scholarly journals A New Distribution for Multiplicities in Leptonic and Hadronic Collisions at High Energies

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Ridhi Chawla ◽  
M. Kaur
Keyword(s):  
Phase Space ◽  
Diffusion Theory ◽  
Data Set ◽  
Adoption Of Innovations ◽  
Gompertz Distribution ◽  
High Energies ◽  
Full Phase Space ◽  
Soft Interactions ◽  
Hadronic Collisions ◽  
New Distribution

Charged particles' production in the e+e-, p¯p, and pp collisions in full phase space as well as in the restricted phase space slices, at high energies, is 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 obtained from the superposition of two shifted Gompertz distributions is 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 semihard 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.

scholarly journals Charged-Particle Multiplicity Moments as Described by Shifted Gompertz Distribution in e+e−, pp¯, and pp Collisions at High Energies

2020 ◽  
Vol 2020 ◽  
pp. 1-24
Author(s):  
Aayushi Singla ◽  
M. Kaur
Keyword(s):  
Charged Particle ◽  
Phase Space ◽  
Center Of Mass ◽  
Particle Multiplicity ◽  
Charged Particle Multiplicity ◽  
Distribution Analysis ◽  
Factorial Moments ◽  
Hadronic Interactions ◽  
Gompertz Distribution ◽  
Full Phase Space

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 using the shifted Gompertz distribution, a detailed analysis of the normalized moments and normalized factorial moments is reported here. A two-component model in which a probability distribution function is obtained from the superposition of two shifted Gompertz distributions, as 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 performed to predict the moments of multiplicity distribution for the e+e− collisions at s=500 GeV at a future collider.

scholarly journals Cubic Transmuted Gompertz Distribution: As a Life Time Distribution

2020 ◽  
pp. 105-116
Author(s):  
A. A. Ogunde ◽  
Fatoki Olayode ◽  
Audu Adejumoke
Keyword(s):  
Real Life ◽  
Life Time ◽  
Real Data ◽  
Moment Generating Function ◽  
Data Set ◽  
Gompertz Distribution ◽  
Life Data ◽  
Real Life Data ◽  
Mean Variance ◽  
New Distribution

In this work, we proposed and studied the Cubic Transmuted Gompertz (CTG) distribution using the Cubic Transmuted family of distributions which was introduced by Rahman et al. [8] and based on cubic transmutation map. We studied the statistical properties of the new distribution which includes: rth moment, moment generating function order statistics, mean, variance, Renyl entropy. The CTG distribution was fitted to a real data set to demonstrate its flexibility and tractability in modelling real life data.

A New Uncertainty Analysis-Based Framework for Data-Driven Computational Mechanics

2021 ◽  
pp. 1-22
Author(s):  
Xu Guo ◽  
Zongliang Du ◽  
Chang Liu ◽  
Shan Tang
Keyword(s):  
Phase Space ◽  
Uncertainty Analysis ◽  
Distinctive Feature ◽  
Computational Mechanics ◽  
Problem Formulation ◽  
Solution Set ◽  
Data Driven ◽  
Data Set ◽  
Classical Counterpart ◽  
Single Solution

Abstract In the present paper, a new uncertainty analysis-based framework for data-driven computational mechanics (DDCM) is established. Compared with its practical classical counterpart, the distinctive feature of this framework is that uncertainty analysis is introduced into the corresponding problem formulation explicitly. Instated of only focusing on a single solution in phase space, a solution set is sought for in order to account for the influence of the multi-source uncertainties associated with the data set on the data-driven solutions. An illustrative example provided shows that the proposed framework is not only conceptually new, but also has the potential of circumventing the intrinsic numerical difficulties pertaining to the classical DDCM framework.

scholarly journals Transmuted Weibull distribution and its applications

2018 ◽  
Vol 157 ◽  
pp. 08007 ◽  
Author(s):  
Ivana Pobočíková ◽  
Zuzana Sedliačková ◽  
Mária Michalková
Keyword(s):  
Weibull Distribution ◽  
Real Data ◽  
Data Set ◽  
New Distribution ◽  
Modelling Data

In this paper we study new distribution called transmuted Weibull distribution. Some properties of this distribution are described. The usefulness of the distribution for modelling data is illustrated using real data set.

scholarly journals A Study of Soft Interactions at Ultra High Energies

2008 ◽  
Vol 38 (3b) ◽  
Author(s):  
E. Gotsman ◽  
E. Levin ◽  
U. Maor
Keyword(s):  
High Energies ◽  
Soft Interactions

scholarly journals Optimal Shadowing Filter for a Positioning and Tracking Methodology with Limited Information

Sensors ◽  
2019 ◽  
Vol 19 (4) ◽  
pp. 931 ◽  
Author(s):  
Ayham Zaitouny ◽  
Thomas Stemler ◽  
Shannon Algar
Keyword(s):  
Phase Space ◽  
Real Life ◽  
Positional Information ◽  
Irregular Sampling ◽  
Moving Target ◽  
Limited Information ◽  
Uncorrelated Noise ◽  
Full Phase Space

Positioning and tracking a moving target from limited positional information is a frequently-encountered problem. For given noisy observations of the target’s position, one wants to estimate the true trajectory and reconstruct the full phase space including velocity and acceleration. The shadowing filter offers a robust methodology to achieve such an estimation and reconstruction. Here, we highlight and validate important merits of this methodology for real-life applications. In particular, we explore the filter’s performance when dealing with correlated or uncorrelated noise, irregular sampling in time and how it can be optimised even when the true dynamics of the system are not known.

Invariant Manifold Detection From Phase Space Trajectories

2008 ◽  
Author(s):  
Joseph Kuehl ◽  
David Chelidze
Keyword(s):  
Phase Space ◽  
Invariant Manifold ◽  
Invariant Manifolds ◽  
Basins Of Attraction ◽  
Detection Methods ◽  
Trajectory Data ◽  
Space Trajectories ◽  
Data Set ◽  
Phase Space Warping ◽  
Phase Space Trajectories

Invariant manifolds provide important information about the structure of flows. When basins of attraction are present, the stable invariant manifold serves as the boundary between these basins. Thus, in experimental applications such as vibrations problems, knowledge of these manifolds is essential to understanding the evolution of phase space trajectories. Most existing methods for identifying invariant manifolds of a flow rely on knowledge of the flow field. However, in experimental applications only knowledge of phase space trajectories is available. We provide modifications to several existing invariant manifold detection methods which enables them to deal with trajectory only data, as well as introduce a new method based on the concept of phase space warping. The method of Stochastic Interrogation applied to the damped, driven Duffing equation is used to generate our data set. The result is a set of trajectory data which randomly populates a phase space. Manifolds are detected from this data set using several different methods. First is a variation on manifold “growing,” and is based on distance of closest approach to a hyperbolic trajectory with “saddle like behavior.” Second, three stretching based schemes are considered. One considers the divergence of trajectory pairs, another quantifies the deformation of a nearest neighbor cloud, and the last uses flow fields calculated from the trajectory data. Finally, the new phase space warping method is introduced. This method takes advantage of the shifting (warping) experienced by a phase space as the parameters of the system are slightly varied. This results in a shift of the invariant manifolds. The region spanned by this shift, provides a means to identify the invariant manifolds. Results show that this method gives superior detection and is robust with respect to the amount of data.

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