Non-monotonicity of Generalized Dimensions

2018 ◽  
pp. 69-75
Author(s):  
Eric Rosenberg
Keyword(s):  
Generalized Dimensions

Memory and Human Nature and our Developments: Hypothesis from Narrow Dimensions and Generalized Dimensions

2010 ◽  
Vol 33 ◽  
pp. 469-473
Author(s):  
K. Yu ◽  
J.W. Luo
Keyword(s):  
Human Nature ◽  
Fundamental Form ◽  
Basic Functions ◽  
Ancient Times ◽  
Generalized Dimensions ◽  
And Function ◽  
Original Feature

Memory in the nature of primitive features and basic functions, which plays an important role in promoting all the developments from ancient times to nowadays, is the most fundamental form of human nature. This paper will, from both narrow dimensions and generalized dimensions hypothesize and analyze the connection between memory and human nature or our developments; the original feature and function of memory, thereby, will be revealed.

Multifractal and generalized dimensions of gray-tone digital images

1995 ◽  
Vol 42 (2) ◽  
pp. 181-190 ◽  
Author(s):  
Nirupam Sarkar ◽  
B.B. Chaudhuri
Keyword(s):  
Digital Images ◽  
Gray Tone ◽  
Generalized Dimensions

scholarly journals Asymmetric multifractal model for solar wind intermittent turbulence

2008 ◽  
Vol 15 (4) ◽  
pp. 615-620 ◽  
Author(s):  
A. Szczepaniak ◽  
W. M. Macek
Keyword(s):  
Solar Wind ◽  
Solar Maximum ◽  
Solar Wind Plasma ◽  
Intermittent Turbulence ◽  
Proposed Model ◽  
Scaling Parameters ◽  
Generalized Dimensions ◽  
Multifractal Nature ◽  
Turbulent Cascade

Abstract. We consider nonuniform energy transfer rate for solar wind turbulence depending on the solar cycle activity. To achieve this purpose we determine the generalized dimensions and singularity spectra for the experimental data of the solar wind measured in situ by Advanced Composition Explorer spacecraft during solar maximum (2001) and minimum (2006) at 1 AU. By determining the asymmetric singularity spectra we confirm the multifractal nature of different states of the solar wind. Moreover, for explanation of this asymmetry we propose a generalization of the usual so-called p-model, which involves eddies of different sizes for the turbulent cascade. Naturally, this generalization takes into account two different scaling parameters for sizes of eddies and one probability measure parameter, describing how the energy is transferred to smaller eddies. We show that the proposed model properly describes multifractality of the solar wind plasma.

scholarly journals A new method to analyze species abundances in space using generalized dimensions

2015 ◽  
Author(s):  
Leonardo A Saravia
Keyword(s):  
Species Abundance ◽  
Abundance Distribution ◽  
Community Patterns ◽  
Information Dimension ◽  
Generalized Dimension ◽  
Species Abundances ◽  
Species Abundance Distributions ◽  
Species Area ◽  
Generalized Dimensions ◽  
Relationship Of

Species-area relationships (SAR) and species abundance distributions (SAD) are among the most studied patterns in ecology, due to their application to both theoretical and conservation issues. One problem with these general patterns is that different theories can generate the same predictions, and for this reason they cannot be used to detect different mechanisms of community assembly. A solution is to search for more sensitive patterns, for example by extending the SAR to the whole species abundance distribution. A generalized dimension ($D_q$) approach has been proposed to study the scaling of SAD, but to date there has been no evaluation of the ability of this pattern to detect different mechanisms. An equivalent way to express SAD is the rank abundance distribution (RAD). Here I introduce a new way to study SAD scaling using a spatial version of RAD: the species-rank surface (SRS), which can be analyzed using $D_q$. Thus there is an old $D_q$ based on SAR ($D_q^{SAD}$), and a new one based on SRS ($D_q^{SRS}$). I perform spatial simulations to examine the relationship of $D_q$ with SAD, spatial patterns and number of species. Finally I compare the power of both $D_q$, SAD, SAR exponent, and the fractal information dimension to detect different community patterns using a continuum of hierarchical and neutral spatially explicit models. The SAD, $D_q^{SAD}$ and $D_q^{SRS}$ all had good performance in detecting models with contrasting mechanisms. $D_q^{SRS}$, however, had a better fit to data and allowed comparisons between hierarchical communities where the other methods failed. The SAR exponent and information dimension had low power and should not be used. SRS and $D_q^{SRS}$ could be interesting methods to study community or macroecological patterns.

Multifractality at Transition to Chaos Complex-Temperature Singularities

1997 ◽  
Vol 11 (21n22) ◽  
pp. 929-937
Author(s):  
A. Bershadskii
Keyword(s):  
Numerical Simulation ◽  
High Temperature ◽  
Finite Temperature ◽  
Multifractal Spectrum ◽  
Finite Radius ◽  
Transition To Chaos ◽  
Iterative System ◽  
Multifractal Spectra ◽  
Complex Temperature ◽  
Generalized Dimensions

It is shown, that multifractal complex-temperature singularities can play a significant role in the critical strange sets multifractality. These singularities lead to a finite radius of convergence of the real high-temperature expansions and, therefore, to necessity to use a finite-temperature expansions (an analytic continuation). It is shown, using analytic results on multifractality of strange attractors of the baker map and results of numerical computations of the multifractal spectra on all critical points of phase transitions from period-η-tupling to chaos in 1D iterative system (Chinese Phys. Lett.3, 285 (1986) and J. Phys.A25, 589 (1992)) as well as results of a recent numerical simulation of a quantum system with multifractal spectrum (J. Phys.A28, 2717 (1995)), that the finite-temperature expansions give good approximation for the generalized dimensions Dq in a representative interval of q.

scholarly journals Hofstadter rules and generalized dimensions of the spectrum of Harper's equation

1997 ◽  
Vol 30 (1) ◽  
pp. 117-128 ◽  
Author(s):  
Andreas Rüdinger ◽  
Frédéric Piéchon
Keyword(s):  
Generalized Dimensions

scholarly journals Entropy and Multifractality in Relativistic Ion-Ion Collisions

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Shaista Khan ◽  
Shakeel Ahmad
Keyword(s):  
Information Entropy ◽  
Particle Production ◽  
Monte Carlo Model ◽  
Theoretical Models ◽  
Ion Collisions ◽  
Full Phase Space ◽  
Wide Range ◽  
Multiplicity Distributions ◽  
Generalized Dimensions ◽  
Multiparticle Systems

Entropy production in multiparticle systems is investigated by analyzing the experimental data on ion-ion collisions at AGS and SPS energies and comparing the findings with those reported earlier for hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions. It is observed that the entropy produced in limited and full phase space, when normalized to maximum rapidity, exhibits a kind of scaling which is nicely supported by Monte Carlo model HIJING. Using Rényi’s order q information entropy, multifractal characteristics of particle production are examined in terms of generalized dimensions, Dq. Nearly the same values of multifractal specific heat, c, observed in hadronic and ion-ion collisions over a wide range of incident energies suggest that the quantity c might be used as a universal characteristic of multiparticle production in hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions. The analysis is extended to the study of spectrum of scaling indices. The findings reveal that Rényi’s order q information entropy could be another way to investigate the fluctuations in multiplicity distributions in terms of spectral function f(α), which has been argued to be a convenient function for comparison sake not only among different experiments but also between the data and theoretical models.

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