scholarly journals On a growth model for complex networks capable of producing power-law out-degree distributions with wide range exponents

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
J. Esquivel-Gómez ◽  
P. D. Arjona-Villicaña ◽  
E. Stevens-Navarro ◽  
U. Pineda-Rico ◽  
R. E. Balderas-Navarro ◽  
...  
Keyword(s):  
Complex Networks ◽  
Growth Model ◽  
Power Law ◽  
Wide Range

scholarly journals An accelerated growth model to generate complex networks with connectivity distribution slope that varies with time

2019 ◽  
Vol 65 (2) ◽  
pp. 128
Author(s):  
P. Castillo Castillo ◽  
P.D. Arjona-Villicaña ◽  
And J. Acosta-Elias
Keyword(s):  
Complex Networks ◽  
Power Law ◽  
Autonomous System ◽  
Real Life ◽  
System Level ◽  
Wide Range ◽  
Growth Phenomenon ◽  
Accelerated Growth ◽  
Range Of Values ◽  
Connectivity Distribution

Many real-life complex networks have in-degree and out-degree distributions that decay as apower-law. However, the few models that have been able to reproduce both of these properties,cannot reproduce the wide range of values found in real systems. Another limitation of thesemodels is that they add links from nodes which are created into the network, as well as betweennodes already present in this network. However, adding links between existing nodes is not acharacteristic available in all systems. This paper introduces a new complex network growthmodel that, without adding links between existing nodes is able to generate complex topologieswith in-degree and out-degree distributions that decay as a power-law. Moreover, in this growthmodel, the ratio at which links are created is greater than the ratio at which nodes are born, whichproduces an accelerated growth phenomenon that can be found in some real systems, like theInternet at the Autonomous System level.

scholarly journals On the Emergence of Islands in Complex Networks

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
J. Esquivel-Gómez ◽  
R. E. Balderas-Navarro ◽  
P. D. Arjona-Villicaña ◽  
P. Castillo-Castillo ◽  
O. Rico-Trejo ◽  
...  
Keyword(s):  
Complex Networks ◽  
Size Distribution ◽  
Growth Model ◽  
Power Law ◽  
Degree Distribution ◽  
Growth Models ◽  
Island Size ◽  
First Case ◽  
Proposed Model ◽  
Power Law Function

Most growth models for complex networks consider networks comprising a single connected block or island, which contains all the nodes in the network. However, it has been demonstrated that some large complex networks have more than one island, with an island size distribution (Is) obeying a power-law function Is~s-α. This paper introduces a growth model that considers the emergence of islands as the network grows. The proposed model addresses the following two features: (i) the probability that a new island is generated decreases as the network grows and (ii) new islands are created with a constant probability at any stage of the growth. In the first case, the model produces an island size distribution that decays as a power-law Is~s-α with a fixed exponent α=1 and in-degree distribution that decays as a power-law Qi~i-γ with γ=2. When the second case is considered, the model describes island size and in-degree distributions that decay as a power-law with 2<α<∞ and 2<γ<∞, respectively.

scholarly journals A growth model for directed complex networks with power-law shape in the out-degree distribution

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
J. Esquivel-Gómez ◽  
E. Stevens-Navarro ◽  
U. Pineda-Rico ◽  
J. Acosta-Elias
Keyword(s):  
Complex Networks ◽  
Growth Model ◽  
Power Law ◽  
Degree Distribution

scholarly journals Aircraft measurements of gravity waves in the upper troposphere and lower stratosphere during the START08 field experiment

2015 ◽  
Vol 15 (13) ◽  
pp. 7667-7684 ◽  
Author(s):  
Fuqing Zhang ◽  
Junhong Wei ◽  
Meng Zhang ◽  
K. P. Bowman ◽  
L. L. Pan ◽  
...  
Keyword(s):  
Power Law ◽  
Gravity Waves ◽  
Lower Stratosphere ◽  
Potential Temperature ◽  
Shear Instability ◽  
Aircraft Measurements ◽  
Upper Troposphere ◽  
Airborne Measurements ◽  
Wide Range

Abstract. This study analyzes in situ airborne measurements from the 2008 Stratosphere–Troposphere Analyses of Regional Transport (START08) experiment to characterize gravity waves in the extratropical upper troposphere and lower stratosphere (ExUTLS). The focus is on the second research flight (RF02), which took place on 21–22 April 2008. This was the first airborne mission dedicated to probing gravity waves associated with strong upper-tropospheric jet–front systems. Based on spectral and wavelet analyses of the in situ observations, along with a diagnosis of the polarization relationships, clear signals of mesoscale variations with wavelengths ~ 50–500 km are found in almost every segment of the 8 h flight, which took place mostly in the lower stratosphere. The aircraft sampled a wide range of background conditions including the region near the jet core, the jet exit and over the Rocky Mountains with clear evidence of vertically propagating gravity waves of along-track wavelength between 100 and 120 km. The power spectra of the horizontal velocity components and potential temperature for the scale approximately between ~ 8 and ~ 256 km display an approximate −5/3 power law in agreement with past studies on aircraft measurements, while the fluctuations roll over to a −3 power law for the scale approximately between ~ 0.5 and ~ 8 km (except when this part of the spectrum is activated, as recorded clearly by one of the flight segments). However, at least part of the high-frequency signals with sampled periods of ~ 20–~ 60 s and wavelengths of ~ 5–~ 15 km might be due to intrinsic observational errors in the aircraft measurements, even though the possibilities that these fluctuations may be due to other physical phenomena (e.g., nonlinear dynamics, shear instability and/or turbulence) cannot be completely ruled out.

scholarly journals Diamond aggregation

2010 ◽  
Vol 149 (2) ◽  
pp. 351-372
Author(s):  
WOUTER KAGER ◽  
LIONEL LEVINE
Keyword(s):  
Random Walk ◽  
Growth Model ◽  
Power Law ◽  
Simple Random Walk ◽  
Internal Diffusion ◽  
Diffusion Limited Aggregation ◽  
Directional Bias ◽  
Model Based ◽  
Diffusion Limited ◽  
Logarithmic Fluctuations

AbstractInternal diffusion-limited aggregation is a growth model based on random walk in ℤd. We study how the shape of the aggregate depends on the law of the underlying walk, focusing on a family of walks in ℤ2 for which the limiting shape is a diamond. Certain of these walks—those with a directional bias toward the origin—have at most logarithmic fluctuations around the limiting shape. This contrasts with the simple random walk, where the limiting shape is a disk and the best known bound on the fluctuations, due to Lawler, is a power law. Our walks enjoy a uniform layering property which simplifies many of the proofs.

scholarly journals New Developments in Understanding Harper-Dorn, Five- power Law Creep and Power-law Breakdown

2020 ◽  
Author(s):  
michael kassner
Keyword(s):  
Stress Exponent ◽  
Power Law ◽  
Dislocation Network ◽  
Creep Equation ◽  
Self Diffusion ◽  
Wide Range ◽  
Recent Developments ◽  
Initial Dislocation Density ◽  
Power Law Creep ◽  
Edge Dislocations

This paper discusses recent developments in creep, over a wide range of temperature, that mqy change our understanding of creep. The five-power law creep exponent (3.5 to 7) has never been explained in fundamental terms. The best the scientific community has done is to develop a natural three power-law creep equation that falls short of rationalizing the higher stress exponents that are typically five. This inability has persisted for many decades. Computational work examining the stress-dependence of the climb rate of edge dislocations we may rationalize the phenomenological creep equations. Harper-Dorn creep, “discovered” over 60 years ago has been immersed in controversy. Some investigators have insisted that a stress exponent of one is reasonable. Others believe that the observation of a stress exponent of one is a consequence of dislocation network frustration. Others believe the stress exponent is artificial due to the inclusion of restoration mechanisms such as dynamic recrystallization or grain growth that is not of any consequence in the five power-law regime. Also, the experiments in the Harper-Dorn regime, which accumulate strain very slowly (sometimes over a year) may not have attained a true steady state. New theories suggest that absence or presence of Harper-Dorn may be a consequence of the initial dislocation density. Novel experimental work suggests that power-law breakdown may be a consequence of a supersaturation of vacancies which increase self-diffusion.

A Neoclassical Growth Model for Population Dynamics in a Homogeneous Habitat

2001 ◽  
Author(s):  
Peter Vadasz ◽  
Alisa S. Vadasz
Keyword(s):  
Experimental Data ◽  
Growth Model ◽  
Logistic Growth ◽  
Lag Phase ◽  
Growth Stages ◽  
Initial Growth ◽  
Neoclassical Model ◽  
Wide Range ◽  
Logistic Growth Model ◽  
Special Case

Abstract A neoclassical model is proposed for the growth of cell and other populations in a homogeneous habitat. The model extends on the Logistic Growth Model (LGM) in a non-trivial way in order to address the cases where the Logistic Growth Model (LGM) fails short in recovering qualitative as well as quantitative features that appear in experimental data. These features include in some cases overshooting and oscillations, in others the existence of a “Lag Phase” at the initial growth stages, as well as an inflection point in the “In curve” of the population size. The proposed neoclassical model recovers also the Logistic Growth Curve as a special case. Comparisons of the solutions obtained from the proposed neoclassical model with experimental data confirm its quantitative validity, as well as its ability to recover a wide range of qualitative features captured in experiments.

scholarly journals A Survey of Information Entropy Metrics for Complex Networks

Entropy ◽  
2020 ◽  
Vol 22 (12) ◽  
pp. 1417
Author(s):  
Yamila M. Omar ◽  
Peter Plapper
Keyword(s):  
Probability Distribution ◽  
Literature Review ◽  
Complex Networks ◽  
Information Entropy ◽  
Future Research ◽  
Wide Range ◽  
Growing Body ◽  
Narrative Literature ◽  
Narrative Literature Review ◽  
Further Development

Information entropy metrics have been applied to a wide range of problems that were abstracted as complex networks. This growing body of research is scattered in multiple disciplines, which makes it difficult to identify available metrics and understand the context in which they are applicable. In this work, a narrative literature review of information entropy metrics for complex networks is conducted following the PRISMA guidelines. Existing entropy metrics are classified according to three different criteria: whether the metric provides a property of the graph or a graph component (such as the nodes), the chosen probability distribution, and the types of complex networks to which the metrics are applicable. Consequently, this work identifies the areas in need for further development aiming to guide future research efforts.

scholarly journals Decaying turbulence and magnetic fields in galaxy clusters

2019 ◽  
Vol 488 (3) ◽  
pp. 3439-3445 ◽  
Author(s):  
Sharanya Sur
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Galaxy Clusters ◽  
Power Law ◽  
Dynamo Action ◽  
Wide Range ◽  
Major Merger ◽  
Decaying Turbulence ◽  
Field Decay ◽  
The Magnetic Field

Abstract We explore the decay of turbulence and magnetic fields generated by fluctuation dynamo action in the context of galaxy clusters where such a decaying phase can occur in the aftermath of a major merger event. Using idealized numerical simulations that start from a kinetically dominated regime we focus on the decay of the steady state rms velocity and the magnetic field for a wide range of conditions that include varying the compressibility of the flow, the forcing wavenumber, and the magnetic Prandtl number. Irrespective of the compressibility of the flow, both the rms velocity and the rms magnetic field decay as a power law in time. In the subsonic case we find that the exponent of the power law is consistent with the −3/5 scaling reported in previous studies. However, in the transonic regime both the rms velocity and the magnetic field initially undergo rapid decay with an ≈t−1.1 scaling with time. This is followed by a phase of slow decay where the decay of the rms velocity exhibits an ≈−3/5 scaling in time, while the rms magnetic field scales as ≈−5/7. Furthermore, analysis of the Faraday rotation measure (RM) reveals that the Faraday RM also decays as a power law in time ≈t−5/7; steeper than the ∼t−2/5 scaling obtained in previous simulations of magnetic field decay in subsonic turbulence. Apart from galaxy clusters, our work can have potential implications in the study of magnetic fields in elliptical galaxies.

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