comment on Kinematic Scaling and Crossover to Scale Invariance in Martensite Growth,

E. Ben-Naim and P.L. Krapivsky

In a recent letter , Rao et. al. [1] proposed an appealingly simple model describing the formation of martensites. In 2D the model is defined as follows: (i) Segments grow from seeds that are nucleated in a bounded region; (ii) The tips of these segments move with a constant velocity V until they hit either another segment or the boundary; (iii) Any tip grows in one of two possible orthogonal directions. There are two important limiting cases, heterogeneous when all of the seeds are nucleated simultaneously, and homogeneous when the seeds are nucleated uniformly and stochastically in time. The homogeneous model with infinite velocity can be viewed as a multifragmentation process , and both result in similar patterns. In the following comment, we obtain exact asymptotic properties of the homogeneous model using the fragmentation method. The process is characterized by an infinite amount of scales and an infinite set of conserved quantities, and thus exhibits multiscaling. These findings disagree with the ordinary scaling behavior of the segment length distribution reported in [1].


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