Asymptotic decay of pair correlations in a Yukawa fluid

We analyse the $r \to \infty$ asymptotic decay of the total correlation function, $h(r)$, for a fluid composed of particles interacting via a (point) Yukawa pair potential. Such a potential provides a simple model for dusty plasmas. The asymptotic decay is determined by the poles of the liquid structure factor in the complex plane. We use the hypernetted-chain closure to the Ornstein-Zernike equation to determine the line in the phase diagram, well-removed from the freezing transition line, where crossover occurs in the ultimate decay of $h(r)$, from monotonic to damped oscillatory. We show: i) crossover takes place via the same mechanism (coalescence of imaginary poles) as in the classical one-component plasma and in other models of Coulomb fluids and ii) leading-order pole contributions provide an accurate description of $h(r)$ at intermediate distances $r$ as well as at long range.Comment: 5 pages, 3 figure

Strategic Review of Tropical Fisheries Management

This project addresses the constraints to tropical fisheries development with sustainable exploitation through a strategic assessment of tropical fisheries management with the following purposes: (1) To evaluate relevant research methods for the development of assessment models appropriate to the circumstances of tropical coastal fisheries; and (2) To evaluate the utility of existing strategies for the implementation of management advice. The report consists of three substantive chapters. Chapter 2 contains a detailed socio-economic assessment of various instruments and implementation strategies applicable to tropical capture fisheries. In Chapter 3, a detailed assessment of the fisheries for tropical large marine ecosystems has been conducted using a technique developed by FAO (Granger & Garcia 1996). The data used were the FAO statistics published regularly by FAO. This analysis has been conducted for each of the tropical large marine ecosystems and indicates that there is the potential for increased fishing in a number of these ecosystems. One of the clear requirements identified in Chapter 2 and implicit in Chapter 3, is that there is a significant need for simple and robust fisheries assessment methods which can estimate the potential of a particular resource, its capacity in terms of the level of fishing effort and its current status ie whether it is currently exploited sustainably or not. In Chapter 4, these problems are addressed directly and, using two approaches, significant simplification of fishery methods is developed. In the first approach, simple empirical relationships between the life history parameters of a species are used to develop models of potential yield which can be determined by a simple assessment of fish growth. In the second approach, optimal life history theory is applied to the key demographic parameters of exploited fish populations and using estimates of the Beverton & Holt invariants a significant simplifying of the basic stock assessment equations is developed

Coral Reef Fisheries Literature Review and Database Research Report, Final Technical Report

First, coral reef fisheries literature references were obtained and organised into a computer database and a user manual produced. Second, a comprehensive review article summarising and interpreting the disparate literature was written and distributed along with the database. The database and accompanying review should assist research and management of coral reef fisheries in developing countries. In the original project memorandum, it was stated that initial emphasis would be placed on fin-fish fisheries. This emphasis has been maintained throughout the projec

The Statistical Mechanical Theory of Transport Processes. III. The Coefficients of Shear and Bulk Viscosity of Liquids

A molecular theory of the coefficients of shear and bulk viscosity of monatomic liquids is developed on the basis of the general theory of transport processes presented in the first article of this series. With the use of the Lennard-Jones potential and a reasonable analytic approximation to the experimental radial distribution function, calculations of the coefficients of shear and bulk viscosity of liquid argon at 89°K have been carried out. The theory leads explicitly to ratios of the coefficients to the friction constant of the theory of Brownian motion. With a preliminary estimate of the friction constant, a value of the shear viscosity of liquid argon in moderately good agreement with experiment is obtained

The intermittent behavior and hierarchical clustering of the cosmic mass field

The hierarchical clustering model of the cosmic mass field is examined in the context of intermittency. We show that the mass field satisfying the correlation hierarchy $\xi_n\simeq Q_n(\xi_2)^{n-1}$ is intermittent if $\kappa < d$, where $d$ is the dimension of the field, and $\kappa$ is the power-law index of the non-linear power spectrum in the discrete wavelet transform (DWT) representation. We also find that a field with singular clustering can be described by hierarchical clustering models with scale-dependent coefficients $Q_n$ and that this scale-dependence is completely determined by the intermittent exponent and $\kappa$. Moreover, the singular exponents of a field can be calculated by the asymptotic behavior of $Q_n$ when $n$ is large. Applying this result to the transmitted flux of HS1700 Ly$\alpha$ forests, we find that the underlying mass field of the Ly$\alpha$ forests is significantly intermittent. On physical scales less than about 2.0 h$^{-1}$ Mpc, the observed intermittent behavior is qualitatively different from the prediction of the hierarchical clustering with constant $Q_n$. The observations, however, do show the existence of an asymptotic value for the singular exponents. Therefore, the mass field can be described by the hierarchical clustering model with scale-dependent $Q_n$. The singular exponent indicates that the cosmic mass field at redshift $\sim 2$ is weakly singular at least on physical scales as small as 10 h$^{-1}$ kpc.Comment: AAS Latex file, 33 pages,5 figures included, accepted for publication in Ap

Hydrogen atom in phase space. The Kirkwood-Rihaczek representation

We present a phase-space representation of the hydrogen atom using the Kirkwood-Rikaczek distribution function. This distribution allows us to obtain analytical results, which is quite unique because an exact analytical form of the Wigner functions corresponding to the atom states is not known. We show how the Kirkwood-Rihaczek distribution reflects properties of the hydrogen atom wave functions in position and momentum representations.Comment: 5 pages (and 5 figures

Information and communications technologies (ICT) in Higher Education teaching – a tale of gradualism rather than revolution

The widespread adoption of information and communications technologies (ICT) in higher education (HE) since the mid 1990s has failed to produce the radical changes in learning and teaching than many anticipated. Activity theory and Rogers’ model of the adoption of innovations provide analytic frameworks that help develop our understanding of the actual impact of ICT upon teaching practices. This paper draws on a series of large-scale surveys carried out over a 10 year period with distance education tutors at the UK Open University to explore the changing role of ICT in the work of teachers. It investigates how HE teachers in one large distance learning university have, over time, appropriated ICT applications as teaching tools, and the gradual rather than revolutionary changes that have resulted

Self-diffusion coefficients of charged particles: Prediction of Nonlinear volume fraction dependence

We report on calculations of the translational and rotational short-time self-diffusion coefficients $D^t_s$ and $D^r_s$ for suspensions of charge-stabilized colloidal spheres. These diffusion coefficients are affected by electrostatic forces and many-body hydrodynamic interactions (HI). Our computations account for both two-body and three-body HI. For strongly charged particles, we predict interesting nonlinear scaling relations $D^t_s\propto 1-a_t\phi^{4/3}$ and $D^r_s\propto 1-a_r\phi^2$ depending on volume fraction $\phi$, with essentially charge-independent parameters $a_t$ and $a_r$. These scaling relations are strikingly different from the corresponding results for hard spheres. Our numerical results can be explained using a model of effective hard spheres. Moreover, we perceptibly improve the known result for $D^t_s$ of hard sphere suspensions.Comment: 8 pages, LaTeX, 3 Postscript figures included using eps

Theory of Systematic Computational Error in Free Energy Differences

Systematic inaccuracy is inherent in any computational estimate of a non-linear average, due to the availability of only a finite number of data values, N. Free energy differences (DF) between two states or systems are critically important examples of such averages in physical, chemical and biological settings. Previous work has demonstrated, empirically, that the ``finite-sampling error'' can be very large -- many times kT -- in DF estimates for simple molecular systems. Here, we present a theoretical description of the inaccuracy, including the exact solution of a sample problem, the precise asymptotic behavior in terms of 1/N for large N, the identification of universal law, and numerical illustrations. The theory relies on corrections to the central and other limit theorems, and thus a role is played by stable (Levy) probability distributions.Comment: 5 pages, 4 figure

Why do ultrasoft repulsive particles cluster and crystallize? Analytical results from density functional theory

We demonstrate the accuracy of the hypernetted chain closure and of the mean-field approximation for the calculation of the fluid-state properties of systems interacting by means of bounded and positive-definite pair potentials with oscillating Fourier transforms. Subsequently, we prove the validity of a bilinear, random-phase density functional for arbitrary inhomogeneous phases of the same systems. On the basis of this functional, we calculate analytically the freezing parameters of the latter. We demonstrate explicitly that the stable crystals feature a lattice constant that is independent of density and whose value is dictated by the position of the negative minimum of the Fourier transform of the pair potential. This property is equivalent with the existence of clusters, whose population scales proportionally to the density. We establish that regardless of the form of the interaction potential and of the location on the freezing line, all cluster crystals have a universal Lindemann ratio L = 0.189 at freezing. We further make an explicit link between the aforementioned density functional and the harmonic theory of crystals. This allows us to establish an equivalence between the emergence of clusters and the existence of negative Fourier components of the interaction potential. Finally, we make a connection between the class of models at hand and the system of infinite-dimensional hard spheres, when the limits of interaction steepness and space dimension are both taken to infinity in a particularly described fashion.Comment: 19 pages, 5 figures, submitted to J. Chem. Phys; new version: minor changes in structure of pape