Time for the family to celebrate... and to recover from the advent puzzles epidemic 😉

• Advent of Code - with solutions done with HAC
  
• Mathe im Advent
• MATH+ Adventskalender
• EXIT - Das Spiel: Adventskalender

  Merry Christmas to everybody!

Played with a old numerics code of mine rescued from a backup CD, cleaned up, and put now on SourceForge and GitHub (spot the file "three_lakes.adb" in the diff_eq/ode/ directory)...

The problem is to predict the evolution of levels of three lakes connected by two channels, given some knowledge of the inflows and outflows.
Thanks to the magic of differential equations, it is possible!
The variation of each level is a function of the in- and out-flows, and of the flow from / to neighboring lakes.
If lake X is connected to Y, there is a flow from X to Y if X's level is higher than Y's.
When X's level is lower than Y's, the flow reverses.
Obvious, isn't it?


So, the program solves a vectorial differential equation, with the famous Runge-Kutta method.
The unknown x is a vector containing the levels of three lakes (Bienne, Neuchâtel, Morat in Switzerland).
The lakes are connected by two channels (marked with "in out" on the map).
Boundary conditions take the form of natural inflows (marked "in") into the lakes,
and a single, controlled outflow (marked "out") out of one of the lakes (Bienne).
The variation of all levels is x', a function of x and of the boundary conditions.

Even with static boundary conditions, we can have situations where one of the lakes' level goes up, then down, then up again. Finally (due to the artificial static conditions) the flows find an equilibrium.

Click to enlarge

A change in level direction (up/down) of one of the lakes (Neuchâtel) happens at the moment when two connected lakes have the same level, and the connecting channel changes its direction (points marked with arrows). You see also a change of direction of lake of Bienne's level, a bit later.

Of course in reality, the boundary conditions vary all the time, so we can have much more complex situations if these conditions are injected into the simulation.

Related publication:
   Évolution simulée des niveaux dans le système des Trois-Lacs,
   F. & G. de Montmollin,
   Bulletin de la Société vaudoise des sciences naturelles.
   88.2: 121-129, ISSN 0037-9603, 2002

Here is a wonderful picture of the lake of Bienne taken a few days ago (courtesy of Stéphane Perret).

Click to enlarge

New GitHub mirrors, for open-source projects I'm administrator or developer of, are located here.
Please ignore the old mirrors that relied on svn2github. If you see "svn2github" somewhere on a repository address, it's the old one → trash it!

You can find the same projects on SourceForge too, here.

The projects are...

Ada Bar Codes	bar code (1D and 2D) generator in pure Ada
Ada PDF Writer	a standalone, portable package for producing dynamically PDF documents
AZip	a free, portable Zip Archive Manager
Corporate Bullshit Generator	the Corporate Bullshit Generator
Engine_3D	a real-time, pure software, 3D engine for DOS-talgics
Excel Writer	a standalone, portable Ada package for producing Excel spreadsheets
GID	Generic Image Decoder
GLOBE_3D	a real-time 3D Engine written in Ada
GNAVI: GNU Ada Visual Interface	the GNU Ada Visual Interface
GNOGA	the GNU Omnificent GUI for Ada
HAC	HAC Ada Compiler
Ini file manager	a standalone, portable Ada package for configuration files
LEA	Lightweight Editor for Ada
Mathpaqs	collection of mathematical, 100% portable, packages in Ada
Pascal-to-Ada	Pascal to Ada translator
TeXCAD	a program for drawing or retouching {picture}s in LaTeX
Wasabee	a Web browser with safety focus
Zip-Ada	a standalone, portable Ada library for Zip archives