DISTRIBUTIONS OF STRUCTURAL PROPERTIES FOR PERCOLATION CLUSTERS

Fractals ◽  
1995 ◽  
Vol 03 (03) ◽  
pp. 453-463 ◽  
Author(s):  
J.-P. HOVI ◽  
AMNON AHARONY
Keyword(s):  
Structural Properties ◽  
Distribution Functions ◽  
Tail Behavior ◽  
Minimal Path ◽  
Percolation Clusters ◽  
Probability Densities ◽  
Path Lengths ◽  
The Masses ◽  
Self Avoiding Walk ◽  
Mathematical Literature

The distributions of structural properties, which span between two terminals on percolation clusters, are studied using the “H-cell” renormalization group (RG). The RG iteration for these distributions is directly related to a simple Galton-Watson branching process, and we therefore apply theorems developed in the mathematical literature to obtain exact expressions for the asymptotic distribution functions. Distributions of the minimal path lengths, average edge-to-edge self-avoiding walk lengths, and of the masses of percolation clusters are found, and we derive exact exponential forms for the asymptotic tail behavior of the scaled probability densities at both small and large arguments. We also find new results for the multifractal distribution of wave functions on these clusters.

Optical and Structural Properties of α-Si1-xCx Films

1996 ◽  
Vol 423 ◽  
Author(s):  
Zhizhong Chen ◽  
Kai Yang ◽  
Rong Zhang ◽  
Hongtao Shi ◽  
Youdou Zheng
Keyword(s):  
Structural Properties ◽  
Radial Distribution ◽  
Optical Constants ◽  
State Density ◽  
Distribution Functions ◽  
X Ray Diffraction ◽  
Energy Band Gap ◽  
X Ray ◽  
Optical Energy Band Gap ◽  
Atomic Radial Distribution

AbstractIn this paper, we reported experimental results about optical and structural properties of amorphous silicon carbide (α-Si1-xCx). The films of a-Si1-xCx) were grown by CVD on substrate of quartz glass. Optical constants (n-refractive index, a-absorption coefficient, Eg-optical energy band gap) of these films were determined by transmission spectra. The radial distribution functions (RDFs) of α- Sil−xCx) films were drawn out from the data of x-ray diffraction spectra. According to the RDFs, we imagined the statistic scene from which we could obtain the information of atomic radial distribution. The bond lengths and bond numbers of Si-Si, Si-C, and C-C could be also determined by RDFs. From the analysis of Raman spectra, we obtained the information of their vibration state density, and discerned the peaks of bond vibration, which agreed well with the results of α-Si1-xCx) RDF.

scholarly journals Distribution of Minimal Path Lengths when Edge Lengths are Independent Heterogeneous Exponential Random Variables

2012 ◽  
Vol 49 (3) ◽  
pp. 895-900
Author(s):  
Sheldon M. Ross
Keyword(s):  
Joint Distribution ◽  
Shortest Paths ◽  
Random Variables ◽  
Simulated Data ◽  
Minimal Path ◽  
Exponential Random Variables ◽  
Path Lengths

We find the joint distribution of the lengths of the shortest paths from a specified node to all other nodes in a network in which the edge lengths are assumed to be independent heterogeneous exponential random variables. We also give an efficient way to simulate these lengths that requires only one generated exponential per node, as well as efficient procedures to use the simulated data to estimate quantities of the joint distribution.

scholarly journals On the time spent above a level by Brownian motion with negative drift

1986 ◽  
Vol 18 (04) ◽  
pp. 1017-1018 ◽  
Author(s):  
J.-P. Imhof
Keyword(s):  
Brownian Motion ◽  
Limit Theorems ◽  
Distribution Functions ◽  
Probability Densities ◽  
Negative Drift

Limit theorems of Berman involve the total time spent by Brownian motion with negative drift above a fixed or exponentially distributed negative level. We give explicitly the probability densities and distribution functions, obtained via an equivalence of laws.

scholarly journals Multiperiod conditional distribution functions for conditionally normal GARCH(1, 1) models

2005 ◽  
Vol 42 (02) ◽  
pp. 426-445
Author(s):  
Raymond Brummelhuis ◽  
Dominique Guégan
Keyword(s):  
Conditional Probability ◽  
Conditional Distribution ◽  
Probability Distributions ◽  
Random Variables ◽  
Distribution Functions ◽  
Tail Behavior ◽  
Asymptotic Tail

We study the asymptotic tail behavior of the conditional probability distributions of r t+k and r t+1+⋯+r t+k when (r t ) t∈ℕ is a GARCH(1, 1) process. As an application, we examine the relation between the extreme lower quantiles of these random variables.

Simulation studies of nearest-neighbor distribution functions and related structural properties for hard-sphere systems

2000 ◽  
Vol 17 (3) ◽  
pp. 351-356 ◽  
Author(s):  
Soong-Hyuck Suh ◽  
Woong-Ki Min ◽  
Viorel Chihaia ◽  
Jae-Wook Lee ◽  
Soon-Chul Kim
Keyword(s):  
Structural Properties ◽  
Hard Sphere ◽  
Nearest Neighbor ◽  
Distribution Functions ◽  
Simulation Studies

Distributions and moments of structural properties for percolation clusters

1988 ◽  
Vol 52 (1-2) ◽  
pp. 203-236 ◽  
Author(s):  
Avidan U. Neumann ◽  
Shlomo Havlin
Keyword(s):  
Structural Properties ◽  
Percolation Clusters

Lower Tail Estimation of Fatigue Life

2019 ◽  
Author(s):  
D. Gary Harlow
Keyword(s):  
Fatigue Life ◽  
Extreme Value ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Tail Behavior ◽  
Confidence Bounds ◽  
Lower Tail ◽  
Life Data ◽  
Order Of Magnitude ◽  
Value Estimation

Abstract Uncertainty in the prediction of lower tail fatigue life behavior is a combination of many causes, some of which are aleatoric and some of which are systemic. The error cannot be entirely eliminated or quantified due to microstructural variability, manufacturing processing, approximate scientific modeling, and experimental inconsistencies. The effect of uncertainty is exacerbated for extreme value estimation for fatigue life distributions because by necessity those events are rare. In addition, typically, there is a sparsity of data in the region of smaller stress levels in stress–life testing where the lives are considerably longer, extending to giga cycles for some applications. Furthermore, there is often over an order of magnitude difference in the fatigue lives in that region of the stress–life graph. Consequently, extreme value estimation is problematic using traditional analyses. Thus, uncertainty must be statistically characterized and appropriately managed. The primary purpose of this paper is to propose an empirically based methodology for estimating the lower tail behavior of fatigue life cumulative distribution functions, given the applied stress. The methodology incorporates available fatigue life data using a statistical transformation to estimate lower tail behavior at much smaller probabilities than can be estimated by traditional approaches. To assess the validity of the proposed methodology confidence bounds will be estimated for the stress–life data. The development of the methodology and its subsequent validation will be illustrated using extensive fatigue life data for 2024–T4 aluminum alloy specimens readily available in the open literature.

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