# Effect of discontinuity in the threshold distribution on the critical behavior of a random fiber bundle

## Abstract

The critical behavior of a random fiber bundle model with mixed uniform distribution of threshold strengths and global load sharing rule is studied with a special emphasis on the nature of distribution of avalanches for different parameters of the distribution. The discontinuity in the threshold strength distribution of fibers nontrivially modifies the critical stress as well as puts a restriction on the allowed values of parameters for which the recursive dynamics approach holds good. The discontinuity leads to a nonuniversal behavior in the avalanche size distribution for smaller values of avalanche size. We observe that apart from the mean field behavior for larger avalanches, a new behavior for smaller avalanche size is observed as a critical threshold distribution is approached. The phenomenological understanding of the above result is provided using the exact analytical result for the avalanche size distribution. Most interestingly, the prominence of nonuniversal behavior in avalanche size distribution depends on the system parameters.

- Authors:

- Department of Physics, Indian Institute of Technology, Kanpur-208016 (India)

- Publication Date:

- OSTI Identifier:
- 21072269

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; Journal Volume: 75; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevE.75.011117; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANALYTICAL SOLUTION; DISTRIBUTION; EXACT SOLUTIONS; FIBERS; MEAN-FIELD THEORY; RANDOMNESS; STRESS ANALYSIS; STRESSES

### Citation Formats

```
Divakaran, Uma, and Dutta, Amit.
```*Effect of discontinuity in the threshold distribution on the critical behavior of a random fiber bundle*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVE.75.011117.

```
Divakaran, Uma, & Dutta, Amit.
```*Effect of discontinuity in the threshold distribution on the critical behavior of a random fiber bundle*. United States. doi:10.1103/PHYSREVE.75.011117.

```
Divakaran, Uma, and Dutta, Amit. Mon .
"Effect of discontinuity in the threshold distribution on the critical behavior of a random fiber bundle". United States.
doi:10.1103/PHYSREVE.75.011117.
```

```
@article{osti_21072269,
```

title = {Effect of discontinuity in the threshold distribution on the critical behavior of a random fiber bundle},

author = {Divakaran, Uma and Dutta, Amit},

abstractNote = {The critical behavior of a random fiber bundle model with mixed uniform distribution of threshold strengths and global load sharing rule is studied with a special emphasis on the nature of distribution of avalanches for different parameters of the distribution. The discontinuity in the threshold strength distribution of fibers nontrivially modifies the critical stress as well as puts a restriction on the allowed values of parameters for which the recursive dynamics approach holds good. The discontinuity leads to a nonuniversal behavior in the avalanche size distribution for smaller values of avalanche size. We observe that apart from the mean field behavior for larger avalanches, a new behavior for smaller avalanche size is observed as a critical threshold distribution is approached. The phenomenological understanding of the above result is provided using the exact analytical result for the avalanche size distribution. Most interestingly, the prominence of nonuniversal behavior in avalanche size distribution depends on the system parameters.},

doi = {10.1103/PHYSREVE.75.011117},

journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},

number = 1,

volume = 75,

place = {United States},

year = {Mon Jan 15 00:00:00 EST 2007},

month = {Mon Jan 15 00:00:00 EST 2007}

}