9 research outputs found
Mark correlations: relating physical properties to spatial distributions
Mark correlations provide a systematic approach to look at objects both
distributed in space and bearing intrinsic information, for instance on
physical properties. The interplay of the objects' properties (marks) with the
spatial clustering is of vivid interest for many applications; are, e.g.,
galaxies with high luminosities more strongly clustered than dim ones? Do
neighbored pores in a sandstone have similar sizes? How does the shape of
impact craters on a planet depend on the geological surface properties? In this
article, we give an introduction into the appropriate mathematical framework to
deal with such questions, i.e. the theory of marked point processes. After
having clarified the notion of segregation effects, we define universal test
quantities applicable to realizations of a marked point processes. We show
their power using concrete data sets in analyzing the luminosity-dependence of
the galaxy clustering, the alignment of dark matter halos in gravitational
-body simulations, the morphology- and diameter-dependence of the Martian
crater distribution and the size correlations of pores in sandstone. In order
to understand our data in more detail, we discuss the Boolean depletion model,
the random field model and the Cox random field model. The first model
describes depletion effects in the distribution of Martian craters and pores in
sandstone, whereas the last one accounts at least qualitatively for the
observed luminosity-dependence of the galaxy clustering.Comment: 35 pages, 12 figures. to be published in Lecture Notes of Physics,
second Wuppertal conference "Spatial statistics and statistical physics
Classical hybrid Monte-Carlo simulation of the interconversion of hexabromocyclododecane stereoisomers
Supersymmetrization of Quaternion Dirac Equation for Generalized Fields of Dyons
The quaternion Dirac equation in presence of generalized electromagnetic
field has been discussed in terms of two gauge potentials of dyons.
Accordingly, the supersymmetry has been established consistently and thereafter
the one, two and component Dirac Spinors of generalized quaternion Dirac
equation of dyons for various energy and spin values are obtained for different
cases in order to understand the duality invariance between the electric and
magnetic constituents of dyons.Comment: Key words: Supersymmetry, quaternion, Dirac equation, dyons PACS No.:
11.30.Pb, 14.80.Ly, 03.65.G