A model of fads,fashions, and group formation

I develop a model of consumer behavior where agents purchase goods in order to signify personal characteristics. Agents purchase goods in order to imitate agents similar to them and agents they want to emulate. Depending on parameter values of consumer preferences the model generates stable groups, fads, and fashion cycles, or a mixture of both. The model is unique to the economic literature on fads in that the extinction of fads occurs endogenously in the model. © 2004 Wiley Periodicals, Inc. Complexity 9: 51–61, 2004     

On divisibility properties of certain multinomial coefficients—II

A recent conjecture of Myerson and Sander concerns divisibility properties of certain multinomial coefficients. We obtain results in this direction by further pursuing a line of attack developed earlier by the first author.     

An ab initio molecular orbital study of the grignard reagents CH3MgCl and [CH3MgCl]2: The Schlenk equilibrium

Ab initio molecular orbital calculations are used to study the modified Schlenk equilibrium: 2RMgCl (RMgCl)² MgR₂ + MgCl₂ Mg(Cl₂)MgR₂ with R=H and CH₃. In the absence of any solvents, calculations indicate that the formation of the various possible bridged dimers (RMgCl)₂ is substantially exothermic. However, using dimethylether as a model solvent, we show that the formation of the dimer (Me₂O)(CH₃)Mg(Cl₂)Mg(CH₃)(OMe₂) is exothermic only when entropic effects are included.     

Glutaraldehyde crosslinking of arabinoxylan produced from corn ethanol residuals

This study investigated the possibility of substituting petroleum-based polymers with biopolymers for films and paper coatings. Arabinoxylan (AX) was extracted from distillers’ grains, a low-value corn ethanol byproduct, and modified through crosslinking with glutaraldehyde (GA) which was made into films and paper coatings. The effects of degree of substitution (DS) on film and coating properties of GA cross-linked AX, referred to as GAX, were investigated. The GAX films had markedly higher tensile strength, approximately 3 times higher than the unmodified AX films at low DS, with higher DS causing a negative effect on the film tensile strength. Compared to unmodified AX coating, paper coated with GAX also had significantly higher tensile index, presumably due to high adhesion between the coating and paper interface. When used as a coating binder with calcium carbonate pigments, GAX showed comparable performance to polyvinyl alcohol, a common industrial binder, demonstrating the potential to be substituted for the petroleum-based paper coating binder.     

A theoretical study of aqueous solvation of K comparing ab initio, polarizable, and fixed-charge models

The hydration of K(+) is studied using a hierarchy of theoretical approaches, including ab initio Born-Oppenheimer molecular dynamics and Car-Parrinello molecular dynamics, a polarizable force field model based on classical Drude oscillators, and a nonpolarizable fixed-charge potential based on the TIP3P water model. While models based more directly on quantum mechanics offer the possibility to account for complex electronic effects, polarizable and fixed-charges force fields allow for simulations of large systems and the calculation of thermodynamic observables with relatively modest computational costs. A particular emphasis is placed on investigating the sensitivity of the polarizable model to reproduce key aspects of aqueous K(+), such as the coordination structure, the bulk hydration free energy, and the self diffusion of K(+). It is generally found that, while the simple functional form of the polarizable Drude model imposes some restrictions on the range of properties that can simultaneously be fitted, the resulting hydration structure for aqueous K(+) agrees well with experiment and with more sophisticated computational models. A counterintuitive result, seen in Car-Parrinello molecular dynamics and in simulations with the Drude polarizable force field, is that the average induced molecular dipole of the water molecules within the first hydration shell around K(+) is slightly smaller than the corresponding value in the bulk. In final analysis, the perspective of K(+) hydration emerging from the various computational models is broadly consistent with experimental data, though at a finer level there remain a number of issues that should be resolved to further our ability in modeling ion hydration accurately.