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

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

Pedal force asymmetries and performance during a 20-km cycling time trial

It is unclear if applying larger or more symmetrical pedal forces leads to better performance in cycling. The aims of this study were to assess the relationship between pedal force production and performance in a cycling time trial and to evaluate the relationship between asymmetries in pedal force production and performance. Fifteen competitive cyclists/triathletes performed a 20 km cycling time trial on a cycle trainer while bilateral forces applied to the pedals were recorded along with total time. Total forces applied to the pedals were computed and converted into dominant and non-dominant forces using a leg preference inventory. Pedal force asymmetries ranged from 43% (in favour of the dominant limb) to 34% (in favour of the non-dominant limb). The relationship between total pedal force (averaged from both pedals) and performance time was small (r=-.32, effect size=.66) as well as the association between the asymmetry indices and performance time (r=.01, effect size=.06). In conclusion, applying large forces on the pedals and balancing pedal force application between the dominant and non-dominant limbs did not lead to better performance in this cycling time trial

Global existence for semilinear reaction-diffusion systems on evolving domains

We present global existence results for solutions of reaction-diffusion systems on evolving domains. Global existence results for a class of reaction-diffusion systems on fixed domains are extended to the same systems posed on spatially linear isotropically evolving domains. The results hold without any assumptions on the sign of the growth rate. The analysis is valid for many systems that commonly arise in the theory of pattern formation. We present numerical results illustrating our theoretical findings.Comment: 24 pages, 3 figure

Two isoperimetric inequalities for the Sobolev constant

In this note we prove two isoperimetric inequalities for the sharp constant in the Sobolev embedding and its associated extremal function. The first such inequality is a variation on the classical Schwarz Lemma from complex analysis, similar to recent inequalities of Burckel, Marshall, Minda, Poggi-Corradini, and Ransford, while the second generalises an isoperimetric inequality for the first eigenfunction of the Laplacian due to Payne and Rayner.Comment: 11 page

Strong Cosmic Censorship and Causality Violation

We investigate the instability of the Cauchy horizon caused by causality violation in the compact vacuum universe with the topology $B\times {\bf S}^{1}\times {\bf R}$, which Moncrief and Isenberg considered. We show that if the occurrence of curvature singularities are restricted to the boundary of causality violating region, the whole segments of the boundary become curvature singularities. This implies that the strong cosmic censorship holds in the spatially compact vacuum space-time in the case of the causality violation. This also suggests that causality violation cannot occur for a compact universe.Comment: corrected version, 8 pages, one eps figure is include

A triple-blinded crossover study to evaluate the short-term safety of sweet manioc starch for the treatment of glycogen storage disease type Ia

BACKGROUND: Glycogen storage disease type 1a (GSD Ia) is characterized by severe fasting hypoglycemia. The clinical management includes the administration of uncooked cornstarch (UCCS). Although such a diet approach is effective in achieving euglycemia, its impact on the quality of life of patients should be considered. In vitro analyses suggest a longer release of glucose when using sweet manioc starch (SMS). METHODS: We compared the efficacy and safety of the administration of SMS and UCCS during a short-fasting challenge in patients with GSD Ia in a randomized, triple-blind, phase I/II, cross-over study. GSD Ia patients aged ≥ 16 years and treated with UCCS were enrolled. Participants were hospitalized for two consecutive nights, receiving UCCS or SMS in each night. After the administration of the starches, glucose, lactate and insulin levels were measured in 1-h interval throughout the hospitalization period. The procedures were interrupted after 10 h of fasting or in a hypoglycemic episode ( 25 kg/m(2)) participated in the study. The average fasting period was 8.2 ± 2.0 h for SMS and 7.7 ± 2.3 h for UCCS (p = 0.04). SMS maintained euglycemia for a greater period over UCCS. Increased lactate concentrations were detected even in absence of hypoglycemia, not being influenced by the different starches investigated (p = 0.17). No significant difference was found in total cholesterol, HDL, triglycerides and uric acid levels in both arms. None of the patients showed severe adverse events. CONCLUSIONS: SMS appears to be non-inferior to UCCS in the maintenance of euglycemia, thus emerging as a promising alternative to the treatment of GSD Ia