Homepage of Ulrich Mutze

Physics animations

• Osmosis, stereo (red-green glasses needed, red for left eye) movie0
• Action principle for the spinning top, movie1
• Comparing exact and separated quantum dynamics, movie2
• Comparison of integrators with respect to interaction picture dynamics of the Kepler oscillator movie3
• Comparison of integrators with respect to interaction picture dynamics of the Kepler oscillator movie4

Talks

• Modeling the Toning Process in Electrophotographic Copiers/Printers (2004) ica1 Additions concerning the Lie algebra of the Euclidean group and on the corresponding exponential function and its logarithm.
• The direct midpoint method as a quantum mechanical integrator III (2007) badhonnef

Curriculum vitae

curriculum vitae

Picture Gallery

gallery

Publications

list of publications   a 1978 paper hosted by project euclid   front pages of published papers   single-authored patent 1   single-authored patent 2  

Cornell University press releases

• Center for Advanced Computing
• Cornell Theory Center

Scientific Software by Ulrich Mutze

is a small and clean sub-language of C++

• particularly suited for physical and mathematical modeling and visualization
• supports multiple precision arithmetic (via MPFC++) and parallel computing (via MPI)
• implements reference counting, copy on write, and safe indexing for all its array types
• treats functions as values
• employes short names which result from descriptive full names by a simple deterministic abbreviation scheme
• side effects of function calls can be read off the function's name
• comes with a large collection of classes for physics, mathematics, graphics, and imaging
• consider the metamorphosis between the two intended meanings of the logo:

line graphics capability

• A diagram which symbolizes the Multiple Path Method of article1. Here is a listing of the code which defines the diagram. It mainly uses the classes Wrt and LineArt, methods to combine such objects into a single one that can be moved in 3D space as a whole and then can again be combined with further objects to a single object that can be moved as a whole ... When, in 1999, I tried to create such a diagram with the commercial drawing program that was available within my Company, the program always crashed long before the work was completed. Notice that file cpmlineartcpp.h, which contains the definition all letters (latin and greek, lower case and upper case, punctuation and special symbols) is with 63 kB the largest of the CPM files. A further diagram which illustrates lines and areal color.
• How the action principle determines the system path for given initial conditions.

stereo (anaglyph) imaging capability

• By editing file cpmconfig.ini one now can vary the colors used in creating stereo images. This allows minimizing color crosstalk for ones own red-green(blue) glasses. Here is a version (with spherical particles instead of polyspherical ones) of Fig. 1 of article12 which gives a clearer effect than the original for my red-green glasses branded Apramax. This functionality was suggested by Bernhard Mutze.

software descriptions and binaries

• On the project
• The tutorial
• Listing of the basic classes
• Listing of all classes, last version without multiple precision arithmetic   current version
• Listing of all files of program vqm2 (visual quantum mechanics 2)
• Listing of all files of program chebyshev
• Listing of all files of program PaLa
• Windows executable pala_distribution of program PaLa (unpack to an arbitrary folder and run palaMS.exe, no installation)

Free code

• Demo project Chebyshev (third project of the tutorial, treating functions as values), chebyshev.zip   exemplary project output
• Demo project tut2 (second project of the tutorial, integrators for dynamical systems), tut2.zip  
• Small demo project test_cpm0, test_cpm0.zip  
• Demo project action (visalization of the action principle in mechanics), action.zip  
• Quantum mechanics project vqm2 (visual quantum mechanics 2), vqm2.zip  
• PaLa (Particle Lab, dynamics of polyspherical particles; the logo shows Cima della Madonna, a summit in the Pala subgroup of the Dolomites, Eastern Alps), pala.zip  
• Research project Spinning Top, studying a novel integrator for rigid body dynamics. This is a convenient project to test since the file set is relatively small and no graphical libraries are needed. Graphical output is as ppm-image-files (which can be viewed e.g. by means of IrfanView). spinningtop.zip  
• Complete file set cpm.zip  
• Who considers using should also consider to send me a mail so that I can help to make this a success.

Free Ruby code

• Applied Mathematics coded in Ruby. So far, only very limited material is presented, all collected in a Ruby module named AppMath. This is intended as a field of experimentation to find out and define coding conventions and tools which allow algorithms of applied mathematics and physics to be written in a manner that the precision, that is the number of digits allowed for the significand of a real number, is completely open. In the present system, one needs a single statement R.prec = 100 (for instance) to enforce throughout a floating point number representation using 100 decimal digits for the significand of a real number. A statement R.prec = 0 lets all real values represented by the standard Ruby type Float. Notice that this is a fixation that is valid for all floating point calculations, so that the precision has not to be inputted in each function call. The user-interface is very much simpler than that of the GMP library. Efficient arbitrary precision arithmetic is a very special topic. The deeper functionality of class R (a class, what else?) is implemented on the basis of class BigDecimal and module BigMath created by Shigeo Kobayashi. What I added was an implementation of all elementary transcendental functions by rapidly convergent series and a unification of R and Float (by extending the interface of Float) so that in designing an algorithm one has not to decide which kind of floating point machinery (and precision) to use for execution. Notice that in R (and in the extended Float)the traditional functions are methods, so that we write x.sin and not sin(x). It is hard to believe how much this adds to the readability of algorithms! The easiest way to test the present code system is to download the zip-file all files zipped and to unpack it into a directory from which you can access ruby.exe. For some programs one needs also Tk. There are presently three applications rnum_app.rb, linalg_app.rb, and kepler_2d_app.rb which allow several selections. For a fast and convenient information, visit the auto-generated documentation files (rdoc files) for the various *.rb files to which the following points refer. Notice that this kind of documentation allows reading the code for all methods and other definitions. That of method step! of class AppMath::Kepler2D is particularly beautyful.
• Real number class R for arbitrary precision arithmetic and transcendental functions. rdoc files
• Complex number class C for arbitrary precision complex arithmetic and transcendental functions. rdoc files
• Extending class Float in order to provide all methods of R rdoc files
• Classes Vec and Mat of vectors and matrices which cooperate with R and C. Includes singular value decomposition (SVD) of real matrices (unfortunately not yet for complex matrices). rdoc files
• Classes Graph and Graphs for graphical representation of functions via Tk. It is striking to see the standard functions like sin or erf be graphically represented (see the screen shot functions) when the algorithms for their evaluation are forced to use only two-digits accuracy! rdoc files
• Class Iv of real intervals rdoc files
• Class Ran of random generators rdoc files
• Classes R2 and Kep2D dealing with the two-dimensional Kepler problem. Here, the quantities, which for exact dynamics are constant in time (energy, angular momentum, Runge-Lenz vector) are shown graphically for a time-discrete simulation by means of the direct midpoint integrator. See the screen shot Kepler. It turns out that the non-constancy of the angular momentum in the simulation is always by numerical noice (and thus becomes arbitrarily small by working with 100 digits, 200 ditgits, .... For the other quantities there are deviations from constancy which are due to the integrator mehod. These become aritrarily small only if the time step of the simulation becomes aritrarily small. rdoc files
• Now all this stuff is also on the RubyForge server packaged as a gem named appmath-0.0.1.gem which is very conveniently installed on any computer which runs RubyGem. See Applied Mathematics.