The Distribution of Simultaneous Fiber Failures in Fiber Bundles

1992 ◽  
Vol 59 (4) ◽  
pp. 909-914 ◽  
Author(s):  
Per C. Hemmer ◽  
Alex Hansen
Keyword(s):  
Power Law ◽  
Load Sharing ◽  
Statistical Distribution ◽  
Fiber Bundles ◽  
Expected Number ◽  
Parallel Fibers ◽  
Breakdown Process ◽  
Universal Power Law ◽  
Complete Failure ◽  
The Individual

A bundle of many parallel fibers, with stochastically distributed thresholds for individual fibers, is loaded until complete failure. Equal load sharing is assumed. During the breakdown process, bursts of several fibers breaking simultaneously at a given load occur. We determine the expected number of such bursts before complete failure, as well as the frequency of bursts in which Δ fibers break simultaneously. This distribution follows asymptotically a universal power-law Δ−5/2, for any statistical distribution of the individual fiber strengths.

The asymptotic strength distribution of a general fiber bundle

1973 ◽  
Vol 5 (2) ◽  
pp. 200-216 ◽  
Author(s):  
S. Leigh Phoenix ◽  
Howard M. Taylor
Keyword(s):  
Tensile Strength ◽  
Fiber Bundle ◽  
Strength Distribution ◽  
Statistical Distribution ◽  
Statistical Characteristics ◽  
Parallel Fibers ◽  
General Fiber ◽  
The Individual

The asymptotic statistical distribution of tensile strength of a bundle of parallel fibers is determined in terms of the statistical characteristics of the individual fibers as the number of fibers in the bundle grows indefinitely large.

The asymptotic strength distribution of a general fiber bundle

1973 ◽  
Vol 5 (02) ◽  
pp. 200-216 ◽  
Author(s):  
S. Leigh Phoenix ◽  
Howard M. Taylor
Keyword(s):  
Tensile Strength ◽  
Fiber Bundle ◽  
Strength Distribution ◽  
Statistical Distribution ◽  
Statistical Characteristics ◽  
Parallel Fibers ◽  
General Fiber ◽  
The Individual

The asymptotic statistical distribution of tensile strength of a bundle of parallel fibers is determined in terms of the statistical characteristics of the individual fibers as the number of fibers in the bundle grows indefinitely large.

scholarly journals Size Distribution of Emitted Energies in Local Load Sharing Fiber Bundles

2021 ◽  
Vol 9 ◽  
Author(s):  
Subhadeep Roy ◽  
Soumyajyoti Biswas
Keyword(s):  
Size Distribution ◽  
Power Law ◽  
Linear Relation ◽  
Fiber Bundle ◽  
Average Energy ◽  
Load Sharing ◽  
Local Load ◽  
Fiber Bundles ◽  
Avalanche Size ◽  
Fiber Bundle Model

We study the local load sharing fiber bundle model and its energy burst statistics. While it is known that the avalanche size distribution of the model is exponential, we numerically show here that the avalanche size (s) and the corresponding average energy burst (〈E〉) in this version of the model have a non-linear relation (〈E〉 ~ sγ). Numerical results indicate that γ ≈ 2.5 universally for different failure threshold distributions. With this numerical observation, it is then possible to show that the energy burst distribution is a power law, with a universal exponent value of −(γ + 1).

scholarly journals Maximal modularity and the optimal size of parliaments

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Luca Gamberi ◽  
Yanik-Pascal Förster ◽  
Evan Tzanis ◽  
Alessia Annibale ◽  
Pierpaolo Vivo
Keyword(s):  
Power Law ◽  
Real World ◽  
Empirical Data ◽  
Random Network ◽  
Functional Relation ◽  
Optimal Size ◽  
Real World Data ◽  
Universal Power Law ◽  
The Empirical Analysis ◽  
Democratic Country

AbstractAn important question in representative democracies is how to determine the optimal parliament size of a given country. According to an old conjecture, known as the cubic root law, there is a fairly universal power-law relation, with an exponent equal to 1/3, between the size of an elected parliament and the country’s population. Empirical data in modern European countries support such universality but are consistent with a larger exponent. In this work, we analyse this intriguing regularity using tools from complex networks theory. We model the population of a democratic country as a random network, drawn from a growth model, where each node is assigned a constituency membership sampled from an available set of size D. We calculate analytically the modularity of the population and find that its functional relation with the number of constituencies is strongly non-monotonic, exhibiting a maximum that depends on the population size. The criterion of maximal modularity allows us to predict that the number of representatives should scale as a power-law in the size of the population, a finding that is qualitatively confirmed by the empirical analysis of real-world data.

Effect of Adsorbed Water and Temperature on the Universal Power Law Behavior of Lepidocrocite-Type Alkali Titanate Ceramics

2021 ◽  
Author(s):  
Saichon Sriphan ◽  
Phieraya Pulphol ◽  
Thitirat Charoonsuk ◽  
Tosapol Maluangnont ◽  
Naratip Vittayakorn
Keyword(s):  
Power Law ◽  
Adsorbed Water ◽  
Universal Power Law ◽  
Titanate Ceramics

A universal power law and proportionate change process characterize the evolution of metabolic networks

2007 ◽  
Vol 57 (1) ◽  
pp. 75-80 ◽  
Author(s):  
S. Singh ◽  
A. Samal ◽  
V. Giri ◽  
S. Krishna ◽  
N. Raghuram ◽  
...  
Keyword(s):  
Power Law ◽  
Change Process ◽  
Metabolic Networks ◽  
Universal Power Law ◽  
Proportionate Change

scholarly journals “TNOs are Cool”: A survey of the trans-Neptunian region

2018 ◽  
Vol 618 ◽  
pp. A136 ◽  
Author(s):  
E. Vilenius ◽  
J. Stansberry ◽  
T. Müller ◽  
M. Mueller ◽  
C. Kiss ◽  
...  
Keyword(s):  
Power Law ◽  
Total Mass ◽  
Size Range ◽  
Family Members ◽  
Far Infrared ◽  
Effective Diameter ◽  
Water Ice ◽  
The Family ◽  
The Individual ◽  
Geometric Albedo

Context. A group of trans-Neptunian objects (TNOs) are dynamically related to the dwarf planet 136108 Haumea. Ten of them show strong indications of water ice on their surfaces, are assumed to have resulted from a collision, and are accepted as the only known TNO collisional family. Nineteen other dynamically similar objects lack water ice absorptions and are hypothesized to be dynamical interlopers. Aims. We have made observations to determine sizes and geometric albedos of six of the accepted Haumea family members and one dynamical interloper. Ten other dynamical interlopers have been measured by previous works. We compare the individual and statistical properties of the family members and interlopers, examining the size and albedo distributions of both groups. We also examine implications for the total mass of the family and their ejection velocities. Methods. We use far-infrared space-based telescopes to observe the target TNOs near their thermal peak and combine these data with optical magnitudes to derive sizes and albedos using radiometric techniques. Using measured and inferred sizes together with ejection velocities, we determine the power-law slope of ejection velocity as a function of effective diameter. Results. The detected Haumea family members have a diversity of geometric albedos ~0.3–0.8, which are higher than geometric albedos of dynamically similar objects without water ice. The median geometric albedo for accepted family members is pV = 0.48−0.18+0.28, compared to 0.08−0.05+0.07 for the dynamical interlopers. In the size range D = 175−300 km, the slope of the cumulative size distribution is q = 3.2−0.4+0.7 for accepted family members, steeper than the q = 2.0 ± 0.6 slope for the dynamical interlopers with D < 500 km. The total mass of Haumea’s moons and family members is 2.4% of Haumea’s mass. The ejection velocities required to emplace them on their current orbits show a dependence on diameter, with a power-law slope of 0.21–0.50.

"MULTIPLE-COMPARISONS" PROBLEM

PEDIATRICS ◽  
1989 ◽  
Vol 84 (6) ◽  
pp. A30-A30
Author(s):  
Student
Keyword(s):  
Null Hypothesis ◽  
Multiple Comparisons ◽  
P Value ◽  
Expected Number ◽  
P Values ◽  
A Value ◽  
True Null Hypotheses ◽  
The Individual

Often investigators report many P values in the same study. The expected number of P values smaller than 0.05 is 1 in 20 tests of true null hypotheses; therefore the probability that at least one P value will be smaller than 0.05 increases with the number of tests, even when the null hypothesis is correct for each test. This increase is known as the "multiple-comparisons" problem...One reasonable way to correct for multiplicity is simply to multiply the P value by the number of tests. Thus, with five tests, an orignal 0.05 level for each is increased, perhaps to a value as high as 0.25 for the set. To achieve a level of not more than 0.05 for the set, we need to choose a level of 0.05/5 = 0.01 for the individual tests. This adjustment is conservative. We know only that the probability does not exceed 0.05 for the set.

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