Abstract.By direct statistical analysis we show that over almost all their range of scales and to within typically better than ±1%, atmospheric fields obtained from analyses and numerical integrations of atmospheric models have the multifractal structure predicted by multiplicative cascade models. We quantify this for the horizontal wind, temperature, and humidity fields at 5 different pressure levels for the ERA40 reanalysis, the Canadian Meteorological Centre Global Environmental Multiscale (CMC, GEM) model, as well as the National Oceanographic and Atmospheric Administration Global Forecasting System (NOAA, GFS). We investigate the additional prediction that the cascade belongs to a universal multifractal basin of attraction. By demonstrating a "Levy collapse" of the statistical moments to within ±2 to ±5% over most of the range of scales, we conclude that there is good evidence for this. Finally, we discuss how this stochastic multiplicative cascade structure can be exploited in improving ensemble forecasts.

The phase-field-crystal (PFC) modeling paradigm is rapidly emerging as the model of choice when investigating materials phenomena with atomistic scale effects over diffusive time scales. Recent variants of the PFC model, so-called structural PFC (XPFC) models introduced by Greenwood et al., have further increased the capability of the method by allowing for easy access to various structural transformations in pure materials [Phys. Rev. Lett. 105, 045702 (2010)] and binary alloys [Phys. Rev. B. 84, 064104, (2011)]. We present an amplitude expansion of these XPFC models, leading to a mesoscale complex order-parameter (amplitude), i.e., phase-field representation, model for two dimensional square-triangular structures. Amplitude models retain the salient atomic scale features of the underlying PFC models, while resolving microstructures on mesoscales as in traditional phase-field models. The applicability and capability of this complex amplitude model is demonstrated with simulations of peritectic solidification and grain growth exhibiting the emergence of secondary phase structures.

A phase field crystal model is used to investigate the mechanisms of formation and growth of early clusters in quenched/aged dilute binary alloys, a phenomenon typically outside the scope of molecular dynamics time scales. We show that formation of early sub-critical clusters is triggered by the stress relaxation effect of quenched-in defects, such as dislocations, on the energy barrier and the critical size for nucleation. In particular, through analysis of system energetics, we demonstrate that the growth of sub-critical clusters into overcritical sizes occurs due to the fact that highly strained areas in the lattice locally reduce or even eliminate the free energy barrier for a first-order transition.

Phase field crystal methodology is applied, for the first time, to study the effect of alloy composition on the clustering behavior of a quenched/aged supersaturated ternary Al alloy system. An analysis of the work of formation is built upon the methodology developed in Fallah et al. to describe the dislocation-mediated formation mechanisms of early clusters in binary alloys [Phys. Rev. B., DOI: 10.1103/PhysRevB.00.004100]. Consistent with the experiments, we demonstrate that the addition of Mg to an Al-1.1Cu alloy increases the nucleation rate of clusters in the quenched/aged state by increasing the effective driving force for nucleation, enhancing the dislocation stress relaxation and decreasing the surface energy associated with the Cu-rich Cu-Mg co-clusters. Furthermore, we show that it is thermodynamically favourable for small sub-critical clusters to have higher affinity for Mg than larger overcritical Cu-rich clusters, particularly depicting a two-stage clustering phenomenon.arXiv:1210.4977v1 [cond-mat.mtrl-sci] 17 Oct 2012With the above approximations at hand, the 3-component PFC energy functional for species A, B and C can be shown