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Register a new userCompelling evidence of oscillatory behaviour of hadronic multiplicities in the shifted Gompertz distribution
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Study of charged particle multiplicity distribution in high energy interactions of particles helps in revealing the dynamics of particle production and the underlying statistical patterns, which these distributions follow. Several distributions derived from statistics have been employed to understand its behaviour. In one of our earlier papers, we introduced the shifted Gompertz distribution to investigate this variable and showed that the multiplicity distributions in a variety of processes at different energies can be very well described by this distribution. The fact that the shifted Gompertz distribution, which has been extensively used in diffusion theory, social networks and forecasting has been used for the first time in high energy physics collisions, remains interesting. In this paper we investigate the phenomenon of oscillatory behaviour of the counting statistics observed in the experimental data, resulting from different types of recurrence relations defining the probability distributions. We search for such oscillations in the multiplicity distributions well described by the shifted Gompertz distribution and compare our results with the analysis proposed by G. Wilk et al.
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In continuation of our earlier work, in which we analysed the charged particle multiplicities in leptonic and hadronic interactions at different center of mass energies in full phase space as well as in restricted phase space with the shifted Gompertz distribution, a detailed analysis of the normalized and factorial moments is reported here. A two-component model in which probability distribution function is obtained from the superposition of two shifted Gompertz distributions introduced in our earlier work has also been used for the analysis. This is the first analysis of the moments with the shifted Gompertz distribution. Analysis has also been done to predict the moments of multiplicity distribution for the electron-positron collisions at c.m. energy of 500 GeV at a future Collider.
Charged particles production in the electron-positron, pbarp and pp collisions in full phase space as well as in the restricted phase space slices, at high energies are described with predictions from shifted Gompertz distribution, a model of adoption of innovations. The distribution has been extensively used in diffusion theory, social networks and forecasting. A two-component model in which PDF is obtained from the superposition of two shifted Gompertz distributions has been introduced to improve the fitting of the experimental distributions by several orders. The two-components correspond to the two subgroups of a data set, one representing the soft interactions and the other semi-hard interactions. Mixing is done by appropriately assigning weights to each subgroup. Our first attempt to analyse the data with shifted Gompertz distribution has produced extremely good results. It is suggested that the distribution may be included in the host of distributions more often used for the multiplicity analyses.
This work presents an empirical study of the evolution of the personal income distribution in Brazil. Yearly samples available from 1978 to 2005 were studied and evidence was found that the complementary cumulative distribution of personal income for 99% of the economically less favorable population is well represented by a Gompertz curve of the form $G(x)=exp [exp (A-Bx)]$, where $x$ is the normalized individual income. The complementary cumulative distribution of the remaining 1% richest part of the population is well represented by a Pareto power law distribution $P(x)= beta x^{-alpha}$. This result means that similarly to other countries, Brazils income distribution is characterized by a well defined two class system. The parameters $A$, $B$, $alpha$, $beta$ were determined by a mixture of boundary conditions, normalization and fitting methods for every year in the time span of this study. Since the Gompertz curve is characteristic of growth models, its presence here suggests that these patterns in income distribution could be a consequence of the growth dynamics of the underlying economic system. In addition, we found out that the percentage share of both the Gompertzian and Paretian components relative to the total income shows an approximate cycling pattern with periods of about 4 years and whose maximum and minimum peaks in each component alternate at about every 2 years. This finding suggests that the growth dynamics of Brazils economic system might possibly follow a Goodwin-type class model dynamics based on the application of the Lotka-Volterra equation to economic growth and cycle.
A systematic study of hadron masses and widths shows regular oscillations that can be fitted by a simple cosine function. This property can be observed when the difference between adjacent masses of each family is plotted versus the mean mass.
Whether or not the rich star cluster population in the Large Magellanic Cloud (LMC) is affected by significant disruption during the first few x 10^8 yr of its evolution is an open question and the subject of significant current debate. Here, we revisit the problem, adopting a homogeneous data set of broad-band imaging observations. We base our analysis mainly on two sets of self-consistently determined LMC cluster ages and masses, one using standard modelling and one which takes into account the effects of stochasticity in the clusters stellar mass functions. On their own, the results based on any of the three complementary analysis approaches applied here are merely indicative of the physical conditions governing the cluster population. However, the combination of our results from all three different diagnostics leaves little room for any conclusion other than that the optically selected LMC star cluster population exhibits no compelling evidence of significant disruption -- for clusters with masses, M_cl, of log(M_cl/M_sun) >= 3.0-3.5 -- between the age ranges of [3-10] Myr and [30-100] Myr, either infant mortality or otherwise. In fact, there is no evidence of any destruction beyond that expected from simple models just including stellar dynamics and stellar evolution for ages up to 1 Gyr. It seems, therefore, that the difference in environmental conditions in the Magellanic Clouds on the one hand and significantly more massive galaxies on the other may be the key to understanding the apparent variations in cluster disruption behaviour at early times.
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