Some exact solutions to the Lighthill Whitham Richards Payne traffic flow equations II: moderate congestion

We find a further class of exact solutions to the Lighthill Whitham Richards Payne (LWRP) traffic flow equations. As before, using two consecutive Lagrangian transformations, a linearization is achieved. Next, depending on the initial density, we either obtain exact formulae for the dependence of the car density and velocity on x, t, or else, failing that, the same result in a parametric representation. The calculation always involves two possible factorizations of a consistency condition. Both must be considered. In physical terms, the lineup usually separates into two offshoots at different velocities. Each velocity soon becomes uniform. This outcome in many ways resembles not only Rowlands, Infeld and Skorupski J. Phys. A: Math. Theor. 46 (2013) 365202 (part I) but also the two soliton solution to the Korteweg-de Vries equation. This paper can be read independently of part I. This explains unavoidable repetitions. Possible uses of both papers in checking numerical codes are indicated at the end. Since LWRP, numerous more elaborate models, including multiple lanes, traffic jams, tollgates etc. abound in the literature. However, we present an exact solution. These are few and far between, other then found by inverse scattering. The literature for various models, including ours, is given. The methods used here and in part I may be useful in solving other problems, such as shallow water flow.Comment: 15 pages, 7 figure

Stability analysis of three-dimensional breather solitons in a Bose-Einstein Condensate

We investigate the stability properties of breather soliton trains in a three-dimensional Bose-Einstein Condensate with Feshbach Resonance Management of the scattering length. This is done so as to generate both attractive and repulsive interaction. The condensate is con ned only by a one dimensional optical lattice and we consider both strong, moderate, and weak con nement. By strong con nement we mean a situation in which a quasi two dimensional soliton is created. Moderate con nement admits a fully three dimensional soliton. Weak con nement allows individual solitons to interact. Stability properties are investigated by several theoretical methods such as a variational analysis, treatment of motion in e ective potential wells, and collapse dynamics. Armed with all the information forthcoming from these methods, we then undertake a numerical calculation. Our theoretical predictions are fully con rmed, perhaps to a higher degree than expected. We compare regions of stability in parameter space obtained from a fully 3D analysis with those from a quasi two-dimensional treatment, when the dynamics in one direction are frozen. We nd that in the 3D case the stability region splits into two parts. However, as we tighten the con nement, one of the islands of stability moves toward higher frequencies and the lower frequency region becomes more and more like that for quasi 2D. We demonstrate these solutions in direct numerical simulations and, importantly, suggest a way of creating robust 3D solitons in experiments in a Bose Einstein Condensate in a one-dimensional lattice.Comment: 14 pages, 6 figures; accepted to Proc. Roy. Soc. London

Accounting education : is the house in order? : inaugural lecture delivered at Rhodes University

Inaugural lecture delivered at Rhodes UniversityRhodes University Libraries (Digitisation

Mixed models and multilevel data structures in agriculture

Multilevel data structures can occur in many areas of agricultural research for instance on-farm trials, where there can be information at the village, farm and plot or animal level. Analysis of variance except in balanced or nested designs - has been difficult to apply to data with a multilevel structure. Mixed modelling is becoming a standard approach for analysing these types of data. The mixed model facilities are now available in some of the more powerful statistical packages such as Genstat and SAS. The purpose of this guide book is to review the general concepts of mixed models. The document illustrates by example how to recognise the structure in the data and how to fit and interpret a mixed model analysis. The reader is expected to be familiar with simple analysis of variance methods. Three examples are used in the discussion. Example one, 'fodder production trial', is a fairly traditional agricultural experiment, and is included to show how mixed modelling links to more traditional analysis. Example two, 'concentrate feeding trial', is an on-farm trial with a slightly 'messy' hierarchical structure. It is used to show how the ideas of example one can be extended to other situations, and to demonstrate the benefits of mixed modelling. Example three, 'sheep breeding trial', is a more specialised example of breeding trial. It discusses the implications of formulating models in different ways

Time Domain Mapping of Spin Torque Oscillator Effective Energy

Stochastic dynamics of spin torque oscillators (STOs) can be described in terms of magnetization drift and diffusion over a current-dependent effective energy surface given by the Fokker-Planck equation. Here we present a method that directly probes this effective energy surface via time-resolved measurements of the microwave voltage generated by a STO. We show that the effective energy approach provides a simple recipe for predicting spectral line widths and line shapes near the generation threshold. Our time domain technique also accurately measures the field-like component of spin torque in a wide range of the voltage bias values.Comment: 5 pages, 3 figures. Supplement included: 7 pages, 6 figure

Intrauterine devices and risk of uterine perforation: current perspectives

Uterine perforation is an uncommon complication of intrauterine device insertion, with an incidence of one in 1,000 insertions. Perforation may be complete, with the device totally in the abdominal cavity, or partial, with the device to varying degrees within the uterine wall. Some studies show a positive association between lactation and perforation, but a causal relationship has not been established. Very rarely, a device may perforate into bowel or the urinary tract. Perforated intrauterine devices can generally be removed successfully at laparoscopy

Electric field generation by the electron beam filamentation instability: Filament size effects

The filamentation instability (FI) of counter-propagating beams of electrons is modelled with a particle-in-cell simulation in one spatial dimension and with a high statistical plasma representation. The simulation direction is orthogonal to the beam velocity vector. Both electron beams have initially equal densities, temperatures and moduli of their nonrelativistic mean velocities. The FI is electromagnetic in this case. A previous study of a small filament demonstrated, that the magnetic pressure gradient force (MPGF) results in a nonlinearly driven electrostatic field. The probably small contribution of the thermal pressure gradient to the force balance implied, that the electrostatic field performed undamped oscillations around a background electric field. Here we consider larger filaments, which reach a stronger electrostatic potential when they saturate. The electron heating is enhanced and electrostatic electron phase space holes form. The competition of several smaller filaments, which grow simultaneously with the large filament, also perturbs the balance between the electrostatic and magnetic fields. The oscillations are damped but the final electric field amplitude is still determined by the MPGF.Comment: 14 pages, 10 plots, accepted for publication in Physica Script