The stability characteristics of an infinite horizontal fluid layer excited by a time-periodic, sinusoidally varying free-boundary temperature, have been investigated numerically using the Floquet theory. It has been found that the modulation of the temperature gradient across the fluid layer affects the onset of the Rayleigh–Bénard convection. Modulation can give rise to instability in the subcritical conditions and it can also suppress the instability in the supercritical cases. The instability in the fluid layer manifests itself in the form of either a harmonic or subharmonic flow, controlled by thermal modulation.

A three-layer compartmental model of the geological structure in the Taupo Volcanic Zone of New Zealand is developed, based on the assumptions of isostasy (constant geostatic pressure at 25 km depth) and a constant rate of volcanism. The upper layer consists of volcanic infill to a depth of about 2500 m, then a middle layer of greywacke-like material to a depth of about 15 km, and a lower layer of andesitic-like material to a depth of 25 km. Our model assumptions predict that the area of each layer increases at a constant rate; that there is a constant ratio between the rate of energy production from volcanic activity and geothermal convection; and that there is the possibility of an abrupt change from rhyolitic to basaltic volcanism, if the middle layer becomes sufficiently thin. Two models are considered: a rifting and a spreading model. Both models predict the lower layer has an andesitic-like density. The spreading model has difficulty matching heat output with observed extension rates. The rifting model predicts the observed extension rates, but requires very deep circulation of groundwater to be consistent with observed chemical and isotopic properties of geothermal fluids.

The hyper-Wiener index of a connected graph G is defined as , where V (G) is the set of all vertices of G and d(u,v) is the distance between the vertices u,v∈V (G). In this paper we find an exact expression for the hyper-Wiener index of TUHC6[2p,q], the zigzag polyhex nanotube.

A class of first-order impulsive functional differential equations with forcing terms is considered. It is shown that, under certain assumptions, there exist positive T-periodic solutions, and under some other assumptions, there exists no positive T-periodic solution. Applications and examples are given to illustrate the main results.

In two recent papers a global upper bound is derived for Jensen’s inequality for weighted finite sums. In this paper we generalize this result on positive normalized functionals.

In boats used for competitive rowing it is traditional for the rowers to use strokes in which the angle between the oar shaft and the perpendicular to the hull centre line is much greater at the catch than it is at the end of the power stroke. As a result, the oar blade is even more inefficient in its action at the catch than it is at the end of the power stroke. This paper shows how boat performance in a race would be improved by reducing the difference in these starting and finishing angles. The claim of improved race performance is supported by a detailed investigation of the dynamics involved in the case of a particular coxless pair whose performance has been recorded by the Australian Institute of Sport. We also suggest an easy way to make the necessary change in boat design.

We investigate the perturbation of the palindromic eigenvalue problem for the matrix quadratic with A0,A1∈𝒞n×n and (where or H). The perturbation of eigenvalues in the context of general matrix polynomials, palindromic pencils, (semi-Schur) anti-triangular canonical forms and differentiation is discussed.

Understanding ion transport in conjugated polymers is essential for developing mathematical models of applications of these materials. Previous experimental studies have suggested that cation transport in a conjugated polymer could be either diffusion or drift controlled, with debate over which dominates. In this paper we present a new model of cation transport that explains most of the features seen in a set of recent experiments. This model gives good agreement with measured concentration profiles, except when the profile has penetrated the polymer by more than 60%. The model shows that both diffusion and drift processes can be present. An application of a micro-actuator based on a conjugated polymer is presented to demonstrate that this technology could be used to develop a micro-pump.

The steady response of the free surface of a fluid in a porous medium is considered during extraction of the fluid through a line sink. A conformal-mapping approach is used to derive exact solutions to a family of problems in which the line sink is placed at the apex of a wedge-shaped impermeable base, including the limiting cases of an unbounded aquifer and a flat-bottomed aquifer of finite depth. Both critical cusp solutions and sub-critical solutions are computed exactly as Fourier sine series.

In this paper, we extend the results in the literature for boundary layer flow over a horizontal plate, by considering the buoyancy force term in the momentum equation. Using a similarity transformation, we transform the partial differential equations of the problem into coupled nonlinear ordinary differential equations. We first analyse several special cases dealing with the properties of the exact and approximate solutions. Then, for the general problem, we construct series solutions for arbitrary values of the physical parameters. Furthermore, we obtain numerical solutions for several sets of values of the parameters. The numerical results thus obtained are presented through graphs and tables and the effects of the physical parameters on the flow and heat transfer characteristics are discussed. The results obtained reveal many interesting behaviours that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.

This is a review of progress made since [R. McKibbin, “An attempt at modelling hydrothermal eruptions”, Proc. 11th New Zealand Geothermal Workshop 1989 (University of Auckland, 1989), 267–273] began development of a mathematical model for progressive hydrothermal eruptions (as distinct from “blasts”). Early work concentrated on modelling the underground process, while lately some attempts have been made to model the eruption jet and the flight and deposit of ejected material. Conceptually, the model is that of a boiling and expanding two-phase fluid rising through porous rock near the ground surface, with a vertical high-speed jet, dominated volumetrically by the gas phase, ejecting rock particles that are then deposited on the ground near the eruption site. Field observations of eruptions in progress and experimental results from a laboratory-sized model have confirmed the conceptual model. The quantitative models for all parts of the process are based on the fundamental conservation equations of motion and thermodynamics, using a continuum approximation for each of the components.

In this paper we extend results of Inoan and Kolumban on pseudomonotone set-valued mappings to topological vector spaces. An application is made to a variational inequality problem.

We present an approximate relation for the effective slip length for flows over mixed-slip surfaces with patterning at the nanoscale, whose minimum slip length is greater than the pattern length scale.

The aim of this paper is to find a concrete bound for the error involved when approximating the nth Hermite function (in the oscillating range) by an asymptotic formula due to D. Dominici. This bound is then used to study the accuracy of certain approximations to Hermite expansions and to Fourier transforms. A way of estimating an unknown probability density is proposed.

Some new Gronwall–Ou-Iang type integral inequalities in two independent variables are established. We also present some of its application to the study of certain classes of integral and differential equations.

There is increasing interest in the cost of railway infrastructure access as a variety of private companies operate trains with different lengths over a common rail network. It is important to have a method for evaluating the cost of adding an additional train to a railway timetable. This is particularly so for single line track with occasional passing loops. The concept of a fixed loop capacity is extended to one that is dependent on the trains. We develop a model for scheduling a heterogeneous set of trains on single line systems with loops. Our method minimizes the total weighted delay. A Lagrangian relaxation technique is used that relaxes the capacity constraints for track segments and super segments. We measure the delay for each train and the total weighted delay for the heterogeneous set of trains. Our model allows us to investigate the robustness of the weighted delay to variation in the departure time of individual trains. The paper demonstrates that a Lagrangian relaxation heuristic provides optimal train schedules for instances of small heterogeneous train sets. The method is used primarily to check the effectiveness of heuristic algorithms commonly used to find schedules for practical problems.

A new sharp L2 inequality of Ostrowski type is established, which provides some other interesting results as special cases. Applications in numerical integration are also given.

Zinc oxide is known to produce a wide variety of nanostructures that show promise for a number of applications. The use of electrochemical deposition techniques for growing ZnO nanostructures can allow tight control of the morphology of ZnO through the wide range of deposition parameters available. Here we model the growth of the rods under typical electrochemical conditions, using the Nernst–Planck equations in two dimensions to predict the growth rate and morphology of the nanostructures as a function of time. Generally good quantitative and qualitative agreement is found between the model predictions and recent experimental results.

We give here some extensions of inequalities of Popoviciu and Rado. The idea is to use an inequality [C. P. Niculescu and L. E. Persson, Convex functions. Basic theory and applications (Universitaria Press, Craiova, 2003), Page 4] which gives an approximation of the arithmetic mean of n values of a given convex function in terms of the value at the arithmetic mean of the arguments. We also give more general forms of this inequality by replacing the arithmetic mean with others. Finally we use these inequalities to establish similar inequalities of Popoviciu and Rado type.