Bounds for the first eigenvalue of the elastically supported membrane on convex domains

ISSN:1420-9039ISSN:0044-227

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Bounds for the first eigenvalue of the elastically supportedmembrane on convex domains

Barta's principle and gradient bounds for the torsion function are the main tools for deriving lower bounds for the first eigenvalue. The optimal domains are an infinite strip, a disk or an annulus in different situation

Yukawa potentials in systems with partial periodic boundary conditions II : Lekner sums for quasi-two dimensional systems

Yukawa potentials may be long ranged when the Debye screening length is large. In computer simulations, such long ranged potentials have to be taken into account with convenient algorithms to avoid systematic bias in the sampling of the phase space. Recently, we have provided Ewald sums for quasi-two dimensional systems with Yukawa interaction potentials [M. Mazars, {\it J. Chem. Phys.}, {\bf 126}, 056101 (2007) and M. Mazars, {\it Mol. Phys.}, Paper I]. Sometimes, Lekner sums are used as an alternative to Ewald sums for Coulomb systems. In the present work, we derive the Lekner sums for quasi-two dimensional systems with Yukawa interaction potentials and we give some numerical tests for pratical implementations. The main result of this paper is to outline that Lekner sums cannot be considered as an alternative to Ewald sums for Yukawa potentials. As a conclusion to this work : Lekner sums should not be used for quasi-two dimensional systems with Yukawa interaction potentials.Comment: 25 pages, 5 figures and 1 tabl

Strong-Coupling Theory for Counter-Ion Distributions

The Poisson-Boltzmann approach gives asymptotically exact counter-ion density profiles around charged objects in the weak-coupling limit of low valency and high temperature. In this paper we derive, using field-theoretic methods, a theory which becomes exact in the opposite limit of strong coupling. Formally, it corresponds to a standard virial expansion. Long-range divergences, which render the virial expansion intractable for homogeneous bulk systems, are shown to be renormalizable for the case of inhomogeneous distribution functions by a systematic expansion in inverse powers of the coupling parameter. For a planar charged wall, our analytical results compare quantitatively with extensive Monte-Carlo simulations.Comment: 7 pages, 3 figures; to appear in Europhys. Let

Counterions at charge-modulated substrates

We consider counterions in the presence of a single planar surface with a spatially inhomogeneous charge distribution using Monte-Carlo simulations and strong-coupling theory. For high surface charges, multivalent counterions, or pronounced substrate charge modulation the counterions are laterally correlated with the surface charges and their density profile deviates strongly from the limit of a smeared-out substrate charge distribution, in particular exhibiting a much increased laterally averaged density at the surface.Comment: 7 page

Silicon and oxygen self diffusion in enstatite polycrystals: the Milke et al. (2001) rim growth experiments revisited

Milke et al. (Contrib Mineral Petrol 142:15-26, 2001) studied the diffusion of Si, Mg and O in synthetic polycrystalline enstatite reaction rims. The reaction rims were grown at 1,000°C and 1GPa at the contacts between forsterite grains with normal isotopic compositions and a quartz matrix extremely enriched in 18O and 29Si. The enstatite reaction rim grew from the original quartz-forsterite interface in both directions producing an inner portion, which replaced forsterite and an outer portion, which replaced quartz. Here we present new support for this statement, as the two portions of the rim are clearly distinguished based on crystal orientation mapping using electron backscatter diffraction (EBSD). Milke et al. (Contrib Mineral Petrol 142:15-26, 2001) used the formalism of LeClaire (J Appl Phys 14:351-356, 1963) to derive the coefficient of silicon grain boundary diffusion from stable isotope profiles across the reaction rims. LeClaire's formalism is designed for grain boundary tracer diffusion into an infinite half space with fixed geometry. A fixed geometry is an undesired limitation in the context of rim growth. We suggest an alternative model, which accounts for simultaneous layer growth and superimposed silicon and oxygen self diffusion. The effective silicon bulk diffusivity obtained from our model is approximately equal within both portions of the enstatite reaction rim: D Si,En eff =1.0-4.3×10−16m2s−1. The effective oxygen diffusion is relatively slow in the inner portion of the reaction rim, D O,En eff =0.8-1.4×10−16m2s−1, and comparatively fast, D O,En eff =5.9-11.6×10−16m2s−1, in its outer portion. Microstructural evidence suggests that transient porosity and small amounts of fluid were concentrated at the quartz-enstatite interface during rim growth. This leads us to suspect that the presence of an aqueous fluid accelerated oxygen diffusion in the outer portion of the reaction rim. In contrast, silica diffusion does not appear to have been affected by the spatial variation in the availability of an aqueous flui

Logarithmic interaction under periodic boundary conditions: Closed form formulas for energy and forces

A method is given to obtain closed form formulas for the energy and forces for an aggregate of charges interacting via a logarithmic interaction under periodic boundary conditions. The work done here is a generalization of Glasser's results [M. L. Glasser, J. Math. Phys. 15, 188 (1974)] and is obtained with a different and simpler method than that by Stremler [M. A. Stremler, J. Math. Phys. 45, 3584 (2004)]. The simplicity of the formulas derived here makes them extremely convenient in a computer simulation

Friendship and gender in preschoolers’ conflicts

Investigated the role of friendship and gender on conflict episodes of 48 preschoolers aged approximately 5 years and 8 months. Children were organized in dyads of same-sex friends and non-friends. Conflict situations were coded according to incidence, type, termination strategies, and finalizations. Gender differences were detected for type of conflict, with girls using more reasons for oppositions than boys. Termination strategies were used with a joint effect of friendship and gender: girl-friends preferred the tactic of standing firm whereas boy-friends chose more negotiation as means to deal with a disagreement, compared to the non-friend dyads. As for the results on conflict finalizations, friendship relations accounted for a significant difference found for agreement, while gender showed to be related to the use of disengagement among girls. Combined analysis between termination strategies and conflict finalizations indicated two significant differences: the first was related to friendship, through which children used more negotiation leading to agreement; the second showed a joint effect of friendship and gender, where non-friend girls tended to negotiate to reach disengagement, more often that non-friend boys. Findings for termination strategies – with girl-friends being more incisive and firm with their partners – diverge from the results provided by empirical literature, where boys are described as more autonomy- and domain oriented, and girls are prone to intimacy and social well-being in their relationships. Results are discussed with basis on previous studies conducted on conflict among preschoolers with considerations about the effects of gender and type of relationship

On the lowest eigenvalue of Laplace operators with mixed boundary conditions

In this paper we consider a Robin-type Laplace operator on bounded domains. We study the dependence of its lowest eigenvalue on the boundary conditions and its asymptotic behavior in shrinking and expanding domains. For convex domains we establish two-sided estimates on the lowest eigenvalues in terms of the inradius and of the boundary conditions