Properties of Poly (isoprene) - Model Building in the Melt and in Solution

Properties of 1,4-\textit{trans} poly (isoprene) at ambient conditions are determined by simulations on two length scales based on two different models: a full-atomistic and a mesoscopic one. The models are linked via a mapping scheme such that one mesoscopic bead represents one chemical repeat unit. Melts as well as solutions of several chain lengths were investigated and mapped individually to the meso-scale. The resulting models are compared to each other. The meso-scale models could be simulated over a large variety of chain lengths and time-scales relevant for experimental comparison. Concerning static properties, we determined the persistence length of our systems and the scaling behavior of the radius of gyration. The latter was compared to experiments and the agreement is satisfactory. Furthermore, we find deviations from Rouse dynamics at all chain lengths at ambient conditions.Comment: 11 pictures 7 figure

The Complexity of Computing Optimal Assignments of Generalized Propositional Formulae

We consider the problems of finding the lexicographically minimal (or maximal) satisfying assignment of propositional formulae for different restricted formula classes. It turns out that for each class from our framework, the above problem is either polynomial time solvable or complete for OptP. We also consider the problem of deciding if in the optimal assignment the largest variable gets value 1. We show that this problem is either in P or P^NP complete.Comment: 17 pages, 1 figur

‘The notorious gambling class’: Patterns of gambling among young people in Denmark: a longitudinal qualitative study

In this study, using a three wave qualitative longitudinal data set, we explored patterns of change in gambling behavior among a sample of young Danes. A total of 48 informants participated in all three sweeps of interviews. The overall aim was to explore the complexities and social contexts, as well as the subjective meanings that underlie gambling behavior changes. We identified four different types of gambling pathways, each illustrating different types of movement over time: intensification; reduction; stability, and those that were non-linear. Our overall finding was that transitions or oscillations in behavior are more common than a progressive linear gambling pattern, and that these changes are affected by a number of contextual factors. The implications for further research and policy are discussed

Mapping atomistic to coarse-grained polymer models using automatic simplex optimization to fit structural properties

We develop coarse-grained force fields for poly (vinyl alcohol) and poly (acrylic acid) oligomers. In both cases, one monomer is mapped onto a coarse-grained bead. The new force fields are designed to match structural properties such as radial distribution functions of various kinds derived by atomistic simulations of these polymers. The mapping is therefore constructed in a way to take into account as much atomistic information as possible. On the technical side, our approach consists of a simplex algorithm which is used to optimize automatically non-bonded parameters as well as bonded parameters. Besides their similar conformation (only the functional side group differs), poly (acrylic acid) was chosen to be in aqueous solution in contrast to a poly (vinyl alcohol) melt. For poly (vinyl alcohol) a non-optimized bond angle potential turns out to be sufficient in connection with a special, optimized non-bonded potential. No torsional potential has to be applied here. For poly (acrylic acid), we show that each peak of the radial distribution function is usually dominated by some specific model parameter(s). Optimization of the bond angle parameters is essential. The coarse-grained forcefield reproduces the radius of gyration of the atomistic model. As a first application, we use the force field to simulate longer chains and compare the hydrodynamic radius with experimental data.Comment: 34 pages, 3 tables, 16 figure

Mapping atomistic to coarse-grained polymer models using automatic simplex optimization to fit structural properties

We develop coarse-grained force fields for poly (vinyl alcohol) and poly (acrylic acid) oligomers. In both cases, one monomer is mapped onto a coarse-grained bead. The new force fields are designed to match structural properties such as radial distribution functions of various kinds derived by atomistic simulations of these polymers. The mapping is therefore constructed in a way to take into account as much atomistic information as possible. On the technical side, our approach consists of a simplex algorithm which is used to optimize automatically non-bonded parameters as well as bonded parameters. Besides their similar conformation (only the functional side group differs), poly (acrylic acid) was chosen to be in aqueous solution in contrast to a poly (vinyl alcohol) melt. For poly (vinyl alcohol) a non-optimized bond angle potential turns out to be sufficient in connection with a special, optimized non-bonded potential. No torsional potential has to be applied here. For poly (acrylic acid), we show that each peak of the radial distribution function is usually dominated by some specific model parameter(s). Optimization of the bond angle parameters is essential. The coarse-grained forcefield reproduces the radius of gyration of the atomistic model. As a first application, we use the force field to simulate longer chains and compare the hydrodynamic radius with experimental data.Comment: 34 pages, 3 tables, 16 figure

Corrections to Scaling in the Hydrodynamic Properties of Dilute Polymer Solutions

We discuss the hydrodynamic radius $R_H$ of polymer chains in good solvent, and show that the leading order correction to the asymptotic law $R_H \propto N^\nu$ ($N$ degree of polymerization, $\nu \approx 0.59$) is an ``analytic'' term of order $N^{-(1 - \nu)}$, which is directly related to the discretization of the chain into a finite number of beads. This result is further corroborated by exact calculations for Gaussian chains, and extensive numerical simulations of different models of good--solvent chains, where we find a value of $1.591 \pm 0.007$ for the asymptotic universal ratio $R_G / R_H$, $R_G$ being the chain's gyration radius. For $\Theta$ chains the data apparently extrapolate to $R_G / R_H \approx 1.44$, which is different from the Gaussian value 1.5045, but in accordance with previous simulations. We also show that the experimentally observed deviations of the initial decay rate in dynamic light scattering from the asymptotic Benmouna--Akcasu value can partly be understood by similar arguments.Comment: 13 pages, 10 figures. submitted to J. Chem. Phy

'Risky places?': mapping gambling machine density and socio-economic deprivation

The aims of this project were to map the location and density of gambling machines in Britain; to explore whether geographic areas with higher densities of machines exist and to examine the socio-economic characteristics of these areas relative to others. Using geospatial analysis of premises records, we identified 8861 Machine Zones which were areas with a 400 meter radius around gambling machine venue and 384 High Density Machine Zones (HDMZ) with 1 or more gambling machine per hectare. There was a significant correlation between machine density and socio-economic deprivation. HDMZs had greater levels of income deprivation, more economically inactive people and a younger age profile than other areas; 37 % of those living in HDMZs were economically inactive compared with 33 % of those in non-machine areas. HDMZs were in seaside locations but also New Towns or satellite towns to major urban areas. Area affluence explains some of this pattern; of the New Towns with HDMZs, 78 % were in New Towns with a high proportion of low income areas. We therefore concluded that the distribution of gambling machines in Great Britain, in line with other international jurisdictions, displays a significant association with areas of socio-economic deprivation. The profile of the resident population living in HDMZs mirrors the profile of those most at-risk of experiencing harm from gambling. This spatial pattern has important implications for assessing the relationship between gambling availability and gambling-related harm, and for the future development of policy, harm-prevention and treatment strategies