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

We study numerically the "analyticity breakdown" transition in 1-dimensionalquasi-periodic media. This transition corresponds physically to the transitionbetween pinned down and sliding ground states. Mathematically, it correspondsto the solutions of a functional equation losing their analyticity properties.We implemented some recent numerical algorithms that are efficient and backedup by rigorous results so that we can compute with confidence even close to thebreakdown. We have uncovered several phenomena that we believe deserve atheoretical explanation: A) The transition happens in a smooth surface. B)There are scaling relations near breakdown. C) The scaling near breakdown isvery anisotropic. Derivatives in different directions blow up at differentrates. Similar phenomena seem to happen in other KAM problems.

The Analyticity Breakdown for Frenkel-Kontorova Models in Quasi-periodic Media: Numerical Explorations