Ion binding to polyelectrolytes: Monte Carlo simulations versus classical mean field theories

The influence of ion size and surface charge model in titrations of ionizable polyelectrolytes is studied by means of the Semi Grand Canonical Monte Carlo simulation method in the context of the primitive model. Three models describing a discrete distribution of charged functional groups on the polyelectrolyte and different values for the radius of the background electrolyte spanning from ionic to hydrated radii values were analyzed. The polyelectrolyte titrations were simulated by calculating the degree of ionization versus pH curves at two ionic strengths. The results allow us to quantify the impact of the sizes of the background salt ions and surface functional groups of the polyelectrolyte on the dissociation degree. This influence is explained in terms of the effectiveness of the screening of the charged surface sites. Finally, by comparison with the Non-Linear Poisson–Boltzmann model, the influence of ionic correlations and finite size of the solution ions is assessed.     

Structural assessment under uncertain parameters via interval analysis

An efficient health monitoring system for damage detection in civil engineering structures using on-line monitoring data is being developed to identify any possible damage in short time. The present work is based on the treatment of uncertainties, which is one of the basic common difficulties faced when modelling structures. A methodology, based on interval analysis (IA) theory [R.E. Moore, Interval Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1966] applied to a numerical constraint satisfaction problem (CSP) [J.R. Casas, J.C. Matos, J.A. Figueiras, J. Vehí, O. García, P. Herrero, Bridge monitoring and assessment under uncertainty via interval analysis, in: Ninth International Conference On Structural Safety And Reliability—ICOSSAR2005, 2005. pp. 487–494], is implemented in the damage detection [J.R. Casas, J.C. Matos, J.A. Figueiras, J. Vehí, O. García, P. Herrero, Bridge monitoring and assessment under uncertainty via interval analysis, in: Ninth International Conference On Structural Safety And Reliability—ICOSSAR2005, 2005. pp. 487–494] and modelling system of a long-term monitoring project in order to achieve such an objective. An algorithm is being developed for using such methodology with the obtained data.     

On the variety of rational curves inP n

Summary In this note one defines a stratification of the variety of rational curves inP ⁿ of given degree in terms of the decomposition of the normal bundle (see [E-vdV], [G-S] for the casen=3). The strata are showed to be irreducible and their dimension is computed.     

Dimension of complete simple games with minimum

Weighted majority games have the property that players are totally ordered by the desirability relation (introduced by Isbell in [J.R. Isbell, A class of majority games, Quarterly Journal of Mathematics, 7 (1956) 183–187]) because weights induce it. Games for which this relation is total are called complete simple games. Taylor and Zwicker proved in [A.D. Taylor, W.S. Zwicker, Weighted voting, multicameral representation, and power, Games and Economic Behavior 5 (1993) 170–181] that every simple game (or monotonic finite hypergraph) can be represented by an intersection of weighted majority games and consider the dimension of a game as the needed minimum number of them to get it. They provide the existence of non-complete simple games of every dimension and left open the problem for complete simple games.     

Imaginary vibrational modes in polycyclic aromatic hydrocarbons: a challenging test for the hardness profiles.

In a very recent article (J. Am. Chem. Soc. 2006, 128, 9342-9343) Moran et al. found that electron-correlated methodologies using popular Pople basis sets lead to spurious nonplanar polycyclic aromatic hydrocarbon (PAH) equilibrium structures. Furthermore, some of the present authors have shown that the hardness profiles along a reaction path can be a useful tool to find spurious stationary points in the potential energy surface. Herein, we test the performance of the hardness profiles to detect shortcomings in energy profiles for the challenging case of nonplanar PAHs. The results obtained show that in 41 of the 42 imaginary vibrational modes studied, the hardness profiles indicate the wrong number and type of the potential energy surface stationary points.     

Multi-Class Cost-Constrained Random Coding for Correlated Sources over the Multiple-Access Channel

This paper studies a generalized version of multi-class cost-constrained random-coding ensemble with multiple auxiliary costs for the transmission of N correlated sources over an N-user multiple-access channel. For each user, the set of messages is partitioned into classes and codebooks are generated according to a distribution depending on the class index of the source message and under the constraint that the codewords satisfy a set of cost functions. Proper choices of the cost functions recover different coding schemes including message-dependent and message-independent versions of independent and identically distributed, independent conditionally distributed, constant-composition and conditional constant composition ensembles. The transmissibility region of the scheme is related to the Cover-El Gamal-Salehi region. A related family of correlated-source Gallager source exponent functions is also studied. The achievable exponents are compared for correlated and independent sources, both numerically and analytically.