Solitary waves and their stability in colloidal media: semi-analytical solutions

Spatial solitary waves in colloidal suspensions of spherical dielectric nanoparticles are considered. The interaction of the nanoparticles is modelled as a hard-sphere gas, with the Carnahan-Starling formula used for the gas compressibility. Semi-analytical solutions, for both one and two spatial dimensions, are derived using an averaged Lagrangian and suitable trial functions for the solitary waves. Power versus propagation constant curves and neutral stability curves are obtained for both cases, which illustrate that multiple solution branches occur for both the one and two dimensional geometries. For the one-dimensional case it is found that three solution branches (with a bistable regime) occur, while for the two-dimensional case two solution branches (with a single stable branch) occur in the limit of low background packing fractions. For high background packing fractions the power versus propagation constant curves are monotonic and the solitary waves stable for all parameter values. Comparisons are made between the semi-analytical and numerical solutions, with excellent comparison obtained.Comment: Paper to appear in Dynamics of Continuous, Discrete and Impulsive Systems, Series

Planning a Family:priorities and concerns in rural Tanzanmia

A fertility survey using qualitative and quantitative techniques described a high fertility setting (TFR 5.8) in southern Tanzania where family planning use was 16%. Current use was influenced by rising parity, educational level, age of last born child, breastfeeding status, a\ud preference for longer than the mean birth interval (32 months), not being related to the household head, and living in a house with a tin roof. Three principal concerns amongst women were outlined from the findings. First, that there is a large unmet need for family planning services in the area particularly among teenagers for whom it is associated with induced abortion. Second, that family planning is being used predominantly for spacing but fears\ud associated with it often curtail effective use. Third, that service provision is perceived to be lacking in two main areas — regularity of supply, and addressing rumours and fears associated with family planning. Reproductive health interventions in the area should ultimately be more\ud widespread and, in particular, abortion is highlighted as an urgent issue for further research.\ud The potential for a fast and positive impact is high, given the simplicity of the perceived needs of\ud women from this study. (Afr J Reprod Health 2004; 8[2]:111-123)\u

Observational properties of massive black hole binary progenitors

The first directly detected gravitational waves (GW 150914) were emitted by two coalescing black holes (BHs) with masses of ~36Msun and ~29Msun. Several scenarios have been proposed to put this detection into an astrophysical context. The evolution of an isolated massive binary system is among commonly considered models. Various groups have performed detailed binary-evolution calculations that lead to BH merger events. However, the question remains open as to whether binary systems with the predicted properties really exist. The aim of this paper is to help observers to close this gap by providing spectral characteristics of massive binary BH progenitors during a phase where at least one of the companions is still non-degenerate. Stellar evolution models predict fundamental stellar parameters. Using these as input for our stellar atmosphere code (PoWR), we compute a set of models for selected evolutionary stages of massive merging BH progenitors at different metallicities. The synthetic spectra obtained from our atmosphere calculations reveal that progenitors of massive BH merger events start their lives as O2-3V stars that evolve to early-type blue supergiants before they undergo core-collapse during the Wolf-Rayet phase. When the primary has collapsed, the remaining system will appear as a wind-fed high-mass X-ray binary. We provide feedback parameters, broad band magnitudes, and spectral templates that should help to identify such binaries in the future. Comparisons of empirically determined mass-loss rates with those assumed by evolution calculations reveal significant differences. The consideration of the empirical mass-loss rates in evolution calculations will possibly entail a shift of the maximum in the predicted binary-BH merger rate to higher metallicities, that is, more candidates should be expected in our cosmic neighborhood than previously assumed.Comment: 64 pages, 30 figures, accepted for publication in Astronomy & Astrophysics, v2: typos correcte

Numerical and analytical study of undular bores governed by the full water wave equations and bi-directional Whitham-Boussinesq equations

Undular bores, also termed dispersive shock waves, generated by an initial discontinuity in height as governed by two forms of the Boussinesq system of weakly nonlinear shallow water wave theory, the standard formulation and a Hamiltonian formulation, two related Whitham-Boussinesq equations, and the full water wave equations for gravity surface waves are studied and compared. It is found that the Whitham-Boussinesq systems give solutions in excellent agreement with numerical solutions of the full water wave equations for the positions of the leading and trailing edges of the bore up until the onset on modulational instability. The Whitham-Boussinesq systems, which are far simpler than the full water wave equations, can then be used to accurately model surface water wave undular bores. Finally, comparisons with numerical solutions of the full water wave equations show that the Whitham-Boussinesq systems give a slightly lower threshold for the onset of modulational instability in terms of the height of the initial step generating the undular bore

Transcritical flow of a stratified fluid: The forced extended Korteweg-de Vries model

Transcritical, or resonant, flow of a stratified fluid over an obstacle is studied using a forced extended Korteweg-de Vries model. This model is particularly relevant for a two-layer fluid when the layer depths are near critical, but can also be useful in other similar circumstances. Both quadratic and cubic nonlinearities are present and they are balanced by third-order dispersion. We consider both possible signs for the cubic nonlinear term but emphasize the less-studied case when the cubic nonlinear term and the dispersion term have the same-signed coefficients. In this case, our numerical computations show that two kinds of solitary waves are found in certain parameter regimes. One kind is similar to those of the well-known forced Korteweg-de Vries model and occurs when the cubic nonlinear term is rather small, while the other kind is irregularly generated waves of variable amplitude, which may continually interact. To explain this phenomenon, we develop a hydraulic theory in which the dispersion term in the model is omitted. This theory can predict the occurence of upstream and downstream undular bores, and these predictions are found to agree quite well with the numerical computations. © 2002 American Institute of Physics.published_or_final_versio

Approximate techniques for dispersive shock waves in nonlinear media

Many optical and other nonlinear media are governed by dispersive, or diffractive, wave equations, for which initial jump discontinuities are resolved into a dispersive shock wave. The dispersive shock wave smooths the initial discontinuity and is a modulated wavetrain consisting of solitary waves at its leading edge and linear waves at its trailing edge. For integrable equations the dispersive shock wave solution can be found using Whitham modulation theory. For nonlinear wave equations which are hyperbolic outside the dispersive shock region, the amplitudes of the solitary waves at the leading edge and the linear waves at the trailing edge of the dispersive shock can be determined. In this paper an approximate method is presented for calculating the amplitude of the lead solitary waves of a dispersive shock for general nonlinear wave equations, even if these equations are not hyperbolic in the dispersionless limit. The approximate method is validated using known dispersive shock solutions and then applied to calculate approximate dispersive shock solutions for equations governing nonlinear optical media, such as nematic liquid crystals, thermal glasses and colloids. These approximate solutions are compared with numerical results and excellent comparisons are obtained

Triboelectrostatic Separation of Mineral Matter from Slovakian Coals

V èlánku sú diskutované niektoré technické aspekty triboelektrostatickej separácie a výs-ledky aplikácie tohto postupu pri úprave troch typov uhlia, konkrétne energetického uhlia z Cíg¾a, Handlovej a Novák. Bolo zistené, e úèinnos separácie ve¾mi úzko závisí na druhu separovan uhlia. Prvé výsledky preukázali súvislos medzi úèinnosou separácie obsahom popola v uhlí