The multifractal detrended fluctuation analysis technique is employed to analyze the time series of gold consumer price index (CPI) and the market trend of three world’s highest gold consuming countries, namely China, India and Turkey for the period: 1993–July 2013. Various multifractal variables, such as the generalized Hurst exponent, the multifractal exponent and the singularity spectrum, are calculated and the results are fitted to the generalized binomial multifractal (GBM) series that consists of only two parameters. Special emphasis is given to identify the possible source(s) of multifractality in these series. Our analysis shows that the CPI series and all three market series are of multifractal nature. The origin of multifractality for the CPI time series and Indian market series is found due to a long-range time correlation, whereas it is mostly due to the fat-tailed probability distributions of the values for the Chinese and Turkey markets. The GBM model series more or less describes all the time series analyzed here.

Multifractal characterization of gold market: A multifractal detrended fluctuation analysis

Analysis of freight rate volatility characteristics attracts more attention after year 2008 due to the effect of credit crunch and slowdown in marine transportation. The multifractal detrended fluctuation analysis technique is employed to analyze the time series of Baltic Dry Bulk Freight Rate Index and the market trend of two bulk ship sizes, namely Capesize and Panamax for the period: March 1st 1999–February 26th 2015. In this paper, the degree of the multifractality with different fluctuation sizes is calculated. Besides, multifractal detrending moving average (MF-DMA) counting technique has been developed to quantify the components of multifractal spectrum with the finite-size effect taken into consideration. Numerical results show that both Capesize and Panamax freight rate index time series are of multifractal nature. The origin of multifractality for the bulk freight rate market series is found mostly due to nonlinear correlation.

Finite-size effect and the components of multifractality in transport economics volatility based on multifractal detrending moving average method

We have studied the charged particle density fluctuations in 16O+Ag(Br) and 32S+Ag(Br) interactions at 200A GeV incident energy in the laboratory frame by using the detrended methods. These methods can extract (multi)fractal properties of the underlying distributions after filtering out the average trend of fluctuations associated. Multifractal parameters obtained from data analysis are systematically compared with event samples generated by the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model, where Bose–Einstein correlation (BEC) effect is mimicked via a charge reassignment algorithm implemented as an after burner. Both the experimental and the simulated data are subjected to two different statistical techniques namely the multifractal detrended fluctuation analysis (MFDFA) and multifractal detrended moving average (MFDMA) analysis. The results indicate that for both the interactions considered the pseudorapidity distributions of the shower tracks are multifractal in nature. Qualitatively, both methods of analysis and both interactions considered, result in similar behavior of multifractal parameters. We do however notice significant quantitative differences in certain cases.

Detrended analysis of shower track distribution in nucleus-nucleus interactions at CERN SPS energy

We employ the recently introduced Ising-QCD partition function (N.~G. Antoniou {\it et al.}, Phys. Rev. D 97, 034015 (2018)) to explore in detail the behaviour of the moments of the baryon-number, within the critical region around the critical endpoint. Our analysis is based on the relation of finite-size scaling in real space with intermittency in transverse momentum space. It demonstrates in practice the recent observation (N.~G. Antoniou {\it et al.}, Phys. Rev. D 97, 034015 (2018)) that combined measurements of the intermittency index $\phi_2$ and the freeze-out parameters $\mu_b$ (baryochemical potential), $T$ (temperature), provide us with a powerful tool to detect the critical point. We also show that the finite-size scaling (FSS) region, as a part of the critical region, is very narrow in both the chemical potential and the temperature direction, even for light nuclei. Furthermore, using published experimental results for $(\mu_b,T,\phi_2)$ in A+A collisions at $\sqrt{s_{NN}}=17.2$ GeV (NA49 experiment, CERN-SPS), we are able to make a set of predictions for the freeze-out states of Ar + Sc and Xe + La collisions at the same energy in the NA61/SHINE experiment (CERN-SPS). In particular, we find that the Ar + Sc system freezes out outside the FSS region but very close to its boundary, a property which may leave characteristic traces in intermittency analysis.

Ising-QCD phenomenology close to the critical point

We look for a method to calculate the entropy of a hadrons system and a quark-gluon plasma (QGP) system. Then build a transport model to simulate the evolution from one to another. By calculating the entropy, a crossover between hadron to QGP can clearly show, so people can judge whether the system has reached equilibrium or whether there is new matter produced in high energy collisions.

Phase transition between a hadrons system and QGP from entropy evolution

Nonstatistical dynamical fluctuations by means of the detrended fluctuation analysis (DFA) and multifractal DFA are studied. We used a two-dimensional algorithm for the analyses. By choosing different particles generated by UrQMD code, we show that different particles all have good scaling behaviors with bin size. The correlation between different identified particles are also discussed.

Fractal properties of particles in phase space from urqmd model

This paper deals with the hadronization process of quark system. A phenomenological potential is introduced to describe the interaction between a quark pair. The potential depends on the color charge of those quarks and their relative distances. Those quarks move according to classical equations of motion. Due to the color interaction, coloring quarks are separated to form color neutral clusters which are supposed to be the hadrons.

Hadron formation from interaction among quarks

In this paper, yields of strange hadrons in relativistic heavy-ion collisions are investigated in the framework of the recombination model. Yield ratios of strange to nonstrange hadrons are studied. Strangeness enhancement is shown stronger for higher initial quark densities and for hadrons with more strange quarks.

Strangeness Production in Relativistic Heavy-Ion Collisions in the Quark Recombination Model

Particle production at RHIC is discussed within the framework of quark recombination model. After a short introduction on the anomalies discovered at RHIC, we will first present the basic physics ideas common for all the quark recombination models and different implementations in different research groups. Then the main focus turns to the approach of Oregon group. Feynman and Field's independent fragmentation process is re-interpreted in the quark recombination model. In this approach, hard partons with high virtuality evolves into a shower of semihard partons by radiating gluons which can convert into quark-antiquark pairs. Then different fragmentation functions can be rewritten in terms of only a few shower parton distributions within the recombination model. By fitting the data on the fragmentation functions, the shower parton distributions can be determined and then can be used in other processes together with the assumed exponential distributed soft parton distributions. Applications to the particle production at RHIC for both Au+Au and d+Au collisions in mid-rapidity are discussed. In particular, the suppression for meson production in central Au+Au collisions and Cronin effect in d+Au collisions are naturally explained within the recombination models. Finally, strange particle production is briefly discussed.

Particle production at rhic from quark recombination

The effect of multiplicity correlation between two bins to the dynamical fluctuations is investigated for a second-order phase transition from quark–gluon plasma (QGP) to hadrons, within the Ginzburg–Landau description for the transition. Normalized factorial correlators are used to characterize the dynamical fluctuations. A scaling behavior among the correlators is found, and an approximate universal exponent is obtained with very weak dependence on the details of the phase transition.

Influence of long-range correlation on the scaling properties of the normalized factorial correlators in relativistic heavy-ion collisions

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