Direct test of the Gaussian auxiliary field ansatz in nonconserved order parameter phase ordering dynamics

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


The assumption that the local order parameter is related to an underlying spatially smooth auxiliary field, u(r - ,t), is a common feature in theoretical approaches to non-conserved order parameter phase separation dynamics. In particular, the ansatz that u(r - ,t) is a Gaussian random field leads to predictions for the decay of the autocorrelation function which are consistent with observations, but distinct from predictions using alternative theoretical approaches. In this paper, the auxiliary field is obtained directly from simulations of the time-dependent Ginzburg-Landau equation in two and three dimensions. The results show that u(r - ,t) is equivalent to the distance to the nearest interface. In two dimensions, the probability distribution, P(u), is well approximated as Gaussian except for small values of u/L(t), where L(t) is the characteristic length-scale of the patterns. The behavior of P(u) in three dimensions is more complicated; the non-Gaussian region for small u/L(t) is much larger than that in two dimensions but the tails of P(u) begin to approach a Gaussian form at intermediate times. However, at later times, the tails of the probability distribution appear to decay faster than a Gaussian distribution.

Original languageEnglish (US)
Article number062107
JournalPhysical Review E
Issue number6
StatePublished - Jun 4 2018

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


Dive into the research topics of 'Direct test of the Gaussian auxiliary field ansatz in nonconserved order parameter phase ordering dynamics'. Together they form a unique fingerprint.

Cite this