Cycles of cooperation and free-riding in social systems

Basic evidences on non-profit making and other forms of benevolent-based organizations reveal a rough partition of members between some pure consumers of the public good (free-riders) and benevolent individuals (cooperators). We study the relationship between the community size and the level of cooperation in a simple model where the utility of joining the community is proportional to its size. We assume an idiosyncratic willingness to join the community ; cooperation bears a fixed cost while free-riding bears a (moral) idiosyncratic cost proportional to the fraction of cooperators. We show that the system presents two types of equilibria: fixed points (Nash equilibria) with a mixture of cooperators and free-riders and cycles where the size of the community, as well as the proportion of cooperators and free-riders, vary periodically.     

Theories for network formation in multistage processes

Two different theoretical approaches have been developed to describe network formation in a six-component, three-stage process with the stochastic theory of branching processes. Both approaches make use of probability-generating functions and cascade substitutions. In the POLYM approach, the products of the previous stage, namely, complete (branched) molecules, are used as building units in the subsequent stage. The molar masses and unreacted functionalities are identified by means of dummy variables. In the resulting formulas the sequence of the three stages is clearly visible. In the MONOM approach, the system is treated as a quasi-one-stage process; the original monomers are the building units in all three stages, the sequence of which is only apparent from the input parameters. In the MONOM approach the original monomers are used as building units, irrespective of the stage in which they react. A separate dummy variable is chosen for each possible reaction in each stage in the MONOM approach, so that the two approaches give analytically identical results, but along completely different derivations. This avoids correlation errors in the MONOM approach. Both approaches have incorporated kinetic effects by way of substitution effects in two of the monomers. The two approaches are prefaced by the treatment of several paradigms of increasing complexity to show the unity and strength of the theory and to warn against typical pitfalls.     

Atomic physicochemical parameters for three dimensional structure directed quantitative structure-activity relationships III: Modeling hydrophobic interactions

In an earlier article⁸ the need was demonstrated for atomic physicochemical properties for three dimensional structure directed quantitative structure-activity relationships, and it was shown how atomic parameters can be developed for successfully evaluating the molecular octanol-water partition coefficient, which is a measure of hydrophobicity. In this work we report more refined atomic values of octanol-water partition coefficients derived from nearly twice the number of compounds. Carbon, hydrogen, oxygen, nitrogen, sulfur and halogens are divided into 110 atom types of which 94 atomic values are evaluated from 830 molecules by least squares. These values gave a standard deviation of 0.470 and a correlation coefficient of 0.931. These parameters predicted the octanol-water partition coefficient of 125 compounds with a standard deviation of 0.520 and a correlation coefficient of 0.870. There is only a correlation coefficient of 0.432 between the atomic octanol-water partition coefficients and the atomic contributions to molar refractivity over the 93 atom types used for both the properties. This suggests that both parameters can be used simultaneously to model intermolecular interactions. We evaluated the CNDO/2 gross atomic charge distribution over several molecules to check the validity of our classification. We found that the charge density on the heteroatoms in conjugated systems is strongly affected by the presence of similar atoms in the conjugation which suggests it should be incorporated as a separate parameter in evaluating the partition coefficient.     

Restoration of charpy toughness for “in service” temper embrittled steels

This paper describes a detailed examination which could be conducted during a planned outage. It is concerned with assessing reverse temper embrittlement of CrMoV steel turbine bolts after 120 000 h of service. A small section of material was removed from a non-critical location of all the 92 IP and HP bolts. From this section, the chemical composition, average hardness and average prior austenite grain size were measured. The toughness of the bolts was measured by Charpy impact testing and/or Auger electron spectroscopy. From the various parameters investigated, it was established that grain size and phosphorus level were the only factors which consistently identified whether a bolt was embrittled or non-embrittled. Indeed, at a phosphorus level of 0.01%, bolts with grain sizes less than 20 μm were not embrittled while those with larger grain sizes suffered reverse temper embrittlement during service. An embrittlement estimative diagram was established by plotting grain size versus phosphorus level (%P). This portrayed two distinct regimes, an embrittled and non-embrittled regime which were separated by a critical embrittled-non-embrittled interface which could be described by d × (%P) = 0.18 where d is the grain size in μm. Such an embrittlement estimate diagram represent a cogent and practical route in the identification of in-service embrittled bolts.     

Novel pentacoordinated bridged silicon anions

Both ab initio and semiempirical electronic structure calculations are used to investigate the molecular and electronic structures and eneregetic stabilities of an unusual bridged compound with the general formula [Y? SiH₃? X? SiH₃? Y]^?, with Y = H or F and X = H, CH₃, NH₂, OH, F, or Cl. Most of these bridged anions are quite stable relative to YSiH₃ + XSiH₃Y^?, and the stability is predicted to increase considerably when Y = H is replaced with Y = F.     

Polarization eigenmodes of a QHQ retarder — some new features

A detailed analysis of the polarization eigenmodes of a QHQ retarder (a half-wave plate sandwiched between two identical quarter-wave plates) is presented. These are shown to be discontinuous as a function of the orientation of the half-wave plate, as a function of the wavelength of incident light and as a function of the retardation of the middle waveplate.     

Suppression of interferences in the determination of lead in natural and drinking waters by graphite-furnace atomic absorption spectrometry

The problem of matrix interference encountered in the determination of lead in natural and drinking waters by graphite furnace atomic absorption spectrometry is examined by looking at the individual effects of various constituent salts (NaCl, KCl, MgCl₂ and CaCl₂, Na₂SO₄, KH₂PO₄ and Mg(NO₃)₂), of which MgCl₂ and Na₂SO₄ interfered most severely. The use of the L'vov platform decreased the sulphate interference, but was not successful in removing the other interferences. The mixture of 0.05% (w/v) lanthanum (as LaCl₃) and 1% (v/v) nitric acid previously proposed for wall atomisation was found to be effective in controlling the interferences. Nitric acid alone removed almost completely the effects of MgCl₂ and CaCl₂, but had little effect on the interference of sulphate, which required the addition of lanthanum for suppression. The removal of interferences in real water samples by the lanthanum/nitric acid mixture is demonstrated by comparison of results obtained by this approach with those obtained by atomic fluorescence spectrometry and by flame atomic absorption spectrometry after preconcentration by evaporation.