bluuebunny/crossref_metadata_2025 huggingface dataset:
On a periodically forced, weakly damped pendulum. Part 2: Horizontal forcing
Authors: Bryant Peter J. , Miles John W.
Published: February 2009

We consider the phase-locked solutions of the differential equation governing planar motion of a weakly damped pendulum driven by horizontal, periodic forcing of the pivot with maximum acceleration εg and dimensionless frequency ω. Analytical solutions for symmetric oscillations at smaller values of ε are continued into numerical solutions at larger values of ε. A wide range of stable oscillatory solutions is described, including motion that is symmetric or asymmetric, downward or inverted, and at periods equal to the forcing period T ≡ 2π/ω or integral multiples thereof. Stable running oscillations with mean angular velocity pω/q, where p and q are integers, are investigated also. Stability boundaries are calculated for swinging oscillations of period T, 2T and 4T; 3T and 6T; and for running oscillations with mean angular velocity ω. The period-doubling cascades typically culminate in nearly periodic motion followed by chaotic motion or some independent periodic motion.
On a periodically forced, weakly damped pendulum. Part 3: Vertical forcing
Authors: Bryant Peter J. , Miles John W.
Published: February 2009

We consider the phase-locked solutions of the differential equation governing planar motion of a weakly damped pendulum forced by a prescribed, vertical acceleration εg sin ωt of its pivot, where ω and t are dimensionless, and the unit of time is the reciprocal of the natural frequency. Resonance curves and stability boundaries are presented for downward and inverted oscillations of periods T, 2T, 4T, …, where T (≡ 2π/ω) is the forcing period. Stable, downward oscillations are found to occur in distinct regions of the (ω, ε) plane, reminiscent of the regions of stability of the Mathieu equation (which describes the equivalent undamped, parametrically excited pendulum motion). The regions are dominated by oscillations of frequencies , each region being bounded on one side by a vertical state at rest in stable equilibrium and on the other side by a symmetry-breaking, period-doubling sequence to chaotic motion. Stable, inverted oscillations are found to occur also in distinct regions of the (ω, ε) plane, the principal oscillation in each region being symmetric with period 2T.
Reflection of nonlinear deep-water waves incident onto a wedge of arbitrary angle
Authors: Marchant T. R. , Roberts A. J.
Published: February 2009

Wave reflection by a wedge in deep water is examined, where the wedge can represent a breakwater of finite length or the bow of a ship heading directly into the waves. In addition, the form of the solution allows the results to apply to ships heading at an angle into the waves. We consider a deep-water wavetrain approaching the wedge head on from infinity and being reflected. Far from the wedge there is a field of progressive waves (the incident wavetrain) while close to the wedge there is a short-crested wavefield (the incident and reflected wavetrains). A weakly-nonlinear slowly-varying averaged Lagrangian theory is used to describe the problem (see Whitham [16]) as the theory includes the nonlinear interaction between the incident and reflected wavetrains. This modelling of a short-crested wavefield allows the nonlinear wavefield to be found for broad wedges, as opposed to previous theories which are applicable to thin wedges only.

It is shown that the governing partial differential equations are hyperbolic and that the solution comprises two regions, within which the wave properties are constant separated by a wave jump. Given the wedge angle and the incident wavefield, the jump angle and the wave steepness and wavenumber of the short-crested wave-field behind the wave jump can be determined. Two solution branches are found to exist: one corresponds to regular reflection, while for small amplitudes the other is similar to Mach-reflection and so it is called near Mach-reflection. Results are presented describing both solution branches and the transition between them.
A note on the relationships between convexity and invexity
Authors: Giorgi Giorgio
Published: February 2009

Using the fact that a differentiable quasi-convex function is also pseudo-convex at every point x of its domain where ∇f(x) ≠ 0 recent results relating different forms of convexity and invexity are strengthened.
Nonlinearly constrained optimal control problems involving piecewise smooth controls
Authors: Teo K. L. , Leong K. K. , Goh G. J.
Published: February 2009

In this paper, we consider a class of optimal control problems involving inequality continuous-state constraints in which the control is piecewise smooth. The requirement for this type of control is more stringent than that for the control considered in standard optimal control problems in which the controls are usually taken as bounded measurable functions. In this paper, we shall show that this class of optimal control problems can easily be transformed into an equivalent class of combined optimal parameter selection and optimal control problems. We shall then use the control parametrisation technique to devise a computational algorithm for solving this equivalent dynamic optimisation problem. Furthermore, convergence analysis will be given to support this numerical approach. For illustration, two nontrivial optimal control problems involving transferring cargo via a container crane will be solved using the proposed approach.
A uniform description of an oscillator's resonant transition
Authors: Chapman P. B.
Published: February 2009

A uniform approximation to the description of a linear oscillator's slow resonant transition is calculated. If the time scale of the transition is ɛ−1, the approximation contains explicitly the 0(1) and 0(ɛ½) terms, and fixes a uniform 0(ɛ) error bound.
Discrete variable structure system with pseudo-sliding mode
Authors: Potts R. B. , Yu X.
Published: February 2009

Variable structure systems with sliding modes have been widely discussed and used in many different fields of applications. The precise behaviour at a switching surface is complicated because there the system is non-analytic. The damped simple harmonic oscillator with a nonlinear variable structure is discretised and analysed in detail, revealing the occurrence and structure of pseudo-sliding modes which give insight to the corresponding sliding modes for the continuous system. Necessary and sufficient conditions are obtained and the analysis illustrated with graphs from numerical solutions.
Homotopy continuation method for the numerical solutions of generalised symmetric eigenvalue problems
Authors: Dzeng D. C. , Lin W. W.
Published: February 2009

We consider a generalised symmetric eigenvalue problem Ax = λMx, where A and M are real n by n symmetric matrices such that M is positive semidefinite. The purpose of this paper is to develop an algorithm based on the homotopy methods in [9, 11] to compute all eigenpairs, or a specified number of eigenvalues, in any part of the spectrum of the eigenvalue problem Ax = λMx. We obtain a special Kronecker structure of the pencil A − λM, and give an algorithm to compute the number of eigenvalues in a prescribed interval. With this information, we can locate the lost eigenpair by using the homotopy algorithm when multiple arrivals occur. The homotopy maintains the structures of the matrices A and M (if any), and the homotopy curves are n disjoint smooth curves. This method can be used to find all/some isolated eigenpairs for large sparse A and M on SIMD machines.
Analysis of shallow shells by a combination of finite elements and contour methods
Authors: Bucco D. , Mazumdar J.
Published: February 2009

Two generalised shallow-shell bending elements are developed for the analysis of doubly-curved shallow shells having arbitrarily shaped plan-forms. Although both elements are formulated using the concept of iso-deflection contour lines, one element uses the three displacement componentsU, VandWas the basic unknowns, while the displacement componentWand the stress function ф serve as the unknowns in the other element. A number of illustrative examples are included to demonstrate the accuracy and relative convergence of the proposed shallow-shell elements when employed for static analysis purposes.
Porous medium combustion: ignition, temporal evolution, and parameter dependence
Authors: Tam K. K.
Published: February 2009

A model for the combustion of a porous medium is considered for an infinite slab. The case of ignition by an initial temperature distribution is considered first. The influence of the initial data and parameters on the solution is inferred from the solution of a related ordinary differential equation. The case of ignition by heating on one side of the slab is then considered in the same manner.
Piecewise-constant collocation for first-kind boundary integral equations
Authors: Graham I. G. , Yan Y.
Published: February 2009

We examine the piecewise-constant collocation method, with collocation points the mid-points of subintervals, for first-kind integral equations with logarithmic kernels on polygonal boundaries. Previously this method had been shown to converge subject to certain restrictions on the angles at the corners of the polygon. Here, by considering a slightly modified collocation method, we are able to remove any restrictions on these angles, and to generalise slightly the meshes which may be used. Moreover, the modification leads to new results on the convergence of preconditioned two-(or multi-) grid methods for solving the resultant linear systems.
Some Bianchi type VI0 viscous fluid cosmological models
Authors: Patel L. K. , Koppar Sharda S.
Published: February 2009

The Einstein field equations have been solved for Bianchi type VI0 spacetimes with viscous fluid source. Four cosmological models are derived. They have nonzero expansion and shear. One of them have nonzero constant shear viscosity coefficient.
Continuation and uniqueness for generalised Emden-Fowler systems
Authors: Erbe Lynn H. , Liang Zhongchao
Published: February 2009

We discuss uniqueness and continuation of solutions to the Cauchy problem for a two dimensional Emden-Fowler differential system.
The equations of viscous incompressible non-homogeneous fluids: on the existence and regularity
Authors: Salvi Rodolfo
Published: February 2009

We prove the existence and regularity of the solution of an initial boundary value problem for viscous incompressible non-homogeneous fluids, using a semi-Galerkin approximation and so-called compatibility conditions.
A cylindrical wave-maker problem in a liquid of finite depth with an inertial surface in the presence of surface tension
Authors: Ghosh N. K.
Published: February 2009

The problem of generation of waves in a liquid of uniform finite depth with an inertial surface composed of a thin but uniform distribution of disconnected floating particles, due to forced axisymmetric motion prescribed on the surface of an immersed vertical cylindrical wave-maker of circular cross section under the influence of surface tension at the inertial surface, is discussed. The techniques of Laplace transform in time and the modified Weber transform involving Bessel functions in the radial coordinate have been employed to obtain the velocity potential. The steady-state development to the potential function as well as the inertial surface depression due to time-harmonic forced oscillations of the wave-maker are deduced. It is found that the presence of surface tension at the inertial surface ensures the propagation of time-harmonic progressive waves of any angular frequency.
Planform evolution in convection–an embedded centre manifold
Authors: Roberts A. J.
Published: February 2009

The new motion of embedding a centre manifold in some higher-dimensional manifold leads to a practical approach to the rational low-dimensional approximation of a wide class of dynamical systems; it also provides a simple geometric picture for these approximations. In particular, I consider the problem of finding an approximate, but accurate, description of the evolution of a two-dimensional planform of convection. Inspired by a simple example, the straightforward adiabatic iteration is proposed to estimate an embedding manifold and arguments are presented for its effectiveness. Upon applying the procedure to a model convective planform problem I find that the resulting approximations perform remarkably well–much better than the traditional Swift-Hohenberg approximation for planform evolution.
Collocation with Chebyshev polynomials for Symm's integral equation on an interval
Authors: Sloan I. H. , Stephan E. P.
Published: February 2009

A collocation method for Symm's integral equation on an interval (a first-kind integral equation with logarithmic kernel), in which the basis functions are Chebyshev polynomials multiplied by an appropriate singular function and the collocation points are Chebyshev points, is analysed. The novel feature lies in the analysis, which introduces Sobolev norms that respect the singularity structure of the exact solution at the ends of the interval. The rate of convergence is shown to be faster than any negative power of n, the degree of the polynomial space, if the driving term is smooth.
Optimality and duality in continuous-time nonlinear fractional programming
Authors: Suneja S. , Singh C. , Kaul R. N.
Published: February 2009

Optimality conditions via subdifferentiability and generalised Charnes-Cooper transformation are obtained for a continuous-time nonlinear fractional programming problem. Perturbation functions play a key role in the development. A dual problem is presented and certain duality results are obtained.
One-field equations for two-phase flows
Authors: Rudman Murray
Published: February 2009

A new derivation of the averaged heat and mass transport equations for two-phase flows is presented. A volume averaging technique is used in which averaging is perform over both phases simultaneously in order to derive equations that describe transport the mixture, rather than transport in each phase. The derivation is particularly applicable to incompressible liquid/solid systems in which the two phases are tightly coupled. An example of the numerical solution of the equations is then presented in which a thermally convecting suspension is modelled. It is seen that large-scale instability can result from the interaction of thermal and compositional density gradients.
A two-dimensional model for large-scale bushfire spread
Authors: Forbes Lawrence K.
Published: February 2009

A model for bushfire spread is proposed, in which radiative heat transfer, species consumption and flammable gas production are taken into account. It is shown that fire propagation in this model does not occur as a one-dimensional travelling wave, except for smouldering combustion of wet bushland. Numerical solutions for the evolution of a line fire are obtained using a diagonally implicit finite difference scheme, and the effects of firebreaks and uncleared combustible debris are studied. An energy theorem is presented for the case of a spreading two-dimensional fire, and numerical results are illustrated.
On optimal control of multi-link vertical planar robot arms systems moving under the effect of gravity
Authors: Lee H. W. J. , Teo K. L. , Jennings L. S.
Published: February 2009

How to obtain a workable initial guess to start an optimal control (control parametrization) algorithm is an important question. In particular, for a system of multi-link vertical planar robot arms moving under the effect of gravity and applied torques (which can exhibit chaotic behaviour), a non-workable initial guess of torques may cause integration failure regardless of what numerical packages are used. In this paper, we address this problem by introducing a simple and intuitive “Blind Man” algorithm. Theoretical justification as well as a numerical example is provided.
Differential game with switching controls on Hilbert space
Authors: Yung Siu Pang
Published: February 2009

We study differential game problems in which the players can select different maximal monotone operators for the governing evolution system. Setting up our problem on a real Hilbert space, we show that the Elliott-Kalton upper and lower value of the game are viscosity solution of some Hamilton-Jacobi-Isaacs equations. Uniqueness is obtained by assuming condition analogous to the classical Isaacs condition, and thus the existence of value of the game follows.
Global stability of the endemic equilibrium and uniform persistence in epidemic models with subpopulations
Authors: Lin Xiaodong , So Joseph W.-H.
Published: February 2009

We consider the epidemic model with subpopulations introduced in Hethcote [5]. It is shown that if the endemic equilibrium exists, then the system is uniformly persistent. Moreover, the endemic equilibrium is globally asymptotically stable under the assumption of small effective contact rates between different subpopulations.
Joined dissimilar orthotropic elastic cylindrical membranes under internal pressure and longitudinal tension
Authors: Hart V. G. , Shi Jingyu
Published: February 2009

Following work in an earlier paper, the theory of finite deformation of elastic membranes is applied to the problem of two initially-circular semi-infinite cylindrical membranes of the same radius but of different material, joined longitudinally at a cross-section. The body is inflated by constant interior pressure and is also extended longitudinally. The exact solution found for an arbitrary material is now specialised to the orthotropic case, and the results are interpreted for forms of the strain-energy function introduced by Vaishnav and by How and Clarke in connection with the study of arteries. Also considered in this context is the similar problem where two semi-infinite cylindrical membranes of the same material are separated by a cuff of different material. Numerical solutions are obtained for various pressures and longitudinal extensions. It is shown that discontinuities in the circumferential stress at the joint can be reduced by suitable choice of certain coefficients in the expression defining the strain-energy function. The results obtained here thus solve the problem of static internal pressure loading in extended dissimilar thin orthotropic tubes, and may also be useful in the preliminary study of surgical implants in arteries.
Free-surface flow due to a source submerged in a fluid of infinite depth with two stagnant regions
Authors: Mekias Hocine , Vanden-Broeck Jean-Marc
Published: February 2009

Two-dimensional free-surface flows produced by a submerged source in a fluid of infinite depth are considered. It is assumed that the point on the free surface just above the source is a stagnation point and that the fluid outside two shear layers is at rest. The free-surface profile and the shape of the shear layers are determined numerically by using a series-truncation method. It is shown that there is a solution for each value of the Froude number F > 0. When F tends to infinity, the flow also describes a thin jet impinging in a fluid at rest.
Remarks on the boundary element method for strongly nonlinear problems
Authors: Ruotsalainen Keijo
Published: February 2009

Recently in several papers the boundary element method has been applied to non-linear problems. In this paper we extend the analysis to strongly nonlinear boundary value problems. We shall prove the convergence and the stability of the Galerkin method in Lp spaces. Optimal order error estimates in Lp space then follow. We use the theory of A-proper mappings and monotone operators to prove convergence of the method. We note that the analysis includes the u4 -nonlinearity, which is encountered in heat radiation problems.
Partial differential equations for Eigenvalues: sensitivity and perturbation analysis
Authors: Leipnik Roy B.
Published: February 2009

The well-known Wilkinson expressions for the first derivatives of (ordinary) eigen-values and eigenvectors of simple matrices, in terms of the set of eigenvalues and eigenvectors, are redifferentiated and combined to obtain partial differential equations for the eigenvalues. Analogous expressions are obtained for the first derivatives of generalised eigenvalues and eigenvectors of simple pairs of matrices(A, B), defined by. Again, redifferentiation and combination yields slightly more complicated partial differential equations for the generalised eigenvalues. When the matrices depend on a few parameters θ1, θ2, …, the resulting differential equations for the eigenvalues, with those parameters as independent variables, can easily be derived. These parametric equations are explicit representations of analytic perturbation results of Kato, expressed by him as rather abstract complex matrix integrals. Connections with bounds for eigenvalues derived by Stewart and Sun can also be made. Two applications are exhibited, the first being to a broken symmetry problem, the second being to working out the second-order perturbations for a classical problem in the theory of waves in cold plasmas.
Convergence in Lotka-Volterra type diffusive delay systems without dominating instantaneous negative feedbacks
Authors: Kuang Yang , Smith Hal L.
Published: February 2009

This paper deals with the convergence aspect of diffusive delay Lotka-Volterra systems with infinite delays. It is well known that such a system has a globally asymptotically stable steady state if the negative feedbacks of the intraspecific competitions are dominant and instantaneous. It is shown here that such a globally asymptotically stable steady state continues to exist even if the instantaneous assumption is removed, provided that solutions of the system are eventually uniformly bounded and the delays involved in the intraspecific competitions are small. This work generalises several recent related ones.
The first integrals and their Lie algebra of the most general autonomous Hamiltonian of the form H = T + V possessing a Laplace-Runge-Lenz vector
Authors: Gorringe V. M. , Leach P. G. L.
Published: February 2009

In two dimensions it is found that the most general autonomous Hamiltonian possessing a Laplace-Runge-Lenz vector is The Poisson bracket of the two components of this vector leads to a third first-integral, cubic in the momenta. The Lie algebra of the three integrals under the operation of the Poisson bracket closes, and is shown to be so(3) for negative energy and so(2, 1) for positive energy. In the case of zero energy, the algebra is W(3, 1). The result does not have a three-dimensional analogue, apart from the usual Kepler problem.
Gas and water cresting towards horizontal wells
Authors: McCarthy J. F.
Published: February 2009

The hodograph method for flow in porous media is used to study the problem of simultaneous gas and water cresting towards a horizontal well in a thin oil column reservoir. Shapes of the free interfaces are found and an expression for the optimal placement of the well with respect to the interfaces is given. In addition, a numerical technique is used to find the shape of the free interface and values of critical heights for the case of water cresting towards a horizontal well beneath an impermeable plane.
Symmetric duality in multi-objective programming
Authors: Chandra S. , Prasad M. V. Durga
Published: February 2009

A pair of multi-objective programming problems is shown to be symmetric dual by associating a vector-valued infinite game to the given pair. This symmetric dual pair seems to be more general than those studied in the literature.
Numerical studies on 2-dimensional reaction-diffusion equations
Authors: Tang S. , Qin S. , Weber R. O.
Published: February 2009

Various initial and boundary value problems for a 2-dimensional reaction-diffusion equation are studied numerically by an explicit Finite Difference Method (FDM), a Galerkin and a Petrov-Galerkin Finite Element Method (FEM). The results not only show the transition processes from different local initial disturbances to quasitravelling waves, but also demonstrate the long term behaviour of the solutions, which is determined by the system itself and does not depend on the details of the initial disturbances.
A line element algorithm for curve flow problems in the plane
Authors: Roberts Stephen
Published: February 2009

In this paper we shall describe a numerical method for the solution of curve flow problems in which the normal velocity of the curve depends locally on the position, normal and curvature of the curve. The method involves approximating the curve by a number of line elements (segments) which are only allowed to move in a direction normal to the element. Hence the normal of each line element remains constant throughout the evolution. In regions of high curvature elements naturally tend to accumulate. The method easily deals with the formation of cusps as found in flame propagation problems and is computationally comparable to a naive marker particle method. As a test of the method we present a number of numerical experiments related to mean curvature flow and flows associated with flame propagation and bushfires.
On the constructive approximation of non-linear operators in the modelling of dynamical systems
Authors: Torokhti A. P. , Howlett P. G.
Published: February 2009

In this paper we propose a systematic theoretical procedure for the constructive approximation of non-linear operators and show how this procedure can be applied to the modelling of dynamical systems. We extend previous work to show that the model is stable to small disturbances in the input signal and we pay special attention to the role of real number parameters in the modelling process. The implications of computability are also discussed. A number of specific examples are presented for the particular purpose of illustrating the theoretical procedure.
On a boundary-value problem posed by cancer therapy with neutron beams
Authors: Haidar Nassar H. S.
Published: February 2009

This paper contains a detailed formulation of advanced tumor therapy with neutron beams as a mixed boundary initial value problem for multigroup neutron diffusion in a composite 3D multiregional system. By applying a vector-matrix composite region finite-integral transformation we derive the principal operational solution to this problem as the group-regional neutron flux distribution inside the tumor 3D subregions. The principal solution is then converted into expressions of various order approximation, which may be directly programmed on a computer.
Optimal control of a chemical reactor
Authors: Wong K. H. , Lock N.
Published: February 2009

A chemical reactor problem is considered governed by partial differential equations. We wish to control the input temperature and the input oxygen concentration so that the actual output temperature can be as close to the desired output temperature as possible. By linearizing the differential equations around a nominal equation and then applying a finite-element Galerkin Scheme to the resulting system, the original problem can be converted into a sequence of linearly-constrained quadratic programming problems.
On waves in the presence of vertical porous boundaries
Authors: Rhodes-Robinson P. F.
Published: February 2009

In this paper various wave motions in water of infinite depth containing vertical porous boundaries are determined when the water is of infinite extent on one or both sides. Initially surface tension is ignored and simple solutions for incident waves are obtained before going on to harder wave source and wave-maker solutions. A reduction method is developed to obtain solutions for two-sided boundaries from those for one-sided, which are obtained by standard techniques. The effect of surface tension that precludes simple solutions is also considered, although a present lack of information on dynamical edge behaviour for porous boundaries means that the formal mathematical solutions must be left in terms of arbitrary edge constants. In conclusion, some solutions are noted for finite depth.
Inf-sup conditions for finite-difference approximations of the stokes equations
Authors: Shin Dongho , Strikwerda John C.
Published: February 2009

Inf-sup conditions are proven for three finite-difference approximations of the Stokes equa-tions. The finite-difference approximations use a staggered-mesh scheme and the schemes resulting from the backward and the forward differencings.
A novel finite element method for heat transfer in the continuous caster
Authors: Wu Yong-Hong , Hill James M. , Flint Paul J.
Published: February 2009

In the continuous casting of steel, many problems, such as surface cracks in solidified steel and breakouts of molten steel from the bottom of moulds, frequently occur in practice. It is believed that the occurrence of these problems is directly related to the events in the mould, especially the transfer of heat from the strand surface across the lubricating mould powder and its interface with the mould wall to the mould cooling-water. However, as far as the authors are aware, there is no published work dealing with heat transfer across both the lubricating layer and the interface. Generally, a parameter representing the average overall heat transfer coefficient between the strand surface and the mould cooling-water is employed, instead of including the lubricating layer, the mould wall and their interface in the computation region. The existing treatment consequently does not permit analysis of some of the more important phenomena, such as the effect of mould powder properties and interface thermal contact resistance on the solidification of steel. In this paper, a novel finite element model is developed and the heat transfer across the interface between the lubricating layer and the mould wall is simulated by introducing a new type of element, referred to as the thermal contact element. The proposed model is used to investigate the effect of various casting parameters on heat transfer from the molten steel to the cooling-water. The results indicate that the thermal contact resistance between the mould wall and the mould powder is a key factor which dominates the thickness of the solidified steel shell and the heat extraction rate from the mould wall.
Diffusion and the torsion parameter
Authors: McNabb Alex , Keady Grant
Published: February 2009

The parameters describing the trapping kinetics of a linear model for diffusion, in solids involving a captured immobile phase of the diffusing entity, can be determined by measuring mean residence times for matter in the systems and evaluating the exponents for the final exponential decay rates of the diffusing entity from various shaped solids. The mean residence time for matter in a given region can be expressed in terms of a “torsion parameter” S which in the case of Dirichlet boundary conditions and cylindrical geometries, coincides with the torsional rigidity of the cylinder. The final decay rate is given by the first eigenvalue μ of a Helmholtz problem. Expressions and inequalities are derived for these parameters S and μ for general linear boundary conditions and for geometries relevant to diffusion experiments.
A theorem for a fluid Stokes flow
Authors: Palaniappan D. , Nigam S. D. , Amaranath T.
Published: February 2009

A sphere theorem for non-axisymmetric Stokes flow of a viscous fluid of viscosity μe past a fluid sphere of viscosity μi is stated and proved. The existing sphere theorems in Stokes flow follow as special cases from the present theorem. It is observed that the expression for drag on the fluid sphere is a linear combination of rigid and shear-free drags.
Spectral collocation methods for a partial integro-differential equation with a weakly singular kernel
Authors: Kim Chang Ho , Choi U Jin
Published: February 2009

We propose and analyze the spectral collocation approximation for the partial integro-differential equations with a weakly singular kernel. The space discretization is based on the pseudo-spectral method, which is a collocation method at the Gauss-Lobatto quadrature points. We prove unconditional stability and obtain the optimal error bounds which depend on the time step, the degree of polynomial and the Sobolev regularity of the solution.
The computational approach to commuting ordinary differential operators of orders six and nine
Authors: Latham Geoff A.
Published: February 2009

Entirely elementary methods are employed to determine explicit formulae for the coefficients of commuting ordinary differential operators of orders six and nine which correspond to an elliptic curve. These formulae come from solving the nonlinear ordinary differential equations which are equivalent to the commutativity condition. Most solutions turn out to be rational expressions in one or two arbitrary functions and their derivatives. The corresponding Burchnall-Chaundy curves are computed.
On an integral of Lommel and Bessel functions
Authors: Chaudhry M. Aslam
Published: February 2009

In this paper we have evaluated an infinite integral of product of the Lommel and Bessel functions and powers. Some special cases of the result are discussed.
A boundary value problem of elastoplastic deformation process theory: Existence and uniqueness theorems
Authors: Bich Dao Huy
Published: February 2009

This paper deals with the complete constitutive relations of elastoplastic deformation process theory, based on llyushin's postulate of isotropy and hypotheses of local determinancy and complanarity in plastic stage with complex loading. The formulation of the boundary value problem is given and existence and uniqueness theorems are considered.
Laplace transforms for superexponential functions
Authors: Deakin Michael A. B.
Published: February 2009

It is usually stated that the Laplace transform cannot be applied to most superexponential functions; indeed this limitation is sometimes represented as a deficiency of the technique. It is shown here that a generalisation serves to overcome much of the force of this objection. The generalisation is based on one first proposed over fifty years ago, but which is not widely known, nor was it ever worked out in detail.
Optimal driving strategies for a train journey with speed limits
Authors: Pudney Peter , Howlett Phil
Published: February 2009

How should a vehicle he driven to minimise fuel consumption? In this paper we consider the case where a train is to be driven along a straight, level track, but where speed limits may apply over parts of the track. The journey is to be completed within a specified time using as little fuel as possible.

For a journey without speed limits, the optimal driving strategy typically requires full power, speed holding, coasting and full braking, in that order. The holding speed and braking speed can be determined from the vehicle characteristics and the time available to complete the journey. If the vehicle has discrete control settings, the holding phase should be approximated by alternate coast and power phases between two critical speeds.

For a journey with speed limits, a similar strategy applies. For each given journey time there is a unique holding speed. On intervals of track where the speed limit is below the desired holding speed, the speed must be held at the limit. If braking is necessary on an interval, the speed at which braking commences is determined in part by the holding speed for the interval. For vehicles with discrete control, speed-holding is approximated by alternate coast and power phases between two critical speeds, or between a lower critical speed and the speed limit.
On two lemmas of Brown and Shepp having application to sum sets and fractals
Authors: Pearce C. E. M. , Pečarić J. E.
Published: February 2009

An improvement is made to two results of Brown and Shepp which are useful in calculations with fractal sets.
A three-dimensional numerical model of the response of the Australian North West Shelf to tropical cyclones
Authors: Zhu Songping , Imberger Jörg
Published: February 2009

A three-dimensional barotropic and baroclinic model is developed to simulate currents and temperature changes induced by tropical cyclones traversing the continental shelf and slope region of the Australian North West Shelf. The model is based on a layered, explicit, finite difference formulation using the nonlinear primitive equations with an embedded entrainment scheme; a mixed-surface-layer interface is defined, which is allowed to shift from one interface to another, depending on the strength of a storm. The model has been tested by simulating the currents and temperature changes induced by tropical cyclones Orson and Ian. The modelled currents and temperatures agreed well with the available measured records except near the seabed. It has been found that the pre-storm currents have very little influence on the peak of the storm-induced currents and the currents in the wake of a tropical cyclone. The model contained no coefficients which must be calibrated for a particular application and clearly illustrated the importance of the baroclinic effects on the storm-induced response over the North West Shelf of Australia.
Flow fields associated with in situ mineral leaching
Authors: Forbes Lawrence K. , Watts Anthony M. , Chandler Graeme A.
Published: February 2009

A simple model for underground mineral leaching is considered, in which liquor is injected into the rock at one point and retrieved from the rock by being pumped out at another point. In its passage through the rock, the liquor dissolves some of the ore of interest, and this is therefore recovered in solution. When the injection and recovery points lie on a vertical line, the region of wetted rock forms an axi-symmetric plume, the surface of which is a free boundary. We present an accurate numerical method for the solution of the problem, and obtain estimates for the maximum possible recovery rate of the liquor, as a fraction of the injected flow rate. Limiting cases are discussed, and other geometries for fluid recovery are considered.
Continuity properties of attractors for iterated fuzzy set systems
Authors: Forte B. , Schiavo M. Lo , Vrscay E. R.
Published: February 2009

An N-map Iterated Fuzzy Set System (IFZS), introduced in [4] and to be denoted as (w, Φ), is a system of N contraction maps wi: X → X over a compact metric space (X, d), with associated “grey level” maps øi: [0, 1] → [0, 1]. Associated with an IFZS (w, Φ) is a fixed point u ∈ f*(X), the class of normalized fuzzy sets on X, u: X → [0, 1]. We are concerned with the continuity properties of u with respect to changes in the wi, and the φi. Establishing continuity for the fixed points of IFZS is more complicated than for traditional Iterated Function Systems (IFS) with probabilities since a composition of functions is involved. Continuity at each specific attractor u may be established over a suitably restricted domain of φi maps. Two applications are (i) animation of images and (ii) the inverse problem of fractal construction.
Pointwise estimates for higher order convexity preserving polynomial approximation
Authors: Cao Jia-Ding , Gonska Heinz H.
Published: February 2009

DeVore-Gopengauz-type operators have attracted some interest over the recent years. Here we investigate their relationship to shape preservation. We construct certain positive convolution-type operators Hn, s, j which leave the cones of j-convex functions invariant and give Timan-type inequalities for these. We also consider Boolean sum modifications of the operators Hn, s, j show that they basically have the same shape preservation behavior while interpolating at the endpoints of [−1, 1], and also satisfy Telyakovskiῐ- and DeVore-Gopengauz-type inequalities involving the first and second order moduli of continuity, respectively. Our results thus generalize related results by Lorentz and Zeller, Shvedov, Beatson, DeVore, Yu and Leviatan.
Convergence and stability analysis of an explicit finite difference method for 2-dimensional reaction-diffusion equations
Authors: Li Nian , Steiner Joseph , Tang Shimin
Published: February 2009

The convergence and stability analysis of a simple explicit finite difference method is studied in this paper. Conditional convergence and stability theorems for this method are given. We have also proved that this scheme is stable in a much stronger sense.
A class of discrepancy principles for the simplified regularization of ill-posed problems
Authors: George Santhosh , Nair M. Thamban
Published: February 2009

A class of discrepancy principles for the choice of parameters for the simplified regularization of ill-posed problems is proposed. This procedure does not require knowledge of the unknown solution, and if the smoothness of the unknown solution is known then the convergence rate obtained is optimal. The results of this paper include the Arcangeli's method considered by Groetsch and Guacaneme (1987) for which the convergence rate was not known and also of a result of Guacaneme (1988) for which there is a gap in the proof.
Existence of positive solutions for a class of the p-Laplace equations
Authors: Huang Yin Xi
Published: February 2009

We are concerned with the existence of solutions of

where Δp is the p-Laplacian, p ∈ (1, ∞), and Ω is a bounded smooth domain in ℝn.

For h(x) ≡ 0 and f(x, u) satisfying proper asymptotic spectral conditions, existence of a unique positive solution is obtained by invoking the sub-supersolution technique and the spectral method. For h(x) ≢ 0, with assumptions on asymptotic behavior of f(x, u) as u → ±∞, an existence result is also proved.
A comparative study of simulation techniques for two dimensional data honouring specified exponential semivariograms
Authors: Brooker P. I. , Stewart M. A.
Published: February 2009

The effectiveness of four techniques for producing wide sense stationary data with exponential semivariograms is examined. Comparison is made primarily on the basis of the observed semivariograms. The LU decomposition of the covariance matrix appears to most accurately model specified semivariograms, whilst the more computationally efficient Matrix Polynomial approximation and Turning Bands methods may be more useful in practice.
On the Cauchy problem for the 1+2 complex Ginzburg-Landau equation
Authors: Bu Charles
Published: February 2009

We present analytical methods to investigate the Cauchy problem for the complex Ginzburg-Landau equation u1 = (v + iα)Δu − (κ + iβ) |u|2qu + γu in 2 spatial dimensions (here all parameters are real). We first obtain the local existence for v > 0, κ ≥ 0. Global existence is established in the critical case q = 1. In addition, we prove the global existence when .
Mahony's intriguing stiff equations
Authors: O'Malley Robert E.
Published: February 2009

Professor John Mahony, F.A.A., was a talented and unusual Australian applied mathematician (cf. Fowkes and Silberstein [6]), trained in Manchester in the early 1950s under James Lighthill and Richard Meyer. He may be best remembered today for his early work on multiple scales ([8]), for the soliton equation named after him and his collaborators Brooke Benjamin and Jerry Bona ([2]) and for the many students and colleagues he influenced positively. This note concerns certain illustrative examples listed in the three-part paper Stiff Systems of Ordinary Differential Equations by John and his then postdoc John Shepherd, published in the Journal of the Australian Math. Society (Series B) ([9]). After skimming their eighty-seven pages, it is hard to tell how thoroughly they understood the behavior of solutions to their sample problems (though these descriptions remain the most compelling parts of the papers). I can now admit that, sometime in the late 1970s, I recommended that (perhaps an early version of some of) these papers not be published in (I think) a SIAM journal. I am now glad Series B accepted them. Indeed, with regard to Mahony ([8]), Fowkes and Silberstein ([6]) reported “It is likely, in fact, that the JAMS paper was rejected by other more prestigious journals. This was often the case with John's work; partially because his material was almost always a departure from conventional wisdom, but also because John's writing could be rather formal and obscure.” The junior author of the 1981 papers now has achieved considerable mastery of the subject area, but couldn't have been expected to then take the helm from the opinionated Mahony who had initiated the study through his successful proposal to the Australian Research Council.
On the numerical solution of the diffusion equation subject to the specification of mass
Authors: Gumel A. B.
Published: February 2009

A parallel algorithm is developed for the numerical solution of the diffusion equation ut = uxx, 0 < x < t < T, subject to u(x, 0) = f(x), ux(X, t) = g(t) and the specification of mass .
The inverse fractional matching problem
Authors: Zhang Jianzhong , Liu Zhenhong , Ma Zhongfan
Published: February 2009

This paper presents a method for the inverse fractional matching problem. We show that the dual of this inverse problem can be transformed into the circulation flow problem on a directed bipartite graph which can be solved easily. We also give an algorithm to obtain the primal optimum solution of the inverse problem from its dual optimum solution by solving a shortest path problem. Furthermore, we generalize this method to solve the inverse symmetric transportation problem.
Locating oscillatory orbits of the parametrically-excited pendulum
Authors: Clifford M. J. , Bishop S. R.
Published: February 2009

A method is considered for locating oscillating, nonrotating solutions for the parametrically-excited pendulum by inferring that a particular horseshoe exists in the stable and unstable manifolds of the local saddles. In particular, odd-periodic solutions are determined which are difficult to locate by alternative numerical techniques. A pseudo-Anosov braid is also located which implies the existence of a countable infinity of periodic orbits without the horseshoe assumption being necessary.
Matrix spectral problem with multiple-order jumps and poles
Authors: Jiang Zhuhan
Published: February 2009

The inverse spectral method for a general N × N spectral problem for solving nonlinear evolution equations in one spacial and one temporal dimension is extended to include multi-boundary jumps and high-order poles and their explicit representations. It therefore provides a formalism to generate soliton solutions that correspond to higher-order poles of the spectral data.
Bragg resonances in a two-layer fluid
Authors: McKee W. D.
Published: February 2009

Equations are derived to approximately describe the propagation of small amplitude surface and interfacial waves across small irregularities in depth in a two-layer fluid. When the irregularities are sinusoidal, Bragg interaction effects between an incident surface wave and the bottom corrugations can lead to a large-amplitude reflected interfacial wave or a large-amplitude transmitted interfacial wave if the incident surface wave is relatively long and the lower layer shallow in comparison with the upper layer.
Relative controllability of nonlinear neutral Volterra integrodifferential systems
Authors: Balachandran K. , Dauer J. P.
Published: February 2009

Sufficient conditions are derived for the relative controllability of nonlinear neutral Volterra integrodifferential systems with distributed delays in the control variables. The results are a generalization of previous results and are obtained by using Schauder's fixed-point theorem.
On solution sets of nonconvex Darboux problems and applications to optimal control with endpoint constraints
Authors: Tuan H. D.
Published: February 2009

We prove a continuous version of a relaxation theorem for the nonconvex Darboux problem xlt ε F(t, τ, x, xt, xτ). This result allows us to use Warga's open mapping theorem for deriving necessary conditions in the form of a maximum principle for optimization problems with endpoint constraints. Neither constraint qualification nor regularity assumption is supposed.