Watanabe and Hu Reply
Hiroshi Watanabe, Chin-Kun Hu

TL;DR
This paper is a reply to comments on a previous study, clarifying that certain exponents can be derived from mapping functions, and discusses the implications of these calculations.
Contribution
It demonstrates that the exponents in the 2004 paper can be computed from mapping functions, clarifying previous ambiguities.
Findings
Exponents a and b can be derived from mapping functions.
Clarification of the relationship between exponents and mapping functions.
Response to comments on earlier work.
Abstract
The article is an reply to comments on the paper [H. Watanabe, S. Yukawa, N. Ito, and C.-K. Hu, Phys. Rev. Lett. vol. 93, 19601 (2004)] by G. Pruessner and N. R. Moloney published in [Phys. Rev. Lett. vo. 95, 258901 (2005)]. In this reply, we also point out that the exponents and in the 2004 paper just mentioned can be calculated from mapping functions.
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