A Stochastic Model for Pareto’s Law and the Log-Normal Distribution under the Detailed Balance and Extended-Gibrat’s Law

2009 ◽  
pp. 605-614
Author(s):  
Shouji Fujimoto ◽  
Masashi Tomoyose ◽  
Atushi Ishikawa
Keyword(s):  
Stochastic Model ◽  
Normal Distribution ◽  
Detailed Balance ◽  
Gibrat’S Law ◽  
Gibrat's Law ◽  
Pareto’S Law ◽  
Log Normal ◽  
Log Normal Distribution

A Percolative Approach to Electromigration Modelling

2000 ◽  
Vol 612 ◽  
Author(s):  
C. Pennetta ◽  
L. Reggiani ◽  
Gy. Trefán ◽  
F. Fantini ◽  
A. Scorzoni ◽  
...  
Keyword(s):  
Stochastic Model ◽  
Normal Distribution ◽  
Early Stage ◽  
Random Resistor Network ◽  
Resistor Network ◽  
Metallic Interconnects ◽  
Compositional Effects ◽  
The Times ◽  
Log Normal ◽  
Log Normal Distribution

AbstractWe present a stochastic model which simulates electromigration damage in metallic interconnects by biased percolation of a random resistor network. The main features of experiments including Black's law and the log-normal distribution of the times to failure are well reproduced together with compositional effects showing up in early stage measurements made on Al-0.5%Cu and Al-1%Si lines.

On Pareto’s law and the determinants of Pareto exponents

2004 ◽  
Author(s):  
William J. Reed
Keyword(s):  
Income Distribution ◽  
Stochastic Model ◽  
Population Growth ◽  
Gibrat’S Law ◽  
Income Distributions ◽  
Basic Assumptions ◽  
Rate Analysis ◽  
Gibrat's Law ◽  
Pareto Exponent ◽  
Pareto’S Law

A stochastic model for the generation of observed income distributions is used to provide an explanation for the Pareto law of incomes. The basic assumptions of the model are that the evolution of individual incomes follows Gibrat's law and that the population or workforce is growing at a fixed (probabilistic) rate. Analysis of the model suggests that Paretian behaviour can occur in either or both tails of an income distribution. It is shown that the magnitude of the upper-tail Pareto exponent depends on the interaction between the distribution of the growth in incomes and the growth in the size of the earning population. In particular a small Pareto exponent can be expected to occur for a population exhibiting fast or highly variable growth in incomes coupled with relatively slow population growth.

scholarly journals A Universal Model for the Log-Normal Distribution of Elasticity in Polymeric Gels and Its Relevance to Mechanical Signature of Biological Tissues

Biology ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 64
Author(s):  
Arnaud Millet
Keyword(s):  
Elastic Modulus ◽  
Normal Distribution ◽  
Biological Tissues ◽  
Force Microscopy ◽  
Polymeric Gels ◽  
Atomic Force ◽  
Clear Explanation ◽  
Log Normal ◽  
Log Normal Distribution

The mechanosensitivity of cells has recently been identified as a process that could greatly influence a cell’s fate. To understand the interaction between cells and their surrounding extracellular matrix, the characterization of the mechanical properties of natural polymeric gels is needed. Atomic force microscopy (AFM) is one of the leading tools used to characterize mechanically biological tissues. It appears that the elasticity (elastic modulus) values obtained by AFM presents a log-normal distribution. Despite its ubiquity, the log-normal distribution concerning the elastic modulus of biological tissues does not have a clear explanation. In this paper, we propose a physical mechanism based on the weak universality of critical exponents in the percolation process leading to gelation. Following this, we discuss the relevance of this model for mechanical signatures of biological tissues.

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