bluuebunny/crossref_metadata_2025_split huggingface dataset:
Two-phase flow in Hele-Shaw cells: numberical studies of sweep efficiency in a five-spot pattern
Authors: Sahwartiz Leonard W. , Degregoria Anthony J. 
Published: February 2009

AbstractThe unsteady Hele-Shaw problem is a model nonlinear system that, for a certain parameter ranger, exhibits the phenomenon known as viscous fingering. While not directly applicable to multiphase porous-media flow, it does prove to be an adequate mathematical model for unstable dieplacement in laboratory parallel-plate devices. We seek here to determine, by use of an accurate boundary-integral frount-tracking scheme, the extent to which the simplified system captures the canonical nonlinear behavior of displacement flows and, in particular, to ascertain the role of noise in such systems. We choose to study a particular pattern of injection and production “wells.” The pattern chosen is the isolated “five-spot,” that is a single source surrounded by four symmetrically-placed sinks in an infinite two-dimensional “reservoir.” In cases where the “pusher” fluid has negligible viscosity, sweep efficiency is calculated for a range of values of the single dimensionless parameter τ, an inverse capillary number. As this parameter is reduced, corresponding to increased flow rate or reduced interfacial tension, this efficiency decreases continuously. For small values of τ, these stable displacements change abruptly to a regime characterized by unstable competing fingers and a significant reduction in sweep efficiency. A simple stability argument appears to correctly predict the noise level required to transit from the stable to the competing-finger regimes. Published compilations of experimental results for sweep efficiency as a function of viscosity ratio showed an unexplained divergence when the pusher fluid is less viscous. Our simulations produce a similar divergence when, for a given viscosity ratio, the parameter τ is varied.
The modulation of short gravity waves by long waves or currents
Authors: Grimshaw R. 
Published: February 2009

AbstractThe modulation of short gravity waves by long waves or currents is described for the situation when the flow is irrotational and when the short waves are described by linearised equations. Two cases are distinguished depending on whether the basic flow can be characterised as a deep-water current, or a shallow-water current. In both cases the basic flow has a current which has finite amplitude, while in the first case the free surface slope of the basic flow can be finite, but in the second case is small. The modulation equations are the local dispersion relation of the short waves, the kinematic equation for conservation of wave crests and the wave action equation. The results incorporate and extend the earlier work of Longuet-Higgins and Stewart [10, 11].
The application of centre-manifold theory to the evolution of system which vary slowly in space
Authors: Roberts A. J. 
Published: February 2009

AbstractIn many physical problems, the system tends quickly to a particular structure, which then evolves relatively slowly in space and time. Various methods exist to derive equations describing the slow evolution of the particular structure; for example, the method of multiple scales. However, the resulting equations are typically valid only for a limited range of the parameters. In order to extend the range of validity and to improve the accuracy, correction terms must be found for the equations. Here we describe a procedure, inspired by centre-manifold theory, which provides a systematic approach to calculating a sequence of successively more accurate approximations to the evolution of the principal structure in space and time.The formal procedure described here raises a number of questions for future research. For example: what sort of error bounds can be obtained, do the approximations converge or are they strictly asymptotic, and what sort of boundary conditions are appropriate in a given problem?
A method of accelerating stationary iterative methods for solving linear systems
Authors: Robinson G. K. 
Published: February 2009

AbstractThe speed of convergence of stationary iterative techniques for solving simultaneous linear equations may be increased by using a method similar to conjugate gradients but which does not require the stationary iterative technique to be symmetrisable. The method of refinement is to find linear combinations of iterates from a stationary technique which minimise a quadratic form. This basic method may be used in several ways to construct refined versions of the simple technique. In particular, quadratic forms of much less than full rank may be used. It is suggested that the method is likely to be competitive with other techniques when the number of linear equations is very large and little is known about the properties of the system of equations. A refined version of the Gauss-Seidel technique was found to converge satisfactorily for two large systems of equations arising in the estimation of genetic merit of dairy cattle.
Smoothness and conditioning in generalised smoothing spline calculations
Authors: Osborne M. R. , Prvan Tania 
Published: February 2009

AbstractWe consider a generalisation of the stochastic formulation of smoothing splines, and discuss the smoothness properties of the resulting conditional expectation (generalised smoothing spline), and the sensitivity of the numerical algorithms. One application is to the calculation of smoothing splines with less than the usual order of continuity at the data points.
A square-root fixed-interval discrete-time smoother
Authors: Prvan Tania , Osborne M. R. 
Published: February 2009

AbstractThe square-root fixed-interval discrete-time smoother has been used extensively in discrete recursive estimation since it was first developed by Rauch, Tung and Streibel [10]. Various people, for example Bierman [2], [3], have recognized the inherent instability in employing this kind of smoother in its original form; they have investigated implementing the recursion more stably. Bierman's paper [3] is one such contribution. In this paper we plan to present a more comprehensive development of Bierman's approach, and to show that this algorithm can be implemented more stably as a square-root smoother. Throughout this paper the fixed-interval discrete-time smoother will be referred to as the RTS smoother. Numerical results are given for the usual form of the RTS smoother, Bierman's algorithm and our square-root formulation of his algorithm. These confirm that the square-root formulation is more desirable than Bierman's algorithm, which performs better than the usual implementation of the RTS smoother.
Controllability of generalised dynamical systems with constrained control
Authors: Zhaolin Chen , Huimin Hong , Jifeng Zhang 
Published: February 2009

AbstractThe state controllability for generalised dynamical systems with constrained control is discussed in this paper. The main results of the paper are the following:(1) a necessary and sufficient condition of the state controllability in the sense of control energy or amplitude constrained for generalised dynamical systems is obtained;(2) a control function u(t) is constructed such thata) u(t) satisfies constrained energy or amplitude condition,b) the state driven by u(t) moves from an arbitrary x(0−) = x0 to x(T(x0)) = 0,c) the trajectory driven by u(t) has no impulsive behaviour within (0, T(x0)].
Travelling wave solutions for rich flames of reactive suspensions
Authors: Tam K. K. 
Published: February 2009

AbstractThe modelling of the combustion of dust suspensions leads to a nonlinear eigenvalue problem for a system of ordinary differential equations defined over an infinite interval. The equations contain a number of parameters. In this study, the shooting method is used to prove the existence of a solution. Linearisation is then used to provide an approximate solution, from which an estimate of the eigenvalue and its dependence on the given parameters can be obtained.
Radiating Demianski-type metrics and the Einstein-Maxwell fields
Authors: Patel L. K. , Akabari R. P. , Dave U. K. 
Published: February 2009

AbstractA Demianski-type metric is investigated in connection with the Einstein-Maxwell fields. Using complex vectorial formalism, some exact solutions of Einstein-Maxwell field equations for source-free electromagnetic fields plus pure radiation fields are obtained. The radiating Demianski solution, the Debney-Kerr-Schild solution and the Brill solution are derived as particular cases.
A note on the free surface induced by a submerged source at infinite Froude number
Authors: King A. C. , Bloor M. I. G. 
Published: February 2009

AbstractThe free surface due to a submerged source in a fluid of finite depth at infinite Froude number is reconsidered. A conformal transformation technique is used to formulate this problem as an integral equation for the free-surface angle. An elementary solution is found for the equation, which results in a closed form expression for the free-surface elevation. Comparison is made with previous numerical solutions.
A boundary integral method for contaminant transport in two adjacent porous media
Authors: Landman K. A. 
Published: February 2009

AbstractThe problem of transient two-dimensional transport by diffusion and advection of a decaying contaminant in two adjacent porous media is solved using a boundary-integral method. The method requires the construction of appropriate Green's functions. Application of Green's theorem in the plane then yields representations for the contaminant concentration in both regions in terms of an integral of the initial concentration over the region's interior and integrals along the boundaries of known quantities and the unknown interfacial flux between the two adjacent media. This flux is given by a first-kind integral equation, which can be solved numerically by a discretisation technique. Examples of contaminant transport in fractured porous media systems are presented.
Flux ratios for biological membranes and reciprocity theorems for linear operators
Authors: Bracken A. J. , Holmåker K. , Maloney L. V. , Bass L. 
Published: February 2009

AbstractThe constancy in time of the ratio of unidirectional tracer fluxes, passing in opposite directions through a membrane that has transport properties varying arbitrarily with the distance from a boundary face, has been established recently for successively more sophisticated mathematical models of tracer transport within the membrane. Such results are important in that, when constancy is not observed experimentally, inferences can be drawn about the dimensionality of distributions of transport properties of the membrane. The known theoretical results are shown here to follow from much more general theorems, valid for a wide class of models based on linear-operator equations, including elliptic and hyperbolic partial differential equations as well as the essentially parabolic equations of interest in membrane transport problems. These theorems have the general character of “reciprocity theorems” known for a long time in other areas, such as mechanics, acoustics and elasticity. The general results obtained here clarify the conditions on membrane properties under which constancy of a flux ratio can be expected. In addition, flux ratio theorems of a new type are proved to hold under suitable conditions, for the normal components of flux vectors at points on either side of a membrane, as distinct from previously established theorems for total fluxes through membrane faces. Possible new experiments are suggested by the analysis.
Exact solutions of nonlinear evolution equations of the AKNS class
Authors: Chan W. L. , Zheng Yu-Kun 
Published: February 2009

AbstractThe problem of obtaining explicit and exact solutions of soliton equations of the AKNS class is considered. The technique developed relies on the construction of the wave functions which are solutions of the associated AKNS system; that is, a linear eigenvalue problem in the form of a system of first order partial differential equations. The method of characteristics is used and Bäcklund transformations are employed to generate new solutions from the old. Thus, families of new solutions for the KdV equation, the mKdV equation, the sine-Gordon equation and the nonlinear Schrôdinger equation are obtained, avoiding the solution of some Riccati equations. Our results in the KdV case include those obtained recently by other investigators.
The wave resistance formula of J.H. Michell (1898) and Its significance to recent research in ship hydrodynamics
Authors: Tuck E. O. 
Published: February 2009

AbstractJohn Henry Michell (1863–1940) published scientific papers only between 1890 and 1902, but included in his 23 papers from that short but productive period are some of the most important contributions ever made by an Australian mathematician. In this article I shall concentrate on the extraordinary 1898 paper “The wave resistance of a ship” Phil. Mag.(5) 45, 106–123. There are many reasons why this paper was an astounding achievement, but perhaps the most remarkable is that the resulting formula has not been improved upon to this day. In the computer age, many efforts have been made to do so, but with little success so far. The formula itself involves a triple integral of an integrand constructed from the offset data for the ship's hull, and even the task of evaluating this triple integral is not a trivial one on today's computers; another reason for admiration of Michell's own heroic hand-calculated numerical work in the 1890's. Lack of a routine algorithm for Michell's integral has inhibited its use by naval architects and ship hydrodynamic laboratories, and there has been a tendency for it to receive a bad press based on unfair comparisons, e.g. comparison of model experiments (themselves often suspect) with inaccurate computations or computations for the wrong hull, etc. The original integral is in fact quite reasonable as an engineering tool, and some new results confirming this are shown. Improvement beyond Michell is however needed in some important speed ranges, and indications are given of recent approaches that may be promising.
A functional differential equation arising in modelling of cell growth
Authors: Hall A. J. , Wake G. C. 
Published: February 2009

AbstractA functional differential equation for the steady size distribution of a population is derived from the usual partial differential equation governing the size distribution, in the particular case where birth occurs by one individual of size x dividing into α new individuals of size x/α. This leads, in the case of constant growth and birth rate functions, to the functional differential equation y′(x) = −ay(x) + aαy(αx) together with the integral condition We first look at a number of properties that any solution of this equation and boundary condition must have, and then proceed to find the unique solution by the method of Laplace transforms. Results from number theory on the infinite product found in the solution are presented, and it is shown that y(x) tends to a normal distribution as α → 1+.
Correction of finite difference eigenvalues of periodic Sturm-Liouville problems
Authors: Andrew Alan L. 
Published: February 2009

AbstractComputation of eigenvalues of regular Sturm-Liouville problems with periodic or semiperiodic boundary conditions is considered. A simple asymptotic correction technique of Paine, de Hoog and Anderssen is shown to reduce the error in the centred finite difference estimate of the kth eigenvalue obtained with uniform step length h from O(k4h2) to O(kh2). Possible extensions of the results are suggested and the relative advantages of the method are discussed.
Sufficient optimality criteria and duality for variational problems with generalised invexity
Authors: Mond B. , Husain I. 
Published: February 2009

AbstractA number of Kuhn-Tucker type sufficient optimality criteria for a class of variational problems under weaker invexity assumptions are presented. As an application of these optimality results, various Mond-Weir type duality results are proved under a variety of generalised invexity assumptions. These results generalise many well-known duality results of variational problems and also give a dynamic analogue of certain corresponding (static) results relating to duality with generalised invexity in mathematical programming.
Sensitivity bounds on a GI/M/n/n queueing system
Authors: Coyle Andrew 
Published: February 2009

AbstractA method for determining the upper and lower bounds for performance measures for certain types of Generalised Semi-Markov Processes has been described in Taylor and Coyle [8]. A brief description of this method and its use in finding an upper bound for the time congestion of a GI/M/n/n queueing system will be given. This bound turns out to have a simple form which is quickly calculated and easy to use in practice.
A mathematical model and related problems of optimal management and design in a broadband integrated services network
Authors: Evans Suzanne P. 
Published: February 2009

AbstractThis paper describes a mathematical model for a broadband integrated services network offered traffic of many different types. Performance measures are introduced related to revenue generation and overall grade-of-service, providing criteria for the optimal management of resources. Simple asymptotic expressions are derived for quantities termed the “implied costs”, which measure the effect on performance of changes in parameters that are controllable by network management, or that are subject to variation. These implied costs may be used, both to implement optimal bandwidth allocation polices, and also to indicate which services may share a single facility without adversely affecting performance, and which might require a dedicated facility. Asymptotic results are also used to examine how to make efficient use of capacity that is shared between calls with fluctuating bit-rate requirements.
Fixed point models of loss networks
Authors: Kelly F. P. 
Published: February 2009

AbstractIn this paper we review a simple class of fixed point models for loss networks. We illustrate how these models can readily deal with heterogeneous call types and with simple dynamic routing strategies, and we outline some of the recent mathematical advances in the study of such models. We describe how fixed point models lead to a natural and tractable definition of the implied cost of carrying a call, and how this concept is related to issues of routing and capacity expansion in loss networks.
Monotone iterations for nonlinear obstacle problem
Authors: Korman Philip , Leung Anthony W. , Stojanovic Srdjan 
Published: February 2009

AbstractThe existence, uniqueness and regularity of solutions are proved for the obstacle problem with semilinear elliptic partial differential equations of second order. Computationally effective algorithms are provided and application made to steady state problem for the logistic population model with diffusion and an obstacle to growth.
Degenerate forms of Maxwell's equations
Authors: Carey A. L. , McNamara K. 
Published: February 2009

AbstractThis paper studies degenerate forms of Maxwell's equations which arise from approximations suggested by geophysical modelling problems. The approximations reduce Maxwell's equations to degenerate elliptic/parabolic ones. Here we consider the questions of existence, uniqueness and regularity of solutions for these equations and address the problem of showing that the solutions of the degenerate equations do approximate those of the genuine Maxwell equations.
The numerical solution of Hammerstein equations by a method based on polynomial collocation
Authors: Kumar Sunil 
Published: February 2009

AbstractIn recent papers we have considered the numerical solution of the Hammerstein equationby a method which first applies the standard collocation procedure to an equivalent equation for z(t):= g(t, y(t)), and then obtains an approximation to y by use of the equationIn this paper we approximate z by a polynomial zn of degree ≤ n − 1, with coefficients determined by collocation at the zeros of the nth degree Chebyshev polynomial of the first kind. We then define the approximation to y to beand establish that, under suitable conditions, , uniformly in t.
Nonlinear oscillations and buckling of anisotropic cylindrical shells under large initial stresses
Authors: Bera Rasajit Kumar 
Published: February 2009

AbstractThe large-amplitude oscillations and buckling of an anisotropic cylindrical shell subjected to the initial inplane biaxial normal stresses have been analysed. The concept of anisotropy used by Lekhnitsky has been introduced into the field equations for cylindrical shells of isotropic material deduced by Donnell. The method of Galerkin and the method of successive approximation have been used to obtain the desired approximate solution. The expression for the critical loads for the buckling of anisotropic cylindrical shells has been obtained during intermediate stages of analysis. Some relevant frequency response graphs of the obtained solution are also presented. The minimum critical loads for various classes of anisotropy have also been given at the end of the discussion, to exhibit the effects of large deflections and imperfections on elastic buckling.
Persistence and extinction in a predator-prey model consisting of nine prey genotypes
Authors: So Joseph W.-H. 
Published: February 2009

AbstractA predator-prey model in which the prey population is subdivided into nine genotypes corresponding to a two-locus, two-allele problem is considered. Sufficient conditions are given which lead to extinction of all the prey allele types except one, as well as conditions which guarantee the persistence of all the allele types.
The isotropy mappings of Minkowski space-time generate the orthochronous poincaré group
Authors: Schutz John W. 
Published: February 2009

AbstractMinkowski space-time is specified with respect to a single coordinate frame by the set of timelike lines. Isotropy mappings are defined as automorphisms which leave the events of one timelike line invariant. We demonstrate the existence of two special types of isotropy mappings. The first type of isotropy mapping induce orthogonal transformations in position space. Mappings of the second type can be composed to generate Lorentz boosts. It is shown that isotropy mappings generate the orthochronous Poincaré group of motions. The set of isotropy mappings then maps the single assumed coordinate frame onto a set of coordinate frames related by transformations of the orthochronous Poincaré group.
A boundary-integral method applied to water coning in oil reservoirs
Authors: Lucas S. K. , Blake J. R. , Kucera A. 
Published: February 2009

AbstractIn oil reservoirs, the less-dense oil often lies over a layer of water. When pumping begins, the oil-water interface rises near the well, due to the suction pressures associated with the well. A boundary-integral formulation is used to predict the steady interface shape, when the oil well is approximated by a series of sources and sinks or a line sink, to simulate the actual geometry of the oil well. It is found that there is a critical pumping rate, above which the water enters the oil well. The critical interface shape is a cusp. Efforts to suppress the cone by using source/sink combinations are presented.
A pair of arbitrarily-oriented coplanar cracks in an anisotropic elastic slab
Authors: Ang W. T. 
Published: February 2009

AbstractThe problem of an anisotropic elastic slab containing two arbitrarily-oriented coplanar cracks in its interior is considered. Using a Fourier integral transform technique, we reduce the problem to a system of simultaneous finite-part singular integral equations which can be solved numerically. Once the integral equations are solved, relevant quantities such as the crack energy can be readily computed. Numerical results for specific examples are obtained.