Horizon 2020

H2020-MSCA-RISE-MIXMAX

   Action title:

Development and Implementation of new generation of Pseudo Random Number Generator
based on Anosov-Kolmogorov C-K systems

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sk´lodowska-Curie grant agreement No 644121.

   Summary:

Modern powerful computers open a new era for the application of the Monte Carlo method for the simulation of physical systems of higher complexity. The Monte Carlo simulations are important computational techniques in many areas of natural sciences and have significant application in particle and nuclear physics, quantum physics, statistical physics, quantum chemistry, material science, among many other multidisciplinary applications. In the heart of the Monte Carlo simulations are Pseudo Random Number Generators (RNG). The primary objective of the proposed network is a systematic development and implementation of the state of the art new generation of Pseudo Random Number Generators based on Kolmogorov-Anosov K-systems, which demonstrates excellent statistical properties, into a multidisciplinary usable product. This innovative class of RNG was proposed earlier by the members of the network and relies on the fundamental discoveries and results of Ergodic theory.

   Participants:

1. NATIONAL CENTER FOR SCIENTIFIC RESEARCH "DEMOKRITOS"
2. EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH
3. KOBENHAVNS UNIVERSITET
4. A.I.ALIKHANYAN NATIONAL SCIENCE LABORATORY
5. NANJING UNIVERSITY

   

   Meetings and Workshops:

      FIRST MIXMAX NETWORK MEETING and SUMMER RESEARCH WORKSHOP at CERN, July 3 - July 17, 2015

      SECOND MIXMAX NETWORK MEETING and SUMMER RESEARCH WORKSHOP at CERN, July 4 - July 18, 2016

      CONFERENCE and MIXMAX MTR NETWORK MEETING at NCSR "Demokritos", September 5, 2016,

      MIXMAX Network Meeting: Overview of the ROOT and Geant4 Software at CERN at NCSR "Demokritos", May 3, 2017

   The MIXMAX code in C and C++11 standard interface can be found here

   The MIXMAX code for GSL - GNU Scientific Library can be found here.

   The MIXMAX "thermodynamical" parameters: Dimension, Entropy, Decorrelation time, Relaxation time

   There is a rather detailed MIXMAX Manual and the demonstaration of the generated numbers in 2D planes

   The BigCrush testU01 of the MIXMAX generator of dimension N=256.

   The CAcert Research Lab test of the MIXMAX generator of dimension N=240.

   The BigCrush testU01 of various RNGs .

   Chapter on MIXMAX in the book: "using C++" .

   Publications:

  1. George Savvidy and Natalia Savvidy.
    On the Problem of Monte Carlo Modelling of Physical Systems
    EFI-865-16-86-YEREVAN, EFI-865(16)-86, Jan 1986. 13pp.
  2. George Savvidy and Natalia Savvidy
    On the Monte Carlo Simulation of Physical Systems.
    J.Comput.Phys. 97 (1991) 566
  3. Konstantin Savvidy,
    The MIXMAX random number generator
    Computer Physics Coomunications 196 (2015) 161
    e-print arXiv:1403.5355
  4. George Savvidy,
    Anosov C-systems and Random Number Generator
    Theor.Math.Phys. 188 (2016) 1155-1171; e-print arXiv:1507.06348
  5. Konstantin Savvidy and George Savvidy,
    Spectrum and Entropy of C-systems. MIXMAX random number generator.
    Chaos Fractals Solitons 91 (2016) 33; e-print arXiv:1510.06274
  6. Andrzej Görlich, Marios Kalomenopoulos, Konstantin Savvidy and George Savvidy,
    Distribution of periodic trajectories of C-K systems. MIXMAX pseudorandom number generator
    J.Mod.Phys. C28 (2016) 1750032; e-print arXiv:1608.03496
  7. Talk at CERN on "PRNGs based on Anosov-Kolmogorov C-K-systems"
    George Savvidy (SFT Group Meeting, CERN, Switzerland, March 2014)
  8. Talk at CERN on "The MIXMAX Random Number Generator.
    Integration of the MIXMAX engine into the CERN Scientific Software ROOT and Geant4"

    George Savvidy (SFT Group Meeting, CERN, Switzerland, May 2017)
    https://indico.cern.ch/event/308953/
  9. MIXMAX in ROOT Release 6.04/06 on 2015-10-13,
  10. MIXMAX in CLHEP/GEANT4 Release 2.3.1.1 on 2015-11-10