SELF-SIMILAR AND SELF-AFFINE PIONIZATION IN NUCLEAR INTERACTIONS AT A FEW AGeV

2004 ◽  
Vol 13 (06) ◽  
pp. 1179-1189 ◽  
Author(s):  
DIPAK GHOSH ◽  
ARGHA DEB ◽  
KEYA DUTTA (CHATTOPADHYAY) ◽  
RINKU SARKAR ◽  
ISHITA SEN (DUTTA)
Keyword(s):  
Phase Space ◽  
Hurst Exponent ◽  
Factorial Moment ◽  
Two Dimensional ◽  
Nuclear Interactions ◽  
Fluctuation Pattern ◽  
Self Similar

Self-affine multiplicity scaling is investigated in the framework of two-dimensional factorial moment methodology using the concept of the Hurst exponent (H) considering different bins of the phase space. We have investigated the fluctuation pattern of emitted pions in 24 Mg - AgBr interactions at 4.5 AGeV and this study reveals that the fluctuation is self-similar in some bins, whereas it is self-affine in other bins, that is, the multiplicity scaling is bin-dependent.

ENERGY DEPENDENCE OF MULTIDIMENSIONAL FRACTAL BEHAVIOR OF PIONS IN NUCLEAR COLLISION

Fractals ◽  
2007 ◽  
Vol 15 (03) ◽  
pp. 223-235 ◽  
Author(s):  
DIPAK GHOSH ◽  
ARGHA DEB ◽  
RUPA DAS ◽  
SITARAM PAL ◽  
JAYITA GHOSH
Keyword(s):  
Phase Space ◽  
Energy Dependence ◽  
Hurst Exponent ◽  
Factorial Moment ◽  
Nuclear Collision ◽  
Two Dimensional ◽  
Self Similarity ◽  
Positive Evidence ◽  
Fluctuation Pattern ◽  
Multifractal Behavior

This paper reports a study on multidimensional fractal behavior of pions emitted in 16 O - AgBr interactions at 2.1 and 60 AGeV by dividing the full bin range into different sub-bin ranges. Analysis is performed in (Xη - Xϕ) space following two-dimensional factorial moment methodology using the concept of Hurst exponent, which takes into account the anisotropy of phase space. Different scaling behavior is observed in different bins at two different energies. The data show a positive evidence of change of fluctuation pattern from self-similarity to self-affinity with increase of energy. Multifractal dimensions have been calculated in each case and it is observed that pions at both energies exhibit multifractal behavior.

Self-affine fluctuations of pions and protons and nonthermal phase transition in hadron–nucleus interactions

2008 ◽  
Vol 86 (12) ◽  
pp. 1449-1459 ◽  
Author(s):  
D Ghosh ◽  
A Deb ◽  
S Pal ◽  
J Ghosh
Keyword(s):  
Phase Transition ◽  
Phase Space ◽  
Production Process ◽  
Hurst Exponent ◽  
Factorial Moment ◽  
Multiparticle Production ◽  
Two Dimensional ◽  
Dimensional Phase Space ◽  
Compound Multiplicity ◽  
Multiplicity Distributions

The paper reports a study revealing self-affine fluctuations in pion, proton, and compound multiplicity (of pions combined with protons) spectra obtained from the interactions of 350 GeV pions with AgBr nuclei. The study is performed in the transformed two-dimensional phase space of the emission and azimuthal angles using the factorial moment methodology and the concept of the Hurst exponent. Evidence of a nonthermal phase transition is obtained for self-affine fluctuations of pions along with an indication for such a regime to be seen in similar fluctuations of proton and compound multiplicity distributions. The study bridges the anisotropic nature of the multiparticle production process and an evidence of the nonthermal phase transition with similar earlier findings from hadron–hadron and nucleus–nucleus interactions and shows the same effects to be peculiar features of the multiplicity distributions of the different species of particles produced. All this brings important information about the underlying dynamics of the hadroproduction process.PACS Nos.: 25.80.Hp, 24.60.Ky, 13.85.–t

MULTIFRACTALITY AND MULTIFRACTAL PIONIC SPECIFIC HEAT IN NUCLEAR COLLISIONS — TARGET EXCITATION DEPENDENCE

Fractals ◽  
2007 ◽  
Vol 15 (04) ◽  
pp. 391-398 ◽  
Author(s):  
DIPAK GHOSH ◽  
ARGHA DEB ◽  
SRIMONTI DUTTA
Keyword(s):  
Phase Space ◽  
Specific Heat ◽  
Hurst Exponent ◽  
Factorial Moment ◽  
Two Dimensions ◽  
One Dimensional ◽  
Nuclear Collisions ◽  
Generalized Dimension ◽  
Fluctuation Pattern ◽  
Multifractal Behavior

This paper deals with the target excitation dependence of the multifractal specific heat of pions produced in nucleus-nucleus collisions at 60 and 200 AGeV. Fluctuation pattern of pions is studied in two dimensions considering anisotropy of phase space. The parameter characterizing the anisotropy of phase space, Hurst exponent, is extracted by fitting one-dimensional factorial moment saturation curves. Values of intermittency exponent αq and generalized dimension Dq are determined. The fluctuation pattern reveals multifractal behavior at all target excitations at both energies. The multifractal specific heat c is found to depend on target excitation and the dependence is found to be more pronounced at lower energy. The results are discussed in detail.

FLUCTUATION PATTERN OF SHOWER AND COMPOUND MULTIPLICITY DISTRIBUTIONS IN NUCLEUS–NUCLEUS INTERACTIONS AT A FEW GeV

2011 ◽  
Vol 20 (05) ◽  
pp. 1287-1306
Author(s):  
DIPAK GHOSH ◽  
ARGHA DEB ◽  
MADHUMITA BANERJEE LAHIRI ◽  
PASUPATI MANDAL ◽  
SUBRATA BISWAS ◽  
...  
Keyword(s):  
Negative Binomial Distribution ◽  
Hurst Exponent ◽  
Multiplicity Distribution ◽  
Negative Binomial ◽  
Factorial Moment ◽  
Two Dimensional ◽  
Fluctuation Pattern ◽  
Frame Work ◽  
Compound Multiplicity ◽  
Multiplicity Distributions

This work presents a study on the multiplicity distribution of shower and compound multiplicity (pions + target protons) emitted from 12 C – AgBr and 24 Mg – AgBr interactions at 4.5 AGeV in terms of negative binomial distribution (NBD) and also on the fluctuation pattern of shower and compound multiplicity in the frame work of two-dimensional factorial moment methodology using the concept of Hurst exponent.

scholarly journals Wavelet-Based Entropy Measures to Characterize Two-Dimensional Fractional Brownian Fields

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 196 ◽  
Author(s):  
Orietta Nicolis ◽  
Jorge Mateu ◽  
Javier E. Contreras-Reyes
Keyword(s):  
Shannon Entropy ◽  
Simulation Study ◽  
Hurst Exponent ◽  
Wavelet Spectrum ◽  
Two Dimensional ◽  
Entropy Measures ◽  
Rényi Entropies ◽  
Self Similar ◽  
Fractional Brownian Field ◽  
Renyi Entropies

The aim of this work was to extend the results of Perez et al. (Physica A (2006), 365 (2), 282–288) to the two-dimensional (2D) fractional Brownian field. In particular, we defined Shannon entropy using the wavelet spectrum from which the Hurst exponent is estimated by the regression of the logarithm of the square coefficients over the levels of resolutions. Using the same methodology. we also defined two other entropies in 2D: Tsallis and the Rényi entropies. A simulation study was performed for showing the ability of the method to characterize 2D (in this case, α = 2 ) self-similar processes.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

Plastic Ploughing of a Sinusoidal Asperity on a Rough Surface

2015 ◽  
Vol 82 (7) ◽  
Author(s):  
H. Song ◽  
R. J. Dikken ◽  
L. Nicola ◽  
E. Van der Giessen
Keyword(s):  
Friction Stress ◽  
Dislocation Dynamics ◽  
Two Dimensional ◽  
Unit Process ◽  
Contact Models ◽  
Self Similar ◽  
Dynamics Simulations ◽  
Micrometer Scale ◽  
Edge Dislocations ◽  
Flat Contact

Part of the friction between two rough surfaces is due to the interlocking between asperities on opposite surfaces. In order for the surfaces to slide relative to each other, these interlocking asperities have to deform plastically. Here, we study the unit process of plastic ploughing of a single micrometer-scale asperity by means of two-dimensional dislocation dynamics simulations. Plastic deformation is described through the generation, motion, and annihilation of edge dislocations inside the asperity as well as in the subsurface. We find that the force required to plough an asperity at different ploughing depths follows a Gaussian distribution. For self-similar asperities, the friction stress is found to increase with the inverse of size. Comparison of the friction stress is made with other two contact models to show that interlocking asperities that are larger than ∼2 μm are easier to shear off plastically than asperities with a flat contact.

scholarly journals Dirac’s Method for the Two-Dimensional Damped Harmonic Oscillator in the Extended Phase Space

Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 180 ◽  
Author(s):  
Laure Gouba
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Canonical Quantization ◽  
Extended Phase Space ◽  
Two Dimensional ◽  
Class Constraint ◽  
Extended Phase ◽  
Damped Harmonic Oscillator ◽  
Points Of View ◽  
Space Description

The system of a two-dimensional damped harmonic oscillator is revisited in the extended phase space. It is an old problem that has already been addressed by many authors that we present here with some fresh points of view and carry on a whole discussion. We show that the system is singular. The classical Hamiltonian is proportional to the first-class constraint. We pursue with the Dirac’s canonical quantization procedure by fixing the gauge and provide a reduced phase space description of the system. As a result, the quantum system is simply modeled by the original quantum Hamiltonian.

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