A comment on pulsatile pipe flow

This article is concerned with analytic solutions of flows in cylindrical and annular pipes subject to an arbitrary time dependent pressure gradient and arbitrary initial flow

Asymptotics of a small liquid drop on a cone and plate rheometer

A cone and a plate rheometer is a laboratory apparatus used to measure the viscosity and other related parameters of a non-Newtonian liquid subject to an applied force. A small drop, of order millimetres, of the liquid is located between the horizontal plate and the shallow cone of the rheometer. Rotation of the cone ensues, the liquid begins to flow and the plate starts to rotate. Liquid parameters are inferred based on the difference in the applied rotational force and the resulting rotational force of the plate. To describe the flow of the drop, the initial drop configuration, before rotation commences, must be determined. The equilibrium drop profile is given by the solution to the well-known nonlinear Young-Laplace equation. We formulate asymptotic solutions for the drop profile based on the small Bond number. The modelling of the drop exhibits a rich asymptotic structure consisting of five distinct scalings which are resolved via the method matched asymptotics

Theoretical results of one class of multiderivative methods through order stars

Order stars are applied to Brown (K,L) methods. They are displayed pictorially for a selection of methods and are used to provide succinct proofs of existing results. Asymptotic results concerning their stability are also presented

Simulating Drug-Eluting Stents: Progress Made and the Way Forward

Drug-eluting stents have significantly improved the treatment of coronary artery disease. Compared with their bare metal predecessors, they offer reduced rates of restenosis and thus represent the current gold standard in percutaneous coronary interventions. Drug-eluting stents have been around for over a decade, and while progress is continually being made, they are not suitable in all patients and lesion types. Furthermore there are still real concerns over incomplete healing and late stent thrombosis. In this paper, some modelling approaches are reviewed and the future of modelling and simulation in this field is discussed

A Role for Fenugreek in Altering the Osmoregulatory Capacity in Rainbow Trout (Oncorhynchus Mykiss)

Fenugreek (Trigonella foenum-graecum) is a botanical galactogogue that has been shown to increase milk production and serum prolactin in mammals. Prolactin is classically considered to be a freshwater-adapting hormone in teleost fishes. If fenugreek promotes prolactin synthesis, then it has the potential to decrease perturbations associated with exposure to hypoosmotic conditions in fishes. To test this, rainbow trout (Onchorhynchus mykiss) were fed doses of fenugreek, and endpoints of ionoregulatory ability were assessed. A single dose was used in a hypoosmotic stress experiment. Fenugreek did not disrupt systemic endpoints of salt-and-water balance. Transcript abundance of prolactin receptor in the gill and hypothalamus, and corticosteroid receptors in the gill decreased. Fenugreek resulted in an increase in claudin-7 and -30, and a decrease in claudin-33b. While it was demonstrated that fenugreek can impact salt-water balance, and affect changes similar to freshwater acclimation, it is unlikely that these changes were brought about via prolactin

Reconstruction of the spatial dependency of dielectric and geometrical properties of adhesively bonded structures

An inverse problem motivated by the nondestructive testing of adhesively bonded structures used in the aircraft industry is studied. Using transmission line theory, a model is developed which, when supplied with electrical and geometrical parameters, accurately predicts the reflection coefficient associated with such structures. Particular attention is paid to modelling the connection between the structures and the equipment used to measure the reflection coefficient. The inverse problem is then studied and an optimization approach employed to recover these electrical and geometrical parameters from experimentally obtained data. In particular the approach focuses on the recovery of spatially varying geometrical parameters as this is paramount to the successful reconstruction of electrical parameters. Reconstructions of structure geometry using this method are found to be in close agreement with experimental observations

The shape of a small liquid drop on a cone and plate rheometer

We construct asymptotic solutions for the shape of a small liquid sessile drop in a cone and plate rheometer. The approximation is based on small Bond number or, equivalently, on a characteristic length scale which is much smaller than the capillary length. The drop has a complicated asymptotic structure, consisting of five separate scalings, which is resolved using the method of matched asymptotic expansions. We find that the presence of a substrate above (and below) the drop gives rise to qualitatively new drop configurations

Asymptotic analysis of drug dissolution in two layers having widely differing diffusivities

This paper is concerned with a diffusion-controlled moving-boundary problem in drug dissolution, in which the moving front passes from one medium to another for which the diffusivity is many orders of magnitude smaller. The classical Neumann similarity solution holds while the front is passing through the first layer, but this breaks down in the second layer. Asymptotic methods are used to understand what is happening in the second layer. Although this necessitates numerical computation, one interesting outcome is that only one calculation is required, no matter what the diffusivity is for the second laye

A bounded upwinding scheme for computing convection-dominated transport problems

A practical high resolution upwind differencing scheme for the numerical solution of convection-dominated transport problems is presented. The scheme is based on TVD and CBC stability criteria and is implemented in the context of the finite difference methodology. The performance of the scheme is investigated by solving the 1D/2D scalar advection equations, 1D inviscid Burgers’ equation, 1D scalar convection–diffusion equation, 1D/2D compressible Euler’s equations, and 2D incompressible Navier–Stokes equations. The numerical results displayed good agreement with other existing numerical and experimental data