Equation of State for Parallel Rigid Spherocylinders

The pair distribution function of monodisperse rigid spherocylinders is calculated by Shinomoto's method, which was originally proposed for hard spheres. The equation of state is derived by two different routes: Shinomoto's original route, in which a hard wall is introduced to estimate the pressure exerted on it, and the virial route. The pressure from Shinomoto's original route is valid only when the length-to-width ratio is less than or equal to 0.25 (i.e., when the spherocylinders are nearly spherical). The virial equation of state is shown to agree very well with the results of numerical simulations of spherocylinders with length-to-width ratio greater than or equal to 2

Towards a machine-independent transput section

If the transput section of an ALGOL-68 compiler is to be portable, it must be described in such a way that it is clear which aspects are machine-dependent, and which are not. There should be a clear set of primitives underlying the transput. In this report, a description is proposed which can really be used as an implementation model: the transput is described in pseudo-ALGOL 68, except for the underlying primitives, whose semantics are given in some kind of formalized English. The state of this model is by no means definitive, but may serve as a start for further discussion

Micro-evolutionary diversification among Indian Ocean parrots: temporal and spatial changes in phylogenetic diversity as a consequence of extinction and invasion

Almost 90% of global bird extinctions have occurred on islands. The loss of endemic spe- cies from island systems can dramatically alter evolutionary trajectories of insular species biodiversity, resulting in a loss of evolutionary diversity important for species adaptation to changing environments. The Western Indian Ocean islands have been the scene of evolution for a large number of endemic parrots. Since their discovery in the 16th cen- tury, many of these parrots have become extinct or have declined in numbers. Alongside the extinction of species, a number of the Indian Ocean islands have experienced coloni- zation by highly invasive parrots, such as the Ring-necked Parakeet Psittacula krameri. Such extinctions and invasions can, on an evolutionary timescale, drive changes in spe- cies composition, genetic diversity and turnover in phylogenetic diversity, all of which can have important impacts on species potential for adaptation to changing environmen- tal and climatic conditions. Using mtDNA cytochrome b data, we resolve the taxonomic placement of three extinct Indian Ocean parrots: the Rodrigues Psittacula exsul, Sey- chelles Psittacula wardi and Reunion Parakeets Psittacula eques. This case study quantifies how the extinction of these species has resulted in lost historical endemic phylogenetic diversity and reduced levels of species richness, and illustrates how it is being replaced by non-endemic invasive forms such as the Ring-necked Parakeet. Finally, we use our phylogenetic framework to identify and recommend a number of phylogenetically appro- priate ecological replacements for the extinct parrots. Such replacements may be intro- duced once invasive forms have been cleared, to rejuvenate ecosystem function and restore lost phylogenetic diversity

Neutron scattering and molecular correlations in a supercooled liquid

We show that the intermediate scattering function $S_n(q,t)$ for neutron scattering (ns) can be expanded naturely with respect to a set of molecular correlation functions that give a complete description of the translational and orientational two-point correlations in the liquid. The general properties of this expansion are discussed with special focus on the $q$-dependence and hints for a (partial) determination of the molecular correlation functions from neutron scattering results are given. The resulting representation of the static structure factor $S_n(q)$ is studied in detail for a model system using data from a molecular dynamics simulation of a supercooled liquid of rigid diatomic molecules. The comparison between the exact result for $S_n(q)$ and different approximations that result from a truncation of the series representation demonstrates its good convergence for the given model system. On the other hand it shows explicitly that the coupling between translational (TDOF) and orientational degrees of freedom (ODOF) of each molecule and rotational motion of different molecules can not be neglected in the supercooled regime.Further we report the existence of a prepeak in the ns-static structure factor of the examined fragile glassformer, demonstrating that prepeaks can occur even in the most simple molecular liquids. Besides examining the dependence of the prepeak on the scattering length and the temperature we use the expansion of $S_n(q)$ into molecular correlation functions to point out intermediate range orientational order as its principle origin.Comment: 13 pages, 7 figure

A Simple Shell Model for Quantum Dots in a Tilted Magnetic Field

A model for quantum dots is proposed, in which the motion of a few electrons in a three-dimensional harmonic oscillator potential under the influence of a homogeneous magnetic field of arbitrary direction is studied. The spectrum and the wave functions are obtained by solving the classical problem. The ground state of the Fermi-system is obtained by minimizing the total energy with regard to the confining frequencies. From this a dependence of the equilibrium shape of the quantum dot on the electron number, the magnetic field parameters and the slab thickness is found.Comment: 15 pages (Latex), 3 epsi figures, to appear in PhysRev B, 55 Nr. 20 (1997

Exact/heuristic hybrids using rVNS and hyperheuristics for workforce scheduling

In this paper we study a complex real-world workforce scheduling problem. We propose a method of splitting the problem into smaller parts and solving each part using exhaustive search. These smaller parts comprise a combination of choosing a method to select a task to be scheduled and a method to allocate resources, including time, to the selected task. We use reduced Variable Neighbourhood Search (rVNS) and hyperheuristic approaches to decide which sub problems to tackle. The resulting methods are compared to local search and Genetic Algorithm approaches. Parallelisation is used to perform nearly one CPU-year of experiments. The results show that the new methods can produce results fitter than the Genetic Algorithm in less time and that they are far superior to any of their component techniques. The method used to split up the problem is generalisable and could be applied to a wide range of optimisation problems

The Persistence Length of a Strongly Charged, Rod-like, Polyelectrolyte in the Presence of Salt

The persistence length of a single, intrinsically rigid polyelectrolyte chain, above the Manning condensation threshold is investigated theoretically in presence of added salt. Using a loop expansion method, the partition function is consistently calculated, taking into account corrections to mean-field theory. Within a mean-field approximation, the well-known results of Odijk, Skolnick and Fixman are reproduced. Beyond mean-field, it is found that density correlations between counterions and thermal fluctuations reduce the stiffness of the chain, indicating an effective attraction between monomers for highly charged chains and multivalent counterions. This attraction results in a possible mechanical instability (collapse), alluding to the phenomenon of DNA condensation. In addition, we find that more counterions condense on slightly bent conformations of the chain than predicted by the Manning model for the case of an infinite cylinder. Finally, our results are compared with previous models and experiments.Comment: 13 pages, 2 ps figure

Effect of Polydispersity and Anisotropy in Colloidal and Protein Solutions: an Integral Equation Approach

Application of integral equation theory to complex fluids is reviewed, with particular emphasis to the effects of polydispersity and anisotropy on their structural and thermodynamic properties. Both analytical and numerical solutions of integral equations are discussed within the context of a set of minimal potential models that have been widely used in the literature. While other popular theoretical tools, such as numerical simulations and density functional theory, are superior for quantitative and accurate predictions, we argue that integral equation theory still provides, as in simple fluids, an invaluable technique that is able to capture the main essential features of a complex system, at a much lower computational cost. In addition, it can provide a detailed description of the angular dependence in arbitrary frame, unlike numerical simulations where this information is frequently hampered by insufficient statistics. Applications to colloidal mixtures, globular proteins and patchy colloids are discussed, within a unified framework.Comment: 17 pages, 7 figures, to appear in Interdiscip. Sci. Comput. Life Sci. (2011), special issue dedicated to Prof. Lesser Blu

Light propagation in statistically homogeneous and isotropic universes with general matter content

We derive the relationship of the redshift and the angular diameter distance to the average expansion rate for universes which are statistically homogeneous and isotropic and where the distribution evolves slowly, but which have otherwise arbitrary geometry and matter content. The relevant average expansion rate is selected by the observable redshift and the assumed symmetry properties of the spacetime. We show why light deflection and shear remain small. We write down the evolution equations for the average expansion rate and discuss the validity of the dust approximation.Comment: 42 pages, no figures. v2: Corrected one detail about the angular diameter distance and two typos. No change in result