Welcome to the homepage of Ulrich Mutze

July 2011 
Contact information
Neue Steige 1
D73342 Bad Ditzenbach
 phone: +49(0)7335 5786
 email: ulrichmutze at gmx dot de
 orcid: 0000000171164262
Graphics of the month

Graphical spinoff from testing the direct midpoint integrator

Graphics of the month archive
Testpatterns in high resolution (4k by 4k pixel, PNGformat, 477 kB), free download
This is a lowresolution version of testpattern.png:
The patterns are made of patches of the 9 colors Red, Green, Blue, Magenta,
Yellow, Cyan, Black, Gray, White. For each pair of these colors there are
places in the pattern where these colors meet along a line. This
colorseparating lines can be found to form nearly any angle with the lines
and the columns of the pixel pattern. Further, the color patches all are of
the same shape and vary only in size and orientation. The size varies over
quite large a range. To find a pattern with these properties was suggested
by John Weldy and the solution here was developed by Helmut Domes and me
when we all were working for Eastman Kodak Company.
Latest versions of electronic articles on Computation Inspired Physics, mainly dealing with
computational methods for Classical Mechanics and Quantum Mechanics
For most of these articles an early version is stored in the
preprint archive of the
International Association of Mathematical Physics
or in the
arXiv preprint archive.
 Predicting Classical Motion Directly from the Action Principle II
 keywords: Kepler equation, unharmonic oscillator, symplectic integrator, planetary motion
 Predicting Classical Motion Directly from the Action Principle III
 keywords: motive force function, local action principle, parabolic path, midpoint rule, integrator
 A Simple Variational Integrator for General Holonomic Mechanical Systems
 keywords: direct midpoint method, smooth interpolation, small step action principle, BirkhoffWitt basis
 The Fundamental Theorem of Calculus in R^{n}
 keywords: antiderivative, repeated integrals, electrostatic potential, charge patch, Mathematica
 Quaternions  Redundancy + Efficiency = Ternions
 keywords: rotation vectors, EulerRodrigues parameters, computer graphics
 The direct midpoint method as a quantum mechanical integrator
 keywords: discrete Laplacian, finitedimensional quantum mechanics, scattering, energy conservation, unitarity
 The direct midpoint method as a quantum mechanical integrator II
 keywords: leapfrog method, Chebyshev method, timedependent Hamilton, reversible, symplectic
 Polyspherical grains and their dynamics
 keywords: EulerRodrigues parameters, random generator, surface roughness, energy restoration, PaLa program
 Separated quantum dynamics
 keywords: adjacent nonidentical particles, TDHF, fast integrator, spin chain, energy conservation, norm conservation
 An asynchronous leapfrog method
 keywords:leapfrog integrator, numerical initial value problem, Kepler oscillator, (skew)symplectic integrator,
numerical interaction picture
 Quantum Image Dynamics  an entertainment application of separated quantum dynamics
 keywords: asynchronous leapfrog integrator, image manipulation, animation
 Precisiondependent symmetry breaking in simulated motion of polyspherical grains
now with updates
 keywords: rigid body dynamics, multiple precision arithmetic, mirror symmetry, polyspherical particles
 Higherdimensional antiderivatives and the efficient computation of electrostatic potentials
 keywords: fundamental theorem of calculus, discrete Greens's theorem
 An asynchronous leapfrog method II (Nov 2013, 14 MB, http://www.arxiv.org/abs/1311.6602) now in arXiv
 keywords:leapfrog integrator, numerical initial value problem, Kepler oscillator, (skew)symplectic integrator,
numerical interaction picture, stiff problem, stability, set of absolute stability
 On a deterministic disguise of
orthodox quantum mechanics in arXiv
 keywords: interpretation of quantum mechanics, pseudorandom generator, simulation
Pedagogical remarks on mathematical or physical topics
Work in progress or recently finished
Physics animations, done by means of
Collection of files in the Computable Document Format (cdf). Needs the free Wolfram CDF Player.
Presently the following files work with version 10 of the CDF Player.
Talks
Curriculum vitae
Picture Gallery
Publications
Cornell University press release
Scientific Software by Ulrich Mutze
is a small and clean sublanguage of C++
 particularly suited for physical and mathematical modeling and visualization
 supports multiple precision arithmetic (via gmp and float128)
 cooperates with boost, glut, GL, GLU, gmp, EIGEN
 implements move semantics and 'copy on write' functionality for all
cpm array types
 treats functions as values, makes good use of lambda expressions,
std::function<> and (rarely) concepts
 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:
= C + − = C plus minus = C Plus Minus = CPM =
Classes for Physics and Mathematics =
Classes for Physics and Mathematics
line graphics capability
 A diagram which symbolizes the Multiple Path Method.
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 redgreen(blue) glasses.
Here is a version (with spherical particles instead of polyspherical ones)
of Fig. 1 of Precisiondependent symmetry breaking in simulated motion of polyspherical grains which gives a clearer
effect than the original for my redgreen glasses branded Apramax.
This functionality was suggested by Bernhard Mutze.
software descriptions
code and Code::Blocks project files
 how to use

All cpmsources and some projects in natural directory structure, not zipped here
 Who considers using
should also consider to send me a mail so that I can
help to make this a success.
Free Ruby code
Alpinism
Last modification: 20231031 11:05:03 +0100