Search for multifractal features in cherenkov arrival time

Presenter:A.Razdan ([email protected]), ind-Razdan-A-abs2-og27-poster Extensive air shower products are fractal in nature. Both simulated and experimental Cherenkov images display multifractal properties. In this paper we explore the possibility of searching multifractal features in cherenkov arrival times. Extensive air shower (EAS) is a multifractal process because of multiplicative nature of bremsstrahlung and pair production. It has been shown that EAS products like Cherenkov photons, electron density distribution etc are multifractal in nature [2,3]. In this paper we search for multifractal features in the temporal character of EAS. Fractals are self-similar objects which look same on many different scales of observations. Fractals are defined in terms of Hausdroff-Bescovitch dimensions. Fractal dimensions characterize the geometric support of a structure but can not provide any information about a possible distribution or a probability that may be part of a given structure. This problem has been solved by defining an infinite set of dimensions known as generalized dimensions which are achieved by dividing the object under study into pieces ,each piece is labelled by an index i=0,1,2....N. If we associate a probability p i with each piece of size l i than partition function is obtained which permits to define generalized dimension D q (q − 1)D q = τ (q) (1) Here q is a parameter which can take all values between-∞ to ∞. τ (q) is obtained from scaling properties of the partition function. This formalism is called as multi-fractal formalism which characterizes both the geometry of a given structure and the probability measure associated with it. There are infinite set of other exponents from which information can be obtained by constructing an equivalent picture of the system in terms of scaling indices 'α' for the probability measure defined on a support of fractal dimension f(α). This is achieved by defining probability measure p i in terms of α. α(q)) is the fractal dimension of the set. In this approach suggested by Chhabra et al [3] whole experimental /simulation measure is covered with boxes of size l and probability P i (l) is computed. From this probability construct a one parameter family of normalized measure µ(q)