bluuebunny/crossref_metadata_2025_split huggingface dataset:
Stationary waves forced by topography in a vertically sheared, stratified, rotating fulid
Authors: Fandry C. B. , Hughes R. L. , Leslie L. M. 
Published: February 2009

AbstractThe effect of an isolated topographic bump in a two-layer fluid on a β-plane is investigated. An analytical solution is derived in terms of the appropriate Green's function for arbitrary topography of finite horizontal extent. It is found that the disturbances generated by the bump are composed of two fundamental modes which may be wave-like or evanescent. The wave-like modes are topographically induced Rossby waves which occur only when there is eastward flow in at least one of the layers. These waves are always confined to the downstream (eastward) side of the bump. Whereas previous studies of this type have concentrated on eastward flow over topography, the theory has been extended here to include a wide range of vertically sheared flows. Particularly important is the case of low level westward flow combined with upper level eastward flow, as it has direct application, for example, to the summertime atmospheric circulation over the sub-tropical regions of the continental land.masses. In this case a wave-like disturbance extends far downstream from the bump for sufficiently large shear, and is of smaller amplitude in the upper layer than in the lower layer because of the effects of the stratification. For small shears, the wave-like mode in the lower layer is small and the character of the disturbance is evanescent, confining it to the immediate neighbourhood of the bump. A stability analysis of the solutions shows that the disturbances may be baroclinically unstable for sufficiently large mean shear.
Inversion of the Struve transform of half integer order
Authors: McKellar B. H. J. , Box M. A. , Love E. R. 
Published: February 2009

AbstractDefining a spherical Struve function we show that the Struve transform of half integer order, or spherical Struve transform,where n is a non-negative integer, may under suitable conditions be solved for f(t):where is the sum of the first n + 1 terms in the asymptotic expansion of φn(x) as x → ∞. The coefficients in the asymptotic expansion are identified asIt is further shown that functions φn (x) which are representable as spherical Struve transforms satisfy n + 1 integral constraints, which in turn allow the construction of many equivalent inversion formulae.
A discrete Fourier analysis of coarse mesh rebalancing and some associated iterative methods
Authors: Barry J. M. , Jenkinson J. H. , Pollard J. P. 
Published: February 2009

AbstractIterative methods for solving systems of linear equations may be accelerated by coarse mesh rebalance techniques. The iterative technique, the Method of Implicit Non-stationary Iteration (MINI), is examined through a local-mode Fourier analysis and compared to relaxation techniques as a potential candidate for such acceleration. Results of a global-mode Fourier analysis for MINI, relaxation methods, and the conjugate gradient method are reported for two test problems.
Axisymmertic Stokes flow images in spherical free surfaces with applications to rising bubbles
Authors: Harper J. F. 
Published: February 2009

AbstractA theorem is derived for the hydrodynanuc image of an axially symmetric slow viscous (Stokes) flow in a sphere which is impermeable and free of shear stress. A second theorem establishes a sense in which such a flow past an arbitrary rigid surface or shear-free sphere becomes, on inversion in an arbitrary sphere with its centre on the axis of symmetry, a flow past the rigid or shear-free inverse of that surface or sphere.The theorems are used to simplify the proofs of a number of known results for images of point singularities in plane and spherical rigid and free boundaries, and for a pair of bubbles rising steadily in line in a viscous fluid. They also give for the first time accurate numerical solutions for the velocities of each of a larger number of spherical bubbles rising quasi-steadily in line. These enable one to assess the accuracy of simple approximations to those velocities.
A Galerkin-Petrov method for singular integral equations
Authors: Elliott David 
Published: February 2009

AbstractA Galerkin-Petrov method for the approximate solution of the complete singular integral equation with Cauchy kernel, based upon the use of two sets of orthogonal polynomials, is considered. The principal result of this paper proves convergence of the approximate solutions to the exact solution making use of a convergence theorem previously given by the author. In conclusion, some related topics such as a first iterate of the approximate solution and a discretized Galerkin-Petrov method are considered. The paper extends to a much more general equation many results obtained by other authors in particular cases.
Bounds for the growth of a perturbation in some double-diffusive convection problems
Authors: Gupta J. R. , Sood S. K. , Shandil R. G. , Banerjee M. B. , Banerjee K. 
Published: February 2009

AbstractBounds are presented for the modulus of the complex growth rate p of an arbitrary oscillatory perturbation, neutral or unstable, in some double-diffusive problems of relevance in oceanography, astrophysics and non-Newtonian fluid mechanics.
An asymptotic theory for dispersion of reactive contaminants in parallel flow
Authors: Barton N. G. 
Published: February 2009

AbstractThe classic problem, first treated by Taylor [18], of the dispersion of inert soluble matter in fluid flow continues to attract attention from researchers describing the approach to the asymptotic state [5, 17]. The present article considers some of the complications caused when the solute is chemically active, Dispersing chemically active solutes occur in diverse fields such as chromatography, chemical engineering and environmental fluid mechanics.The asymptotic large-time analysis of Chatwin [5] is re-worked to handle the case of reactive solutes dispersing in parallel flow. Matching between moderate and large-time solutions requires consideration of the integral moments of the reactive contaminant could, and the Aris method of moments is therefore invoked and modified for reaction effects. The results are applied in detail to the outstanding paractical example—the chemical flow reactor (a device used to measure reaction rates for chemical reactions taking place between fluids). For this case, the paper provides a practical alternative to recent variable diffusion coefficient studies [6, 7, 15], and presents further results for the concentration distribution and for the limiting behaviour under weak and vigorous recactions at the boundary of the flow.
Harmless delays in a periodic ecosystem
Authors: Gopalsamy K. 
Published: February 2009

AbstractSufficient conditions are obtained for the existence of a unique linearly asymptotically stable positive periodic solution of an ecosystem model of two species competition in a periodic environment with time lags in interspecific interactions. It is shown that if the self-regulating intraspecific interaction effects are strong enough and act without time delays then time delays of any length in the interspecific interactions cannot destabilise an otherwise stable ecosystem in a periodic environment.
On the application of a numerical algorithm for Hopf bifuraction to the hunting of a wheelset
Authors: Huilgol R. R. , Janus R. , Lohe M. A. , Sag T. W. 
Published: February 2009

AbstractThe main ideas of Hopf bifurcation theory and its relevance to the development of periodic motions of an autonomous system depending on a parameter are presented, and an algorithm for the computation of the orbits is described. It is then shown that a model system for the motion of a wheelset can be cast in the form amenable to Hopf bifurcation theory. Numerical results for the period and amplitudes of the lateral and yaw motions are obtained in terms of the forward speed of the wheelset, and the wheel-rail profile parameters.It is found that the period of oscillation decreases while the lateral and yaw motion amplitudes increase as the forward speed increases, for any given rail and wheel profile. While the effect of wheel curvature on the lateral motions seems to be non-existent, its effect on the yaw motion amplitude and the period is to increase them very slightly as the wheel profile changes from a conical to a curved profile. On the other hand, the effect of rail curvature on the lateral amplitude, for instance, is significant; the larger the curvature the smaller the amplitude for a given forward speed.
On nonlinear overstable convection rolls in a rotating system
Authors: Riahi N. 
Published: February 2009

AbstractFinite amplitude oscillatory convection rolls in the form of travelling waves are studied for a horizontal layer of a low Prandtl number fluid heated from below and rotating rapidly about a vertical axis. The results of the stability and nonlinear analyses indicate that there is no subcritical instability and that the oscillatory rolls are unstable for the ranges of the Prandtl number and the rotation rate considered in this paper.
Infinitely divisible random transition probabilities with application to dependent Markov chains
Authors: Chesson Peter L. 
Published: February 2009

AbstractRandom transition probability matrices with stationary independent factors define “white noise” environment processes for Markov chains. Two examples are considered in detail. Such environment processes can be used to construct several Markov chains which are dependent, have the same transition probabilities and are jointly a Markov chain. Transition rates for such processes are evaluated. These results have application to the study of animal movements.
A unified boundary integral equation method for a class of second order elliptic boundary value problems
Authors: Rezayat M. , Rizzo F. J. , Shippy D. J. 
Published: February 2009

AbstractA generalized integral equation formulation and a systematic numerical solution procedure are presented for a class of boundary value problems governed by a general second-order differential equation of elliptic type. Diverse numerical examples include problems of plane-wave scattering, three-dimensional fluid flow, and plane heat transfer for a body with a moving flame boundary. The last example employs certain representation functions useful to increase solution effectiveness in problems with an isolated integrable singularity.
Minimisation problems for implicit functionals defined by differential equations of liver kinetics
Authors: Bass L. , Bracken A. J. , Vyborny R. 
Published: February 2009

AbstractA substance carried convectively through the liver by the blood undergoes two successive enzymatic transformations. The resulting concentrations of the three forms of the substance are determined, as functions of position along the blood flow in the steady state, by coupled ordinary differential equations of the first order on a finite interval. The densities along the blood flow of the activities of the two (immobile) transforming enzymes are described by two non-negative and normalised functions of position.The problem, suggested by recent experimental results, is to choose these two functions so as to minimise the concentration of the once-transformed (intermediate) form of the substance at one boundary (the liver outlet). That minimisation is particularly significant biologically when the intermediate form is toxic and the second transformation renders it harmless. In this problem of optimal control (exerted perhaps by natural selection), the classical approach through Euler's equations is inapplicable because of the constraints on the two density functions. Moreover, when the enzyme kinetics and hence the differential equations are non-linear, the functional to be minimised is not obtainable explicitly. Instead it appears, after some manipulation of the coupled equations, as the terminal boundary value of the solution of a non-linear Volterra integral equation, which involves the two density functions (one explicitly and one implicitly) as control variables.Appropriate existence, uniqueness and boundedness results are obtained for the solution of this integral equation, and the problem is then solved rigorously for one class of non-linearities (including saturation kinetics). Some unanswered questions are posed for another class (including substrate-inhibition kinetics).
An integral equation for immiscible fluid isplacement in a two-dimensional porous medium or Hele-Shaw cell
Authors: Davidson M. R. 
Published: February 2009

AbstractAn integral equation for the normal velocity of the interface between two immiscible fluids flowing in a two-dimensional porous medium or Hele-Shaw cell (one fluid displaces the other) is derived in terms of the physical parameters (including interfacial tension), a Green's function and the given interface. When the displacement is unstable, ‘fingering’ of the interface occurs. The Saffman-Taylor interface solutions for the steady advance of a single parallel-sided finger in the absence of interfacial tension are seen to satisfy the integral equation, and the error incurred in that equation by the corresponding Pitts approximating profile, when interfacial tension is included, is shown. In addition, the numerical solution of the integral equation is illustrated for a sinusoidal and a semicircular interface and, in each case, the amplitude behaviour inferred from the velocity distribution is consistent with conclusions based on the stability of an initially flat interface.
A note on the instantaneous streamlines, pathlines and pressure contours for a cavitation bubble near a boundary
Authors: Cerone P. , Blake J. R. 
Published: February 2009

AbstractInstantaneous streamlines, particle pathlines and pressure contours for a cavitation bubble in the vicinity of a free surface and near a rigid boundary are obtained. During the collapse phase of a bubble near a free surface, the streamlines show the existence of a stagnation point between the bubble and the free surface which occurs at a different location from the point of maximum pressure. This phenomenon exists when the initial distance of the bubble is sufficiently close to the free surface for the bubble and free surface to move in opposite directions during collapse of the bubble. Pressure calculations during the collapse of a cavitation bubble near a rigid boundary show that the maximum pressure is substantially larger than the equivalent Rayleigh bubble of the same volume.
Buckling analysis of plates of arbitrary shape
Authors: Bucco D. , Mazumdar J. 
Published: February 2009

AbstractA simple and efficient numerical technique for the buckling analysis of thin elastic plates of arbitrary shape is proposed. The approach is based upon the combination of the standard Finite Element Method with the constant deflection contour method. Several representative plate problems of irregular boundaries are treated and where possible, the obtained results are validated against corresponding results in the literature.
An exactly solvable two component classical Coulomb system
Authors: Forrester Peter J. 
Published: February 2009

AbstractA two component classical Coulomb system is considered, in which particles of charge +q and + 2q are constrained to lie on a circle and interact via the two-dimensional Coulomb potential. At a special value of the coupling constant the correlation functions are calculated exactly and the asymptotic form of the truncated charge-charge correlation is found to obey Jancovici's sum rule.
Improved lower bounds for the motion of moving boundaries
Authors: Hill James M. , Dewynne Jeffrey N. 
Published: February 2009

AbstractIn a recent paper the authors give upper and lower bounds for the motion of the moving boundary for the classical Stefan problem for plane, cylindrical and spherical geometries. On comparison with the exact Neumann solution for the plane geometry and no surface radiation the bounds obtained are seen to be quite adequate for practical purposes except for the lower bound at small Stefan numbers. Here improved lower bounds are obtained which in some measure remove this inadequacy. Time dependent surface conditions are also examined and the new lower bounds obtained for the classical problem are illustrated numerically.
A note on hypergeometric polynomials
Authors: Qureshi M. I. , Pathan M. A. 
Published: February 2009

AbstractIn a paper which appeared in this journal, Manocha and Sharma [6] obtained some results of Carlitz [4], Halim and Salain [5] and generalized a few of them by using fractional derivatives. The present paper is concerned with some erroneous results of this paper [6]. Many more sums of the product of hypergeometric polynomials are also obtained.
On the rate of convergence of finite difference schemes on nonuniform grids
Authors: De Hoog Frank , Jackett David 
Published: February 2009

AbstractFinite difference schemes for some two point boundary value problems are analysed. It is found that for schemes defined on nonuniform grids, the order of the local truncation error does not fully reflect the rate of convergence of the numerical approximation obtained. Numerical results are presented that indicate that this is also the case for higher dimensional problems.
Characteristic identities for semi-simple Lie algebras
Authors: Gould M. D. 
Published: February 2009

AbstractWe present a new derivation of the polynomial identities satisfied by certain matricesAwith entriesAij(i, j= 1,…,n) from the universal enveloping algebra of a semi-simple Lie algebra. These polynomial identities are exhibited in a representation-independent way asp(A)= 0 wherep(x)(herein called the characteristic polynomial ofA) is a polynomial with coefficients from the centreZof the universal enveloping algebra. The minimum polynomial identitym(A)= 0 of the matrixAoverZis also obtained and it is shown thatp(x)andm(x)possess properties analogous to the characteristic and minimum polynomials respectively of a matrix with numerical entries. Acting on a representation (finite or infinite dimensional) admitting an infinitesimal character these polynomial identities may be expressed in a useful factored form. Our results include the characteristic identities of Bracken and Green [1] as a special case and show that these latter identities hold also in infinite dimensional representations.
Second order optimality conditions for mathematical prograramming with set functions
Authors: Chou J. H. , Hsia Wei-Shen , Lee Tan-Yu 
Published: February 2009

AbstractSecond order necessary and sufficient conditions are given for a class of optimization problems involving optimal selection of a measurable subset from a given measure subspace subject to set function inequalities. Relations between twice-differentiability at Ω and local convexity at Ω are also discussed.
Generalized functions for applications
Authors: Craven B. D. 
Published: February 2009

AbstractA simple rigorous approach is given to generalized functions, suitable for applications. Here, a generalized function is defined as a genuine function on a superset of the real line, so that multiplication is unrestricted and associative, and various manipulations retain their classical meanings. The superset is simply constructed, and does not require Robinson's nonstandard real line. The generalized functions go beyond the Schwartz distributions, enabling products and square roots of delta functions to be discussed.
A note on the boundary integral equation method for the solutions of second order elliptic equations
Authors: Clements D. L. , Haselgrove M. , Barnett D. M. 
Published: February 2009

AbstractThe boundary integral equation method is obtained by expressing a solution to a particular partial differential equation in terms of an integral taken round the boundary of the region under consideration. Various methods exist for the numerical solution of this integral equation and the purpose of this note is to outline an improvement to one of these procedures.
A nonlinear difference equation with two parameters
Authors: Brown A. 
Published: February 2009

AbstractThe paper is mainly concerned with the difference equationwhere k and m are parameters, with k > 0. This equation arises from a method proposed for solving a cubic equation by iteration and represents a standardised form of the general problem. In using the above equation it is essential to know when the iteration process converges and this is discussed by means of the usual stability criterion. Critical values are obtained for the occurrence of solutions with period two and period three and the stability of these solutions is also examined. This was done by considering the changes as k increases, for a give value of m, which makes it effectively a one-parameter problem, and it turns out that the change with k can differ strongly from the usual behaviour for a one-parameter difference equation. For m = 2, for example it appears that the usual picture of stable 2-cycle solutions giving way to stable 4-cycle solutions is valid for smaller values of k but the situation is recersed for larger values of k where stable 4-cycle solutions precede stable 2-cycle solutions. Similar anomalies arise for the 3-cycle solutions.
Numerical calculation of unstable immiscible fluid displacement in a two-dimensional porous medium or Hele-Shaw cell
Authors: Davidson M. R. 
Published: February 2009

AbstractA numerical procedure for calculating the evolution of a periodic interface between two immiscible fluids flowing in a two-dimensional porous medium or Hele-Shaw cell is described. The motion of the interface is determined in a stepwise manner with its new velocity at exach time step being derived as a numerical solution of a boundary integral equation. Attention is focused on the case of unstable displacement charaterised physically by the “fingering” of the interface and computationally by the growth of numerical errors regardless of the numerical method employed. Here the growth of such error is reduced and the usable part of the calculation extended to finite amplitudes. Numerical results are compared with an exact “finger” solution and the calculated behaviour of an initial sinusoidal displacement, as a function of interfacial tension, initial amplitude and wavelength, is discussed.
Asymptotic estimates for symmetric vortex streets
Authors: Keady G. 
Published: February 2009

AbstractSteady plane inviscid symmetric vortex streets are flows defined in the stripR× (0,b) and periodic inxwith period 2ain which the flow in (−a,a) × (0,b) is irrotational outside a vortex core on which the vorticity takes a prescribed constant value. A family of such vortex street flows, characterised by a variational principle in which the area |Aα| and the centroidycof the vortex coreAαare fixed, will be considered. For such a family, indexed by a parameter α, suppose that the coresAαbecome small in the sense thatAsymptotic estimates on functionals such as flux constant and speed are obtained.
On duality for convex minimization with nested maxima
Authors: Scott C. H. , Jefferson T. R. , Sirri E. 
Published: February 2009

AbstractIn this paper, we consider convex programs with linear constraints where the objective function involves nested maxima of linear functions as well as a convex function. A dual program is constructed which has interpretational significance and may be easier to solve than the primal formulation. A numerical example is given to illustrate the method.
Transient electromagnetic response of a layered conducting medium at asymptotically late times
Authors: O'Brien D. M. , Smith R. S. 
Published: February 2009

AbstractIn this paper we consider a pair of horizontal conducting loops in the air above a horizontally layered ground. The transmitting loop is driven by a current source which rises from zero at time zero to a final constant value at time τ. We first compute the e.m.f. induced in the receiving loop and derive an asymptotic series for the e.m.f. at late times. Secondly, we estimate the error in truncating the asymptotic series at N terms and design a reliable numerical algorithm for summing the asymptotic series.