Comparative Multifractal Detrended Fluctuation Analysis of Heavy Ion Interactions at a Few GeV to a Few Hundred GeV

Abstract

We have studied the multifractality of pion emission process in 16 O-AgBr interactions at 2.1AGeV & 60AGeV, 12 C-AgBr & 24 Mg-AgBr interactions at 4.5AGeV and 32 S-AgBr interactions at 200AGeV using Multifractal Detrended Fluctuation Analysis (MFDFA) method which is capable of extracting the actual multifractal property filtering out the average trend of fluctuation. The analysis revels that the pseudo rapidity distribution of the shower particles is multifractal in nature for all the interactions i.e. pion production mechanism has in built multi-scale self-similarity property. We have employed MFDFA method for randomly generated events for 32 S-AgBr interactions at 200AGeV. Comparison of expt. results with those obtained from randomly generated data set reveals that the source of multifractality in our data is the presence of long range correlation. Comparing the results obtained from different interactions, it may be concluded that strength of multifractality decreases with projectile mass for same projectile energy and for a particular projectile it increases with energy. The values of ordinary Hurst exponent suggest that there is long range correlation present in our data for all the interactions. 5]. Natural systems, which have irregular pattern at different scales, exhibit fractal nature. Fractals are generally classified into two categories i) Monofractal and ii) Multifractals. For monofractals scaling properties of the system is identical throughout the system on the other hand "Multifractals" are more complicated self-similar structure that consist of a number of weighted fractals with different non-integer dimensions. As the scaling properties are dissimilar in different parts of the system, multifractal systems require at least more than one scaling exponent to describe the scaling behavior of the system [6]. Investigation of multifractality is of great importance as its origin may be associated with the presence of long range correlation in the system. Correlation study has the potential to

Multifractal Analysis of Charged Particle Multiplicity Distribution in the Framework of Renyi Entropy

“…Both the G q and the T q techniques have been applied extensively to analyze several high-energy nucleus-nucleus collision data [27][28][29][30][31][32][33][34][35]. Very recently some sophisticated methods have also been applied to study the fractal nature of multiparticle production process [36][37][38][39][40][41][42][43][44][45][46][47].…”

Флуктуационный Анализ Динамики Систем С Меняющимися Во Времени Характеристиками

“…В отличие от автокорреляционной функции он обеспечивает более надежное оценивание характеристик дальних корреляций, особенно при наличии помех и в условиях нестационарности. Несмотря на то что для стационарных случайных процессов существует взаимосвязь между показателем скейлинга метода DFA и характеристиками, описывающими спад автокорреляционной функции или частотную зависимость функции спектральной плотности мощности [1], наличие более универсального подхода, применимого как к стационарным, так и к нестационарным процессам, послужило причиной широкого использования метода DFA в исследованиях динамики сложных систем по экспериментальным данным [3][4][5][6][7][8][9][10]. Как и любой другой метод цифровой обработки сигналов, DFA имеет свои ограничения, которые обсуждались, например, в работах [11][12][13][14].…”

Fluctuation Analysis of the Dynamics of Systems with Time-Varying Characteristics

“…It provides a more reliable estimation of long-range correlation characteristics than does the autocorrelation function, especially in the presence of noises and under nonstationary conditions. For stationary random processes, there exists an interrelation between the scaling exponent of the DFA method and characteristics describing the decrease of the autocorrelation function or the frequency dependence of the spectral power density function [1]; in spite of this fact, the presence of a more universal approach applicable both to stationary and nonstationary processes gave occasion to a wider use of the DFA method in investigations of the complex systems dynamics by experimental data [3][4][5][6][7][8][9][10]. Like any other method of digital signal processing, DFA has limitations, which have been discussed, e.g., in [11][12][13][14].…”

“…They are calculated individually for each segment. Nonstationarity effects can be characterized using the measure (4) which takes small values for a homogeneous process and increases if nonstationarity properties change depending on the initial data segment.…”