Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

The critical behaviors and the scaling functions of a coalescence equationPartially supported by NSFC grant Nos. 11771286 and 11531001.

The critical behaviors and the scaling functions of a coalescence equationPartially supported by... We show that a coalescence equation exhibits a variety of critical behaviors, depending on the initial condition. This equation was introduced a few years ago to understand a toy model studied by Derrida and Retaux to mimic the depinning transition in presence of disorder. It was shown recently that this toy model exhibits the same critical behaviors as the equation studied in the present work. Here we find several families of exact solutions of this coalescence equation, in particular a family of scaling functions which are closely related to the different possible critical behaviors. These scaling functions lead to new conjectures, in particular on the shapes of the critical trees, that we have checked numerically. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Physics A: Mathematical and Theoretical IOP Publishing

The critical behaviors and the scaling functions of a coalescence equationPartially supported by NSFC grant Nos. 11771286 and 11531001.

Loading next page...
 
/lp/iop-publishing/the-critical-behaviors-and-the-scaling-functions-of-a-coalescence-4tMySpQxCF

References

References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.

Copyright
Copyright © 2020 IOP Publishing Ltd
ISSN
1751-8113
eISSN
1751-8121
DOI
10.1088/1751-8121/ab8134
Publisher site
See Article on Publisher Site

Abstract

We show that a coalescence equation exhibits a variety of critical behaviors, depending on the initial condition. This equation was introduced a few years ago to understand a toy model studied by Derrida and Retaux to mimic the depinning transition in presence of disorder. It was shown recently that this toy model exhibits the same critical behaviors as the equation studied in the present work. Here we find several families of exact solutions of this coalescence equation, in particular a family of scaling functions which are closely related to the different possible critical behaviors. These scaling functions lead to new conjectures, in particular on the shapes of the critical trees, that we have checked numerically.

Journal

Journal of Physics A: Mathematical and TheoreticalIOP Publishing

Published: May 15, 2020

There are no references for this article.