English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Computing stationary states is an important topic for phase field crystal(PFC) models. Great efforts have been made for energy dissipation of thenumerical schemes when using gradient flows. However, it is alwaystime-consuming due to the requirement of small effective time steps. In thispaper, we propose an adaptive accelerated proximal gradient method for findingthe stationary states of PFC models. The energy dissipation is guaranteed andthe convergence property is established for the discretized energy functional.Moreover, the connections between generalized proximal operator with classical(semi-)implicit and explicit schemes for gradient flow are given. Extensivenumerical experiments, including two three dimensional periodic crystals inLandau-Brazovskii (LB) model and a two dimensional quasicrystal inLifshitz-Petrich (LP) model, demonstrate that our approach has adaptive timesteps which lead to significant acceleration over semi-implicit methods forcomputing complex structures. Furthermore, our result reveals a deep physicalmechanism of the simple LB model via which the sigma phase is first discovered.

An efficient method for computing stationary states of phase field crystal models