For a bounded Lipschitz domain Ω, we show the existence of a measurable set D ⊂ ∂Ω of given area such that the first eigenvalue of the Laplacian with Dirichlet conditions on D and Neumann conditions on ∂Ω \D becomes minimal. If Ω is a ball, D will be a spherical cap.

The Laurentide Ice Sheet (LIS) was the largest ice sheet in Northern Hemisphere during last glacial cycle. effects of its demise on global climate and sea-level changes subsequent deglaciation are unequivocal. Understanding interplay between sheets long-term or short-term (e.g. abrupt) climatic events is therefore crucial for predicting future rates melting their potential contribution to chang...

BACKGROUND Different enhancement procedures have been suggested for reduction of residual refractive errors after SMILE. The aim of this study is to evaluate an improved cap-preserving technique for enhancement after SMILE (Re-SMILE). METHODS A retrospective case series was conducted at Eye subspecialty center, Cairo, Egypt on 9 eyes with myopia or myopic astigmatism (spherical equivalent - 8...

The effect of soluble surfactants on the unsteady motion and deformation of a bubble rising in an otherwise quiescent liquid contained in an axisymmetric tube is computationally studied by using a finite-difference/front-tracking method. The unsteady incompressible flow equations are solved fully coupled with the evolution equations of bulk and interfacial surfactant concentrations. The surface...

We have produced the first series of spherical harmonic, numerical maps of the time-dependent surface perturbations in the Earth's magnetic field following the onset of substorms. Data from 124 ground magnetometer stations in the Northern Hemisphere at geomagnetic latitudes above 33° were used. Ground station data averaged over 5 min intervals covering 8 years (1998-2005) were used to construct...

This article explores, through experiments and finite element analysis, the ability to plastically deform thin-film semiconductor structures on deformable substrates to spherical cap shapes without cracking the semiconductor layers. The major challenge involves contending with the large strain due to extreme deformation that will crack uniform stiff layers, such as silicon or silicon nitride. B...

Simulated body fluids (SBFs) that mimic human blood plasma are widely used media for in vitro studies an extensive array of research fields, from biomineralization to surface and corrosion sciences. We show these solutions undergo dynamic nanoscopic conformational rearrangements on the timescale minutes hours, even though they commonly considered stable or metastable. In particular, we find cha...