4. Random fields

Random fields are among the most useful mathematical models of random geometric structures, which can be applied to natural phenomena studied in physics. Of particular interest in statistical physics is the modeling of fluctuating fluid interfaces and noisy patterns, which occur, for instance, in chemical reaction diffusion systems or as intensity maps in gamma-ray astronomy. This project deals with the analysis of level and excursion sets of random fields. A special focus is on the Minkowski functionals of these random sets to gain a better understanding of their geometry. Such an approach can be used to detect high-energy sources in H.E.S.S. sky maps. A further topic of this project are geometric properties of self-similar random processes.

See below for further details on the different .

Project Members

• Bruno Ebner (Karlsruhe)
• Daniel Hug (Karlsruhe)
  
• Matthias Hoffmann (Erlangen)
• Eva B. Vedel Jensen (Aarhus)
• Michael Klatt (Erlangen)
  
• Günter Last (Karlsruhe, project leader)
  
• Alexander Laska (Erlangen)
  
• Klaus Mecke (Erlangen, project leader)
  
• Dennis Müller (Karlsruhe)
• Wolfgang Weil (Karlsruhe)
  

Cooperating partners

• Kostya Borovkov
• Peter Mörters
  
• Jonathan Taylor
  
• Hermann Thorisson
  
• Martina Zähle

Subprojects

Morphometric analysis in Gamma ray astronomy

H.E.S.S., an array of four imaging atmospheric Cherenkov telescopes for gamma-rays above 100 GeV, observes an increasing number of large extended sources. To account for these additional structures compared to common point source analyses, a new analysis technique based on the morphology of the sky map is developed.

The here presented morphometric data analysis is a new method to detect sources of gamma-ray emission, which is especially designed for the detection of faint structured sources. Minkowski functionals quantify the structure of the count map, which is then compared to the expected structure of a pure Poisson background with gamma-ray sources leading to significant deviations from background structure.

The standard likelihood ratio method of Li and Ma is exclusively based on the number of excess counts and discards all further structure information of large extended sources. The morphometric data analysis incorporates this additional geometric information in an unbiased analysis, i.e. without the need of any prior knowledge about the source.

Pasta matter

At densities below the normal nuclear density, the nearly spherical nuclei lower their total surface area by forming exotic nuclear configurations called pasta shapes. Minkowski functionals identify and characterize the pasta shapes and provide a robust and comprehensive morphological analysis.

Publications

Impressum