However, in the realistic ion-channel context, no second-order convergent PNP algorithm has ever been reported in the literature, due to many numerical obstacles, including discontinuous coefficients, singular charges, geometric singularities, and nonlinear couplings.
Recently, the matched interface and boundary (MIB) method has been utilized to develop the first second order accurate PB solver that is numerically stable in dealing with discontinuous dielectric coefficients, complex geometric singularities and singular source charges.
( {mathrm{Hf}}_{mathrm{Al}}^ ) means that Hf4+ occupies the position of Al3+ in Al2O3 lattice, with singular positive charge.
Where ( {mathrm{Al}}_{mathrm{Hf}}^{prime } ) means that Al3+ occupies the position of Hf4+ in HfO2 lattice, with singular negative charge.
His idiosyncratic visual language is informed by the fierce emotion and lavish style of his Latin American heritage, filtered by an exquisitly mannered elegance saturated with singular erotic charge".
In this paper we developed accurate finite element methods for solving 3-D Poisson Nernst Planck (PNP) equations with singular permanent charges for simulating electrodiffusion in solvated biomolecular systems.
They often subinfeudated their countships, and they needed officials called advocates (Vögte; singular Vogt) to take charge of the higher jurisdiction in the territories that their churches possessed by royal grant.
For the Bush administration, a conviction on any charge represented a singular victory, partly because a case brought on Mr. Hamdan's behalf reached the Supreme Court in 2006.
Separated out from what successive magistrates repeatedly emphasised as "the extremely serious context of unrest, looting and violence", most of the charges had a singular, and often banal, quality.
Every line in Howe's anthology felt alive, heterodox, and improvisational, charged with that singular, Yiddish-inflected music, at once embracing and at war with it too, as if in some Oedipal process of fusion and fission, of tearing loose and re-assemblage.
From this singular integral equation, we solve for the charge density distribution and thus the capacitance.
