scholarly journals A signature of power law network dynamics

2014 ◽  
Author(s):  
Ashish Bhan ◽  
Animesh Ray

Can one hear the ‘sound’ of a growing network? We address the problem of recognizing the topology of evolving biological or social networks. Starting from percolation theory, we analytically prove a linear inverse relationship between two simple graph parameters—the logarithm of the average cluster size and logarithm of the ratio of the edges of the graph to the theoretically maximum number of edges for that graph—that holds for all growing power law graphs. The result establishes a novel property of evolving power-law networks in the asymptotic limit of network size. Numerical simulations as well as fitting to real-world citation co-authorship networks demonstrate that the result holds for networks of finite sizes, and provides a convenient measure of the extent to which an evolving family of networks belongs to the same power-law class.

Fractals ◽  
1999 ◽  
Vol 07 (03) ◽  
pp. 249-255 ◽  
Author(s):  
TAKAMICHI TERAO ◽  
TAKUYA KOIZUMI ◽  
SHINICHIRO SUZUKI ◽  
TSUNEYOSHI NAKAYAMA

We study the vibrational dynamics of cluster-cluster aggregations(CCA) by computer simulation with emphasis on the localization nature of vibrational excitations on the CCA. The frequency dependence of the inverse participation ratio P-1(ω) obeys a power law such as P-1(ω)∝ω1.07±0.06 in two-dimensional system. In addition, we show that the time development of the average cluster size can be scaled by a characteristic time tc. After a sufficiently long time, the cluster size obeys the power law behavior, depending on the sticking probability between particles.


2004 ◽  
Vol 82 (4) ◽  
pp. 323-329
Author(s):  
A Ulug ◽  
M Karakaplan ◽  
B Ulug

Clustering in some two- and three-dimensional lattices is investigated using an algorithm similar to that of Hoshen–Kopelman. The total number of clusters reveals a maximum at an occupation probability, pmax, where the average cluster size, 2.03 ± 0.07, is found to be independent of the size, dimension, coordination number, and the type of lattice. We discussed the fact that the clustering effectively begins at pmax. The percolation threshold, pc, and pmax are found to get closer to each other as the coordination number increases. PACS Nos.: 64.60.Ht, 64.60.Qb, 82.30.Nr


2014 ◽  
Vol 25 (12) ◽  
pp. 1441004 ◽  
Author(s):  
Giuseppe Gonnella ◽  
Antonio Lamura ◽  
Antonio Suma

A systems of self-propelled dumbbells interacting by a Weeks–Chandler–Anderson potential is considered. At sufficiently low temperatures the system phase separates into a dense phase and a gas-like phase. The kinetics of the cluster formation and the growth law for the average cluster size are analyzed.


2000 ◽  
Vol 610 ◽  
Author(s):  
Reza Kasnavi ◽  
Peter B. Griffin ◽  
James D. Plummer

AbstractWe have studied dose loss for B11 and BF2 implants with energies ranging from 10 keV to 1keV for B11 and 45 keV to 2keV for BF2. We found that B11 implants during a 1050C-10s RTA anneal segregate mainly to the bulk of the oxide. High dose BF2 implants on the other hand, show significantly larger amounts of dose loss after stripping the oxide, due to a pile-up of boron at the Si/SiO2 interface. In order to simulate B11 diffusion we have introduced a simple average cluster size model to simulate Boron-Interstitial-Cluster (BIC) evolution. For BF2 implants, we have simulated the effect of F by reducing the damage and we have used interface traps to account for the dose loss observed experimentally. Using these models, we have been able to fit the SIMS profiles across the whole matrix of implant conditions for both B11 and BF2 implants.


2020 ◽  
Author(s):  
Ilya Zaliapin ◽  
Yehuda Ben-Zion

<p>We attempt to track and quantify preparation processes leading to large earthquakes using two complementary approaches. (a) Localization of brittle deformation manifested by evolving fractional volume with seismic activity, and (b) Coalescence of earthquakes into clusters. We analyze seismicity catalogs from Southern California (SoCal), Parkfield section of the San Andreas Fault (SAF), and region around the 1999 Izmit and Duzce earthquakes in Turkey.</p><p>Localization of deformation is estimated using the Receiver Operating Characteristic (ROC) approach. Specifically, we consider temporal evolution of the fractional volume 0 ≤ V(q) ≤ 1 occupied by the fraction 0 ≤ q ≤ 1 of active voxels with mainshocks. We also consider the localization of the spatial intensity of mainshocks within a sliding time window with respect to the time-averaged distribution, quantified by Gini coefficient G. The significance of the results is assessed using reshuffled catalogs. Analysis within the rupture zones of large earthquakes indicate decrease of V(q) and increase of G (increased localization) prior to the Landers (1992, M7.3), El Mayor-Cucapah (2010, M7.2), Ridgecrest (2019, M7.1), and Duzce (1999, M7.2) mainshocks. We also observe ongoing damage production by the background seismicity around these rupture zones several years before their occurrences. In contrast, we observe increase of V(q) and decrease of G prior to the Parkfield (2004, M6.0) mainshock in the creeping section of the SAF. Next, we examine the quasi-linear region in the Eastern part of Southern California around the Imperial fault, Brawley seismic zone, southern SAF and Eastern California Shear Zone. We document four cycles of background localization, measures by V(q) and G, well aligned in time with the largest events in the region: Landers, Hector Mine, El Mayor-Cucapah, and Ridgecrest. The coalescence process is represented by a time-oriented graph that connects each earthquake in the examined catalog to all earlier earthquakes at the earthquake nearest-neighbor proximity below a specified threshold. We examine the size of the clusters that correspond to low thresholds, and hence represent active clustering episodes. We document increase of the average cluster size prior to the Landers, El Mayor-Cucapah, Ridgecrest and Duzce mainshocks, and decrease of the average cluster size prior to the Parkfield mainshock.</p><p>The results of our complementary localization and coalescent analyses consistently indicate progressive localization of damage prior to the largest earthquakes on non-creeping faults and de-localization on the creeping Parkfield section of SAF. These findings are consistent with analysis of acoustic emission data. The study is a step towards developing methodology for analyzing the dynamics of seismicity in relation to preparation processes of large earthquakes, which is robust to spatio-temporal fluctuations associated with aftershock sequences, data incompleteness and common catalog errors.</p>


2004 ◽  
Author(s):  
Ki-Yong Kim ◽  
Vinod Kumarappan ◽  
Howard M. Milchberg

1993 ◽  
Vol 27 (2) ◽  
pp. 185-192 ◽  
Author(s):  
A. Martino ◽  
M. Benslimane ◽  
M. Ch�telet ◽  
C. Crozes ◽  
F. Prad�re ◽  
...  

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