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 Plus annual

Presents the access of premium content as premium feature

Premium Content

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 annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Within a recently developed framework of dynamical Monte Carlo algorithms, wecompute the roughness exponent $\zeta$ of driven elastic strings at thedepinning threshold in 1+1 dimensions for different functional forms of the(short-range) elastic energy. A purely harmonic elastic energy leads to anunphysical value for $\zeta$. We include supplementary terms in the elasticenergy of at least quartic order in the local extension. We then find aroughness exponent of $\zeta \simeq 0.63$, which coincides with the oneobtained for different cellular automaton models of directed percolationdepinning. The quartic term translates into a nonlinear piece which changes theroughness exponent in the corresponding continuum equation of motion. Wediscuss the implications of our analysis for higher-dimensional elasticmanifolds in disordered media.Comment: 4 pages, 2 figure

Origin of the Roughness Exponent in Elastic Strings at the Depinning Threshold