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

We introduce and study a general framework for modeling the evolution ofcrack networks. The evolution steps are triggered by exponential clockscorresponding to local micro-events, and thus reflect the state of the pattern.In an appropriate simultaneous limit of pattern domain tending to infinity andtime step tending to zero, a continuous time model, specifically a system ofODE is derived that describes the dynamics of averaged quantities. Incomparison with the previous, discrete time model, studied recently by two ofthe present three authors, this approach has several advantages. In particular,the emergence of non-physical solutions characteristic to the discrete timemodel is ruled out in the relevant nonlinear version of the new model. We alsocomment on the possibilities of studying further types of pattern formationphenomena based on the introduced general framework.

An evolution model for polygonal tessellations as models for crack networks and other natural patterns