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.

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.

The Log Normal Distribution 1

2020 ◽  
pp. 150-188
Author(s):  
Richard Holland ◽  
Richard St. John
Keyword(s):  
Normal Distribution ◽  
Log Normal ◽  
Log Normal Distribution
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