Welcome to the homepage of Ulrich Mutze

July 2011

Contact information

• phone: +49(0)7335 5786
• email: ulrichmutze at gmx dot de
• orcid: 0000-0001-7116-4262

Graphical spin-off from testing the direct midpoint integrator

archive

This is a low-resolution version of testpattern.png:

• testpattern.png
• testpattern2.png

Latest versions of electronic articles on Computation Inspired Physics, mainly dealing with computational methods for Classical Mechanics and Quantum Mechanics

• 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, Birkhoff-Witt basis
• The Fundamental Theorem of Calculus in Rⁿ
keywords: anti-derivative, repeated integrals, electrostatic potential, charge patch, Mathematica
• Quaternions - Redundancy + Efficiency = Ternions
keywords: rotation vectors, Euler-Rodrigues parameters, computer graphics
• The direct midpoint method as a quantum mechanical integrator
keywords: discrete Laplacian, finite-dimensional quantum mechanics, scattering, energy conservation, unitarity
• The direct midpoint method as a quantum mechanical integrator II
keywords: leap-frog method, Chebyshev method, time-dependent Hamilton, reversible, symplectic
• Polyspherical grains and their dynamics
keywords: Euler-Rodrigues parameters, random generator, surface roughness, energy restoration, PaLa program
• Separated quantum dynamics
keywords: adjacent non-identical particles, TDHF, fast integrator, spin chain, energy conservation, norm conservation
• An asynchronous leap-frog method
keywords:leap-frog 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 leap-frog integrator, image manipulation, animation
• Precision-dependent symmetry breaking in simulated motion of polyspherical grains now with updates
keywords: rigid body dynamics, multiple precision arithmetic, mirror symmetry, polyspherical particles
• Higher-dimensional 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:leap-frog 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, pseudo-random generator, simulation

Pedagogical remarks on mathematical or physical topics

• On Vectors, Points, Rotations, and Rigid Bodies (a living document) including a probably novel Hamiltonian formulation of rigid body dynamics based on Euler-Rodrigues parameters as generalized coordinates.
• Mathe mit Sahne (a living essay on mathematical foundations, in German)
• Defining hereditarily finite sets as words of a formal language (a living essay on mathematical foundations)
• On notational differences in physics and in mathematics (a living essay)
• Computational power needed to propagate a non-relativistic n-particle wave function (April 2014)
• On Dirac wave function in 1D

Work in progress or recently finished

• worklog

Physics animations, done by means of

• Osmosis, stereo (red-green glasses needed, red for left eye)
• Action principle for the spinning top
• Comparing exact and separated quantum dynamics
• Comparison of integrators with respect to interaction picture dynamics of the Kepler oscillator 1
• Comparison of integrators with respect to interaction picture dynamics of the Kepler oscillator 2
• Comparing the collision of two identical fermions with the collision of two identical bosons (September 2014 and April 2024)
• Motion of a quantum particle in 1-dimensional space under the influence of an external potential (October 2022)
• Source code of the function main that created the images from which the above videos were made
• Data input to the above source code.
• Crossway system (December 2022)
• Classical crossway system (December 2022)
• Classical crossway system (January 2023)
• Quantum crossway system (January 2023)
• Quantum crossway system with Bohmian particles (February 2023)
• Kepler oscillator and integrators.
• Extensive Quantum Mechanics (March 2023)
• Fading Potential Well: Dynamics of a quantum particle in a time-dependent potential (February 2024)
• Whole directory 'animations'

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.

• Stability of numerical methods
• Predator prey population dynamics (Lodka-Volterra)
• a non-linear complex ODE initial value problem
• Riding the swingboat with rollover (March 2014)

Talks

• Modeling the Toning Process in Electrophotographic Copiers/Printers (2004)
• The direct midpoint method as a quantum mechanical integrator III (2007)

Curriculum vitae

curriculum vitae

Picture Gallery

• art by my parents
• computer art

Publications

• list of publications including my contributions to the Wolfram Demonstrations Project
• all publications in peer-reviewed journals
• single-authored patent 1
• single-authored patent 2

Cornell University press release

• Center for Advanced Computing

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 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:

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 red-green(blue) glasses. Here is a version (with spherical particles instead of polyspherical ones) of Fig. 1 of Precision-dependent symmetry breaking in simulated motion of polyspherical grains which gives a clearer effect than the original for my red-green glasses branded Apramax. This functionality was suggested by Bernhard Mutze.

software descriptions

• On the project
• The tutorial
• Listing of the basic classes
• Listing of all classes, last version without multiple precision arithmetic   last version with lean vector template Vl   current version

code and Code::Blocks project files

• how to use
• All cpm sources together with a selection of my project folders (in their their natural directory structure) are available from the following zip file
• Who wants to bring one of my projects to life has to unzip cpm.zip into a new void directory and has to open the Code::Blocks project file of one of the seven projects in the Code::Blocks ID. In case Code::Blocks is not an option for you have to study the project file and to extract the information that your project building process requires.
• Who considers using should also consider to send me a mail so that I can help to make this a success.

Free Ruby code

• ruby stuff

Alpinism

• My climbing routes (in German)