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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In two phase materials, each phase having a non-local response in time, ithas been found that for some driving fields the response somehow untangles atspecific times, and allows one to directly infer useful information about thegeometry of the material, such as the volume fractions of the phases. Motivatedby this, and to obtain an algorithm for designing appropriate driving fields,we find approximate, measure independent, linear relations between the valuesthat Markov functions take at a given set of possibly complex points, notbelonging to the interval [-1,1] where the measure is supported. The problem isreduced to simply one of polynomial approximation of a given function on theinterval [-1,1] and to simplify the analysis Chebyshev approximation is used.This allows one to obtain explicit estimates of the error of the approximation,in terms of the number of points and the minimum distance of the points to theinterval [-1,1]. Assuming this minimum distance is bounded below by a numbergreater than 1/2, the error converges exponentially to zero as the number ofpoints is increased. Approximate linear relations are also obtained thatincorporate a set of moments of the measure. In the context of the motivatingproblem, the analysis also yields bounds on the response at any particular timefor any driving field, and allows one to estimate the response at a givenfrequency using an appropriately designed driving field that effectively isturned on only for a fixed interval of time. The approximation extends directlyto Markov-type functions with a positive semidefinite operator valued measure,and this has applications to determining the shape of an inclusion in a bodyfrom boundary flux measurements at a specific time, when the time-dependentboundary potentials are suitably tailored.

An extremal problem arising in the dynamics of two-phase materials that directly reveals information about the internal geometry