The Neumann sieve problem and dimensional reduction: a multiscale approach

Details The Neumann sieve problem and dimensional reduction: a multiscale approach The Neumann sieve problem and dimensional reduction: a multiscale approach

2006-05-30

arxiv.org/abs/math/0605769v1

Mathematics

Analysis of PDEs

43 pages, 4 figures

Scientific paper

We perform a multiscale analysis for the elastic energy of a $n$-dimensional bilayer thin film of thickness $2\delta$ whose layers are connected through an $\epsilon$-periodically distributed contact zone. Describing the contact zone as a union of $(n-1)$-dimensional balls of radius $r\ll \epsilon$ (the holes of the sieve) and assuming that $\delta \ll \epsilon$, we show that the asymptotic memory of the sieve (as $\epsilon \to 0$) is witnessed by the presence of an extra interfacial energy term. Moreover we find three different limit behaviors (or regimes) depending on the mutual vanishing rate of $\delta$ and $r$. We also give an explicit nonlinear capacitary-type formula for the interfacial energy density in each regime.

Affiliated with

Also associated with

No associations

Rating

The Neumann sieve problem and dimensional reduction: a multiscale approach does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Neumann sieve problem and dimensional reduction: a multiscale approach, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Neumann sieve problem and dimensional reduction: a multiscale approach will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-711381