \mathbf{u}}{d t}= \nu \nabla^2 \mathbf{u} - \nabla p/\rho ,

where \mathbf{u} is the velocity field, p is the pressure, \nu=\mu/\rho is the kinematic viscosity, and \rho is the fixed density of the fluid. The time derivative is a total derivative:

\frac{d \mathbf{u}}{d t} =  \frac{\partial \mathbf{u}}{\partial t} + (\mathbf{u} \cdot \nabla) \mathbf{u}

It is common to choose parameters that simplify the equations, but that can obscure the role of the different parameters. In the following, I provide expressions with all relevant parameters included, with their physical dimensions. I later pass to dimensionless, or reduced, units, in terms of the Reynolds and Courant numbers.

 

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Curriculum del Ministerio

Tres horribles palabras. Para cada convocatoria de cualquier proyecto se suele exigir en España un CV normalizado del Ministerio. (Bueno, son cuatro palabras.)

Una solución a la perspectiva de tener que actualizar a mano un documento (generalmente, con word) es la siguiente:

  • Utilizar el servicio de almacenamiento de CVs del Ministerio. Es un poco primitivo (intentar ordenar una lista larga puede ser frustrante), pero al menos es accesible desde cualquier sitio y cualquier convocatoria.
  • Ojo, hay campos opcionales que hay que rellenar: poner “0 investigadores” en un proyecto o da un error.
  • También está disponible en formae una versión offline en java de la herramienta.
  • Pedir una conversión a rtf. O, mejor, a LaTeX.
  • Corregirla:  ordenando listas de manera adecuada, borrando campos absurdos o vacíos (0 investigadores), poniendo bonita la parte de “Otros méritos” (con itemizes).
  • Compilar. El comando “\textbf{\hline}” que genera la apliación funciona, pero LaTeX se queja cada vez. Se puede sustituir por “\hbox to \textwidth{\hrulefill}”, que no da errores.

wikipedia: reliable sources

Here is what, for many, is a weak point in wikipedia: the sources. What is accepted as “true”. Here is a list of claims that may have been challenged in wikipedia, or not. See how many you get right!

  • About the katakana Japanese syllabary:  in a manga, the speech of a foreign character or a robot may be represented by, for example, コンニチワ konnichiwa (“hello”) instead of the more usual hiragana こんにちは.
  • About Hugo_Stiglitz (a character in Inglourious_Basterds): Fittingly, the character’s guitar riff theme is taken from Slaughter, a blaxploitation movie starring Jim Brown.
  • In the article about the film Watchmen: Classical music excerpts include Wagner’s “Ride of the Valkyries” in a Vietnam battle (a reference to Apocalypse now) and Mozart’s Requiem at the resolution in Antarctica.
  • Getting serious:  In the article about the well-known D’Alembert’s_paradox of hydrodynamics: Recently the following alternative resolution of d’Alembert’s paradox was claimed [7][8][9] … This is a different resolution from that by Prandtl and it is claimed to be supported by both theory, computation and experiment. Notice that Refs. 7, 8, and 9 correspond to two articles in peer-reviewed journals and a book published by Springer!

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The alpha shapes

Typical problem in computational geometry: given a set of points, what is its shape? This may often be intuitive for a human being, but try to define this concept mathematically, then implement it numerically.

One of the proposals is called the “α shape”, and is closely related to the Delaunay triangulation. More details below.

See also alpha shapes, for a recent application of this concept to molecular simulation. Check out the movie too!

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The CGAL project

CGAL logo

I have been following and using this project for some years now, on and off. In my opinion, a very remarkable cooperative effort of several research centers, coordinated at INRIA Sophia Antipolis. They provide very robust implementations of algorithms on computational geometry: Delaunay triangulations, Voronoi diagrams ski sums, meshes, alpha shapes, convex hulls, all that. Warning: very abstract C++ is needed (I actually learned C++ because of these libraries).

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La movida superficie de un líquido

(Yet another post in Spanish, since the news article is in this language! ). Se insiste mucho en esto, y por fin nos hemos decidido a tenerlo en cuenta: la divulgación de los resultados de la investigación. Aqui está La movida superficie de un líquido, que divulga nuestro último artículo en el JCP: en madrid+d y en plataformasinc. Continue reading

SklogWiki

SklogWiki is a wiki for people interested in simple liquids, complex fluids, and soft condensed matter. SklogWiki is particularly oriented towards theoretical and computational studies.

That seems to wrap it up. Speciallized wikis are a great idea (see wikia), and this one was created for topics that interest me a lot. The name comes from the famous formula for the entropy S = k log W, by Boltzmann (even if it seems he never wrote it this way).