Clustering in some randomly occupied two- and three-dimensional lattices

2004 ◽  
Vol 82 (4) ◽  
pp. 323-329
Author(s):  
A Ulug ◽  
M Karakaplan ◽  
B Ulug
Keyword(s):  
Percolation Threshold ◽  
Coordination Number ◽  
Cluster Size ◽  
Three Dimensional ◽  
Occupation Probability ◽  
Average Cluster Size ◽  
Number Of Clusters ◽  
Size Dimension ◽  
Average Cluster

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

Cluster Study in the Three-Dimensional 3-State Potts Model

1997 ◽  
Vol 08 (05) ◽  
pp. 1081-1084
Author(s):  
M. Aydin ◽  
T. Çelik ◽  
Y. Gündüç
Keyword(s):  
Potts Model ◽  
Cluster Size ◽  
Three Dimensional ◽  
Size Distributions ◽  
Average Cluster Size ◽  
Histogram Method ◽  
True Nature ◽  
First Order ◽  
Average Cluster

The three-dimensional 3-state Potts model has been investigated by examining the average cluster size distributions. Cluster distributions give evidence for the weak first-order nature of the transition for lattice sizes as small as 163, where the energy histogram method fails to exhibit the true nature of the transition.

scholarly journals Phase segregation in a system of active dumbbells

2014 ◽  
Vol 25 (12) ◽  
pp. 1441004 ◽  
Author(s):  
Giuseppe Gonnella ◽  
Antonio Lamura ◽  
Antonio Suma
Keyword(s):  
Low Temperatures ◽  
Cluster Size ◽  
Cluster Formation ◽  
Phase Segregation ◽  
Average Cluster Size ◽  
Dense Phase ◽  
Kinetics Of ◽  
Average Cluster ◽  
System Phase

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.

A Comparative Study of Dose Loss and Diffusion for B11 and BF2 Implants

2000 ◽  
Vol 610 ◽  
Author(s):  
Reza Kasnavi ◽  
Peter B. Griffin ◽  
James D. Plummer
Keyword(s):  
Comparative Study ◽  
Cluster Size ◽  
The Other ◽  
High Dose ◽  
Interface Traps ◽  
Average Cluster Size ◽  
Pile Up ◽  
And Diffusion ◽  
Average Cluster ◽  
Simple Average

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.

Quantifying preparation process of large earthquakes: Damage localization and coalescent dynamics

2020 ◽  
Author(s):  
Ilya Zaliapin ◽  
Yehuda Ben-Zion
Keyword(s):  
Cluster Size ◽  
Southern California ◽  
Time Window ◽  
Oriented Graph ◽  
Seismic Zone ◽  
Average Cluster Size ◽  
Emission Data ◽  
Aftershock Sequences ◽  
Large Earthquakes ◽  
Average Cluster

<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>

Measurement of the average cluster size and density of clusters in gas jets

2004 ◽  
Author(s):  
Ki-Yong Kim ◽  
Vinod Kumarappan ◽  
Howard M. Milchberg
Keyword(s):  
Cluster Size ◽  
Average Cluster Size ◽  
Gas Jets ◽  
Average Cluster

Average cluster size determination in supersonic beams from angular distribution measurements after scattering by a buffer gas

1993 ◽  
Vol 27 (2) ◽  
pp. 185-192 ◽  
Author(s):  
A. Martino ◽  
M. Benslimane ◽  
M. Ch�telet ◽  
C. Crozes ◽  
F. Prad�re ◽  
...  
Keyword(s):  
Angular Distribution ◽  
Cluster Size ◽  
Buffer Gas ◽  
Size Determination ◽  
Average Cluster Size ◽  
Supersonic Beams ◽  
Average Cluster

Alternative Length Scales for Polycrystalline Materials

1990 ◽  
Vol 209 ◽  
Author(s):  
C.S. Nichols ◽  
R.F. Cook ◽  
D.R. Clarke ◽  
D.A. Smith
Keyword(s):  
Mechanical Properties ◽  
Grain Boundary ◽  
Cluster Size ◽  
Constitutive Relations ◽  
Physical And Mechanical Properties ◽  
Polycrystalline Materials ◽  
Length Scale ◽  
Average Cluster Size ◽  
Average Cluster ◽  
Relevant Length Scale

AbstractIt is well established from studies of bicrystals that the properties of a grain boundary depend on the atomic structure of the boundary. However, constitutive relations for the properties of polycrystalline materials do not currently take into account this boundary-toboundary variability. Instead, such relations depend on a single length scale, typically the average grain diameter. We extend the traditional viewpoint by proposing that boundaries may be divided into two distinct categories, depending on their misorientation angle. The relevant length scale in constitutive relations for polycrystals is then the average cluster size, where clusters consist of grains connected by boundaries in the same misorientation category. A brief discussion of this additional length scale and how it may be reflected in various constitutive relations for physical and mechanical properties of polycrystals is given.

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