bluuebunny/crossref_metadata_2025 huggingface dataset:
Flow caused by a point sink in a fluid having a free surface
Authors: Forbes Lawrence K. , Hocking Graeme C.
Published: February 2009

The flow caused by a point sink immersed in an otherwise stationary fluid is investigated. Low Froude number solutions are sought, in which the flow is radially symmetric and possesses a stagnation point at the surface, directly above the sink. A small-Froude-number expansion is derived and compared with the results of a numerical solution to the fully nonlinear problem. It is found that solutions of this type exist for all Froude numbers less than some maximum value, at which a secondary circular stagnation line is formed at the surface. The nonlinear solutions are reasonably well predicted by the small-Froude-number expansion, except for Froude numbers close to this maximum.
Comparison principles for impulsive parabolic equations with applications to models of single species growth
Authors: Erbe L. H. , Freedman H. I. , Liu X. Z. , Wu J. H.
Published: February 2009

This paper establishes some maximum and comparison principles relative to lower and upper solutions of nonlinear parabolic partial differential equations with impulsive effects. These principles are applied to obtain some sufficient conditions for the global asymptotic stability of a unique positive equilibrium in a reaction-diffusion equation modeling the growth of a single-species population subject to abrupt changes of certain important system parameters.
On certain new and exact solutions of the Emden-Fowler equation and Emden equation via invariant variational principles and group invariance
Authors: Bhutani O. P. , Vijayakumar K.
Published: February 2009

After formulating the alternate potential principle for the nonlinear differential equation corresponding to the generalised Emden-Fowler equation, the invariance identities of Rund [14] involving the Lagrangian and the generators of the infinitesimal Lie group are used for writing down the first integrals of the said equation via the Noether theorem. Further, for physical realisable forms of the parameters involved and through repeated application of invariance under the transformation obtained, a number of exact solutions are arrived at both for the Emden-Fowler equation and classical Emden equations. A comparative study with Bluman-Cole and scale-invariant techniques reveals quite a number of remarkable features of the techniques used here.
On the microwave hotspot problem
Authors: Coleman C. J.
Published: February 2009

When an object is heated by microwaves, isolated regions of excessive heating can often occur. The present paper investigates such hotspots by both perturbation and numerical means. For quite normal materials, it is shown that small temperature anomalies can grow to form hotspots. Furthermore, such effects do not need to be associated with thermal runaway.
Inertial manifold for a reaction diffusion equation model of competition in a chemostat
Authors: So Joseph Wai Hung
Published: February 2009

The existence of an inertial manifold for a reaction-diffusion equation model of the chemostat is established.
Numerical study of Fisher's equation by a Petrov-Galerkin finite element method
Authors: Tang S. , Weber R. O.
Published: February 2009

Fisher's equation, which describes a balance between linear diffusion and nonlinear reaction or multiplication, is studied numerically by a Petrov-Galerkin finite element method. The results show that any local initial disturbance can propagate with a constant limiting speed when time becomes sufficiently large. Both the limiting wave fronts and the limiting speed are determined by the system itself and are independent of the initial values. Comparing with other studies, the numerical scheme used in this paper is satisfactory with regard to its accuracy and stability. It has the advantage of being much more concise.
A mathematical analysis of wind effects on a long-jumper
Authors: de Mestre Neville
Published: February 2009

A perturbation model is used to predict the distance jumped by a long-jumper for a range of tailwinds and headwinds. The zeroth-order approximation is based on gravity being the only force present, the effects of drag and lift only being included in the first-order corrections. The difference in predicted distances produced by the zeroth and first-order approximations is less than 2% for headwinds or tailwinds upto 4 ms−1. Most increases or decreases due to wind are caused by changes in the run-up speed, and consequently the take-off angle and speed.
Chaotic breakdown of a periodically forced, weakly damped pendulum
Authors: Bryant Peter J.
Published: February 2009

An investigation is made of the transition from periodic solutions through nearly-periodic solutions to chaotic solutions of the differential equation governing forced coplanar motion of a weakly damped pendulum. The pendulum is driven by horizontal, periodic forcing of the pivot with maximum acceleration Є g and dimensionless frequency ω As the forcing frequency ω is decreased gradually at a sufficiently large forcing amplitude Є, it has been shown previously that the pendulum progresses from symmetric oscillations of period T (= 2 π/ω) into a symmetry-breaking, period-doubling sequence of stable, periodic oscillations. There are two related forms of asymmetric, stable oscillations in the sequence, dependent on the initial conditions. When the frequency is decreased immediately beyond the sequence, the oscillations become unstable but remain in the neighbourhood in (θ,) phase space of one or other of the two forms of periodic oscillations, where θ(t) is the pendulum angle with the downward vertical. As the frequency is decreased further, the oscillations move intermittently between the neighbourhoods in (θ,) phase space of each of the two forms of periodic oscillations, in paired nearly-periodic oscillations. Further decrease of the forcing frequency leads to time intervals in which the motion is strongly unstable, with the pendulum passing intermittently over the pivot, interspersed with time intervals when the motion is nearly-periodic and only weakly unstable. The strongly-unstable intervals dominate in fully chaotic oscillations. Windows of independent, stable, periodic oscillations occur throughout the frequency range investigated. It is shown in an appendix how the Floquet method may be interpreted to describe the linear stability of the periodic and nearly-periodic solutions, and the windows of periodic oscillations in the investigated frequency range are listed in a second appendix.
Oscillation and comparison theorems for certain neutral difference equations
Authors: Lalli B. S. , Zhang B. G.
Published: February 2009

Some comparison theorems and oscillation criteria are established for the neutral difference equation

as well as for certain neutral difference equations with coefficients of arbitrary sign. Neutral difference equations with mixed arguments are also considered.
Fourth-order nonlinear evolution equations for surface gravity waves in the presence of a thin thermocline
Authors: Bhattacharyya Sudebi , Das K. P.
Published: February 2009

Two coupled nonlinear evolution equations correct to fourth order in wave steepness are derived for a three-dimensional wave packet in the presence of a thin thermocline. These two coupled equations are reduced to a single equation on the assumption that the space variation of the amplitudes takes place along a line making an arbitrary fixed angle with the direction of propagation of the wave. This single equation is used to study the stability of a uniform wave train. Expressions for maximum growth rate of instability and wave number at marginal stability are obtained. Some of the results are shown graphically. It is found that a thin thermocline has a stabilizing influence and the maximum growth rate of instability decreases with the increase of thermocline depth.
Bilinear and bilateral generating functions of generalized polynomials
Authors: Mohammad Ch. Wali
Published: February 2009

The paper contains mainly three theorems involving generating functions expressed in terms of single and double Laplace and beta integrals. The theorems, in turn, yield, as special cases, a number of bilinear and bilateral generating functions of generalized functions particularly general double and triple hypergeometric series. One variable special cases of the generalized functions are important in several applied problems.
On the convergence of an iterative method for the minimax problem
Authors: Sun Wenyu
Published: February 2009

In this paper we present an Extended Linear-Quadratic Programming method for the minimax problem. We show that the Extended Linear-Quadratic Programming method for the minimax problem is equivalent to the Josephy-Newton method for generalized equation, and establish the local convergence result. Furthermore, we obtain the global convergence result for the minimax problem by means of the equivalence relation between the generalized equation and the normal equation.
The likely antecedents of improbable events: optimal search strategies
Authors: Fink A. M. , Bass L.
Published: February 2009

We use the “Brownian Bridge” of Schrödinger to model a statistical search problem in which the initial and final distributions of a random motion are given. We raise the question of how to use this information to optimally reconstruct a likely past event.
Variational principles, duality, Legendre transformations and mine shaft ventilation
Authors: Watts A. M.
Published: February 2009

The calculation of flows in pipe networks and in networks of mine shafts and the calculations of the currents in electrical circuits can be represented as variational problems. There are two approaches: the nodal method and the loop method. There is a variational representation for each of these. This paper describes the relationship between the two representations and in particular shows that the loop formulation is the Wolfe dual of the nodal formulation after the application of Legendre transformations to the variables and to the objective function.
On a nonlinear reaction-diffusion boundary-value problem: application of a Lie-Bäcklund symmetry
Authors: Broadbridge Philip , Rogers Colin
Published: February 2009

By a systematic search for Lie-Bäetcklund symmetries, a class of linearisable reaction-diffusion equations is obtained that has, as a canonical form, ut= u2uxx+ 2u2. One such nonlinear equation is θt= ∂x[a(b- θ)-2θx] -ma(b-θ)-2θx-q exp(-mx). This represents an extension of Fokas-Yortsos-Rosen equation (q= 0) to incorporate a reaction term. It is relevant to the modelling of unsaturated flow in a soil with a volumetric extraction mechanism, such as a web of plant roots. Here, a reciprocal transformation is used to solve a nonlinear boundary-value problem for transient flow into a finite layer of a soil subject to a constant flux boundary condition to compensate for such water extraction.
Radial flow through deformable porous shells
Authors: Barry S. I. , Aldis G. K.
Published: February 2009

The problem of radially directed fluid flow through a deformable porous shell is considered. General nonlinear diffusion equations are developed for spherical, cylindrical and planar geometries. Solutions for steady flow are found in terms of an exact integral and perturbation solutions are also developed. For unsteady flow, perturbation methods are used to find approximate small-time solutions and a solution valid for slow compression rates. These solutions are used to investigate the deformation of the porous material with comparisons made between the planar and the cylindrical geometries.
Linearised evaporation about a shallow half-plane pond
Authors: Weir G. J.
Published: February 2009

The Wiener-Hopf technique is applied to the quasi-linear infiltration problem of flow from a shallow half-plane pond. Fully-saturated conditions hold immediately under the pond, while on the surface away from the pond the linearised evaporative loss is assumed to be proportional to the local relative permeability.

Evaporation from the non-wetted region increases the water flow from the pond into the soil, thereby coupling to the effects from capillarity. Linearised evaporation introduces an additional length scale and additional logarithmic expressions to those derived previously. The total rate of volumetric flow into the soil from the pond per unit length of perimeter, in addition to the usual gravity flow, increases somewhat slowly as evaporation increases. The most extreme case considered in this paper yielded an additional flow rate 63% greater than that obtained in the absence of evaporation.

The interaction between evaporation and capillarity is enhanced in poorlydraining soils, where the reduced ability to transmit liquid water need not be compensated by a corresponding reduction in evaporative losses. However, in freelydraining soils the interaction between evaporation and capillarity is probably small.
Flow induced by a line sink in a quiescent fluid with surface-tension effects
Authors: Forbes Lawrence K. , Hocking Graeme C.
Published: February 2009

When a line sink is placed beneath the free surface of an otherwise quiescent fluid of infinite depth, two different flow types are now known to be possible. One type of flow involves the fluid being drawn down toward the sink, and in the other type, a stagnation point forms at the surface immediately above the position of the sink.

This paper investigates the second of these two flow types, which involves a free-surface stagnation point. The effects of surface tension are included, and even when small, these are shown to have a very significant effect on the overall solution behaviour. We demonstrate by direct numerical calculation that there are regions of genuine non-uniqueness in the nonlinear solution, when the surface-tension parameter does not vanish. In addition, an asymptotic solution valid for small Froude number is derived.
Isospectral flows and linear programming
Authors: Helmke U.
Published: February 2009

Brockett has studied the isospectral flow Ḣ = [H, [H, N]], with [A, B] = AB ∔ BA, on spaces of real symmetric matrices. The flow diagonalises real symmetric matrices and can be used to solve linear programming problems with compact convex constraints. We show that the flow converges exponentially fast to the optimal solution of the programming problem and we give explicit estimates for the time needed by the flow to approach an ε-neighbourhood of the optimum. An interior point algorithm for the standard simplex is analysed in detail and a comparison is made with a continuous time version of Karmarkar algorithm.
Some accurate solutions of the lifting surface integral equation
Authors: Tuck E. O.
Published: February 2009

This note describes a simple numerical method for solution of the lifting surface integral equation of aerodynamics, and provides benchmark computations of up to 7 figure accuracy for flat rectangular wings of arbitrary aspect ratio. The nature of the large aspect ratio limit is also investigated numerically and asymptotically. This enables determination of the limiting behaviour near the wing tips, which is compared to the predictions of lifting line theory. Generalisations to non-rectangular wings are discussed.
Improved model of water cresting
Authors: McCarthy J. F.
Published: February 2009

An improved model of water cresting towards horizontal wells is presented, using a hodograph solution to the lateral edge drive model with a constant potential boundary at a finite outer radius. In this model, the water crest tends to a horizontal asymptote far from the well, correcting previous approaches which led to the unphysical result of a crest which never levels off but, rather, tends to a parabolic curve. The hodograph solution yields the shape of the free water-oil interface. It also yields integral representations for the lengths of boundary segments, and these have enabled the derivation of an explicit expression for the critical rate in terms of the outer radius. The critical rates calculated using the improved model do not differ significantly from those calculated using previous approaches. The main advantage of the model, therefore, is not a correction to the quantitative predictions of the critical rate, but the removal of physical inconsistencies in the underlying theory.
Source solutions for the nonlinear diffusion-convection equation
Authors: Sander G. C. , Braddock R. D. , Cunning I. F. , Norbury J. , Weeks S.W.
Published: February 2009

In the paper King [8], a new class of source solutions was derived for the nonlinear diffusion equation for diffusivities of the form D(c) = D0cm/(l - vc)m+2. Here we extend this method for the nonlinear diffusion and convection equation

to obtain mass-conserving source solutions for a nonlinear conductivity function K(c) = K0cm+2/(l - vc)m+1. In particular we consider the cases m = -1,0, and 1, where fully analytical solutions are available. Furthermore we provide source solutions for the exponential forms of the diffusivity and conductivity as given by D(c) = D0c−2e−n/c and K(c) = K0ce−n/c.
A unified approach to problems of scattering of surface water waves by vertical barriers
Authors: Chakrabarti A. , Banerjea Sudeshna , Mandal B. N. , Sahoo T.
Published: February 2009

A unified analysis involving the solution of multiple integral equations via a simple singular integral equation with a Cauchy type kernel is presented to handle problems of surface water wave scattering by vertical barriers. Some well known results are produced in a simple and systematic manner.
Stability analysis from fourth order evolution equation for small but finite amplitude interfacial waves in the presence of a basic current shear
Authors: Dhar A. K. , Das K. P.
Published: February 2009

A fourth-order nonlinear evolution equation is derived for a wave propagating at the interface of two superposed fluids of infinite depths in the presence of a basic current shear. On the basis of this equation a stability analysis is made for a uniform wave train. Discussions are given for both an air-water interface and a Boussinesq approximation. Significant deviations are noticed from the results obtained from the third-order evolution equation, which is the nonlinear Schrödinger equation. In the Boussinesq approximation, it has been possible to compare the present results with the exact numerical analysis of Pullin and Grimshaw [12], and they are found to agree rather favourably.
Pulsatile flow in circular tubes of varying cross-section with suction/injection
Authors: Chandra Peeyush , Prasad J. S. V. R. Krishna
Published: February 2009

We consider here pulsatile flow in circular tubes of varying cross-section with permeable walls. The fluid exchange across the wall is accounted for by prescribing the normal velocity of the fluid at the wall. A perturbation analysis has been carried out for low Reynolds number flows and for small amplitudes of oscillation. It has been observed that the magnitude of the wall shear stress and the pressure drop decrease as the suction velocity increases. Further, as the Reynolds number is increased, the magnitude of wall shear stress increases in the convergent portion and decreases in the divergent portion of a constricted tube.
Piecewise constant collocation for first-kind boundary integral equations
Authors: Graham I. G. , Yan Y.
Published: February 2009

We wish to correct a minor error in the recent paper [2]. That paper was concerned with an integral equation defined on a closed polygon Γ with r corners at the points x0, x2, …, x2r = x0. We parameterized Γ using a mapping γ:[−π,π] → Γ defined as follows. For each l, introduce the mid-point x2l−1 of the side joining x2l—2 to x2l. Then introduce 2r + 1 points in parameter space

with the property that for each j = 1, …, 2r

where mj are integers and . Then γ(s) is defined by

for j = 1, …, 2r. The {Sj} are then the preimages of the {xj} under γ. Moreover, in view of (1), a family of uniform meshes can be constructed on [−π, π] which include {Sj} as the break-points. Then γ maps these to meshes which are uniform on each segment joining xj−1 to xj (which we denote Γj). These meshes are used to discretize the integral equation.
On the scattering of waves by nearly hard or soft incomplete vertical barriers in water of infinite depth
Authors: Rhodes-Robinson P. F.
Published: February 2009

In this paper the scattered progressive waves are determined due to progressive waves incident normally on certain types of partially immersed and completely submerged vertical porous barriers in water of infinite depth. The forms are approximate only, and are obtained using perturbation theory for nearly hard or soft barriers having high and low porosities respectively. The results for arbitrary porosity are difficult to obtain, in contrast to the well known hard limit of impermeable barriers.
Reflection of water waves in the presence of surface tension by a nearly vertical porous wall
Authors: Chakrabarti A. , Sahoo T.
Published: February 2009

In the present paper the problem of reflection of water waves by a nearly vertical porous wall in the presence of surface tension has been investigated. A perturbational approach for the first-order correction has been employed as compared with the corresponding vertical wall problem. A mixed Fourier transform together with the regularity property of the transformed function along the positive real axis has been used to obtain the potential functions along with the reflection coefficients up to first order. Whilst the problem of water of infinite depth is the subject matter of the present paper, a similar approach is applicable to problems associated with water of finite depth.
Scattering of water waves by a submerged thin vertical wall with a gap
Authors: Banerjea Sudeshna , Mandal B. N.
Published: February 2009

A train of surface water waves normally incident on a thin vertical wall completely submerged in deep water and having a gap, experiences reflection by the wall and transmission through the gaps above and in the wall. Using Havelock's expansion of water wave potential, two different integral equation formulations of the problem are presented. While the first formulation involves multiple integral equations which are solved here by reducing them to a singular integral equation with Cauchy kernel in a double interval, the second formulation involves a first-kind singular integral equation in a double interval with a combination of logarithmic and Cauchy kernel, the solution of which is obtained by utilizing the solution of a singular integral equation with Cauchy kernel in (0, ∞) and also in a double interval. The reflection coefficient is evaluated by both the methods.
Integration of trivariate polynomials over linear polyhedra in Euclidean three-dimensional space
Authors: Rathod H. T. , Rao H. S. Govinda
Published: February 2009

This paper concerns with analytical integration of trivariate polynomials over linear polyhedra in Euclidean three-dimensional space. The volume integration of trivariate polynomials over linear polyhedra is computed as sum of surface integrals in R3 on application of the well known Gauss's divergence theorem and by using triangulation of the linear polyhedral boundary. The surface integrals in R3 over an arbitrary triangle are connected to surface integrals of bivariate polynomials in R2. The surface integrals in R2 over a simple polygon or over an arbitrary triangle are computed by two different approaches. The first algorithm is obtained by transforming the surface integrals in R2 into a sum of line integrals in a one-parameter space, while the second algorithm is obtained by transforming the surface integrals in R2 over an arbitrary triangle into a parametric double integral over a unit triangle. It is shown that the volume integration of trivariate polynomials over linear polyhedra can be obtained as a sum of surface integrals of bivariate polynomials in R2. The computation of surface integrals is proposed in the beginning of this paper and these are contained in Lemmas 1–6. These algorithms (Lemmas 1–6) and the theorem on volume integration are then followed by an example for which the detailed computational scheme has been explained. The symbolic integration formulas presented in this paper may lead to an easy and systematic incorporation of global properties of solid objects, for example, the volume, centre of mass, moments of inertia etc., required in engineering design processes.
Eigenvalue characterization for (n · p) boundary-value problems
Authors: Wong Patricia J. Y. , Agarwal Ravi P.
Published: February 2009

We consider the (n, p) boundary value problem

where λ > 0 and 0 ≤ p ≤ n - l is fixed. We characterize the values of λ such that the boundary value problem has a positive solution. For the special case λ = l, we also offer sufficient conditions for the existence of positive solutions of the boundary value problem.
On nonlinear programming and matrix game equivalence
Authors: Preda Vasile
Published: February 2009

In the framework of Mond-Weir duality a new equivalence between nonlinear programming and a matrix game is given. Finally, certain conclusions about convex programming with nested maxima and matrix games are also included.
Perturbations of nonlinear autonomous oscillators
Authors: Chapman P. B.
Published: February 2009

A general theory is given for autonomous perturbations of non-linear autonomous second order oscillators. It is found using a multiple scales method. A central part of it requires computation of Fourier coefficients for representation of the underlying oscillations, and these coefficients are found as convergent expansions in a suitable parameter.
On a family of logarithmic and exponential integrals occurring in probability and reliability theory
Authors: Chaudhry M. Aslam
Published: February 2009

We define an integral functionIμ(α,x; a, b) for non-negative integral values of μ by

It is proved thatIμ(α,x; a, b) satisfies a functional recurrence relation which is exploited to find a closed form evaluation of some incomplete integrals. New integral representations of the exponential integral and complementary error functions are found as special cases.
A numerical scheme for the electromagnetic response in thin conductors of arbitrary planar shape
Authors: Siew P. F.
Published: February 2009

A calculation of the electromagnetic response of a thin conductor in the presence of an exciting primary magnetic field has been attempted by various authors. Analytic solutions are obtainable when either the conductor is of infinite extent or when the problem possesses some symmetry. The loss of symmetry makes the problem difficult to solve except for the simplest shape – that of a circular conductor. A numerical method has been used for the rectangular conductor by other authors. In this paper we consider the response due to a thin plane conductor of arbitrary shape. The method involves the numerical generation of a set of body-fitted orthogonal curvilinear coordinates which maps the conductor onto a unit square. Good orthogonal grids can be generated for shapes that do not deviate too far from the rectangular. In terms of these curvilinear coordinates the vector potential for the area current density satisfies an integro-differential equation which is solved numerically.
Cost-time trade-off in three-axial sums' transportation problem
Authors: Bandopadhyaya Lakshmisree
Published: February 2009

The bi-objective Cost-time Trade-off Three Axial Sums' Transportation Problem is shown to be equivalent to a single-objective standard Three Axial Sums' problem, which can be solved easily by the existing efficient methods. The equivalence is established for some specially defined solutions termed as Lexicographic optimal solutions with minimum pipe-line.
Analysis of a differential equation occurring in the theory of flame fronts
Authors: Grimshaw R. , Gan J.
Published: February 2009

Ronney and Sivashinsky [2] and Buckmaster and Lee [1] have proposed a certain non-autonomous first order ordinary differential equation as a simple model for an expanding spherical flame front in a zero-gravity environment. Here we supplement their preliminary numerical calculations with some analysis and further numerical work. The results show that the solutions either correspond to quenching, or to steady flame front propagation, or to rapid expansion of the flame front, depending on two control parameters. A crucial component of our analysis is the construction of a barrier orbit which divides the phase plane into two parts. The location of this barrier orbit then determines the fate of orbits in the phase plane.
On the solution of a nonlinear problem in cell membrane theory
Authors: Arthurs A. M. , Clegg J.
Published: February 2009

Methods for integral equations are used to derive upper and lower pointwise bounds for the solution of a nonlinear boundary value problem arising in the steady-state finite cable model of cell membranes. Test calculations are performed to illustrate the results and the accuracy achieved is significantly better than that obtained previously by other methods.
Convergence of discrete approximations for constrained minimization
Authors: Craven B. D.
Published: February 2009

If a constrained minimization problem, under Lipschitz or uniformly continuous hypotheses on the functions, has a strict local minimum, then a small perturbation of the functions leads to a minimum of the perturbed problem, close to the unperturbed minimum. Conditions are given for the perturbed minimum point to be a Lipschitz function of a perturbation parameter. This is used to study convergence rate for a problem of continuous programming, when the variable is approximated by step-functions. Similar conclusions apply to computation of optimal control problems, approximating the control function by step-functions.
The Taylor series for bandlimited signals
Authors: Veron M. A. Hernandez
Published: February 2009

We study a special type of infinite product, called an infinite product of Cardano type, and we obtain its Taylor series. We prove that Hadamard's factorization of bandlimited signals is given by an infinite product of Cardano type, and apply our results to obtain the Taylor series for bandlimited signals.
Controllability of nonlinear neutral Volterra integrodifferential systems
Authors: Balachandran K. , Balasubramaniam P.
Published: February 2009

Sufficient conditions for the controllability of nonlinear neutral Volterra integrodifferential systems with implicit derivative are established. The results are a generalisation of the previous results, through the notions of condensing map and measure of noncompactness of a set.
On an optimization problem with cost of rapid variation of control
Authors: Idczak D. , Kibalczyc K. , Walczak S.
Published: February 2009

In the paper we give sufficient conditions for the existence of a solution for a Darboux-Goursat optimization problem with a cost functional depending on the number of switchings of a control and the rapidity of its changes. An application is given to a gas absorption problem.
Poisson approximations for telecommunications networks
Authors: Brown T. C. , Pollett P. K.
Published: February 2009

Professor Andrew Barbour (Institut für Angewandte Mathematik, Universität Zürich) has pointed out to us that the conditional intensity specified on Page 356 of our paper is incorrect and, consequently, so too is the bound (14) and the expression on Page 358 for the variance of the conditional intensity, given by (15). This variance should be 0 if ω = 1, where recall that ω = ω (r) is uniquely determined by rω = k, while if ω > 1, the variance is given by
Aspects of laser Lorenz dynamics
Authors: Chapman P. B.
Published: February 2009

The laser Lorenz equations are studied by reducing them to a form suitable for application of an extension of a method developed by Kuzmak. The method generates a flow in a Poincaré section from which it is inferred that a certain Hopf bifurcation is always subcritical.
The maximum principle for a type of hereditary semilinear differential equation
Authors: He Feiyue
Published: February 2009

An optimal control problem governed by a class of delay semilinear differential equations is studied. The existence of an optimal control is proven, and the maximum principle and approximating schemes are found. As applications, three examples are discussed.
A gradient technique for an optimal control problem governed by a system of nonlinear first order partial differential equations
Authors: Kazemi Mohammad A.
Published: February 2009

In this paper a class of optimal control problems with distributed parameters is considered. The governing equations are nonlinear first order partial differential equations that arise in the study of heterogeneous reactors and control of chemical processes. The main focus of the present paper is the mathematical theory underlying the algorithm. A conditional gradient method is used to devise an algorithm for solving such optimal control problems. A formula for the Fréchet derivative of the objective function is obtained, and its properties are studied. A necessary condition for optimality in terms of the Fréchet derivative is presented, and then it is shown that any accumulation point of the sequence of admissible controls generated by the algorithm satisfies this necessary condition for optimality.
Smoothing approximations to nonsmooth optimization problems
Authors: Yang X.Q.
Published: February 2009

We study certain types of composite nonsmooth minimization problems by introducing a general smooth approximation method. Under various conditions we derive bounds on error estimates of the functional values of original objective function at an approximate optimal solution and at the optimal solution. Finally, we obtain second-order necessary optimality conditions for the smooth approximation prob lems using a recently introduced generalized second-order directional derivative.
Travelling waves in phase field models of solidification
Authors: Barber Michael N. , Singleton David
Published: February 2009

The existence and selection of steady-state travelling planar fronts in a set of typical phase field equations for solidification are investigated by a combination of numerical and analytical methods. Such solutions are conjectured to exist only for a unique velocity of propagation and to be unique except for translation. This behaviour is in marked contrast to the situation in conventional Stefan models in which travelling fronts exist for all velocities. The value of the steady-state velocity depends upon the various material parameters which enter the phase field equations. Numerical and, in certain tractable limits, analytical results for the velocity are presented for a number of physical situations.
Scattering of water waves by a submerged nearly circular cylinder
Authors: Mandal B. N. , Banerjea Sudeshna
Published: February 2009

The problem of scattering of surface water waves by a horizontal circular cylinder totally submerged in deep water is well studied in the literature within the framework of linearised theory with the remarkable conclusion that a normally incident wave train experiences no reflection. However, if the cross-section of the cylinder is not circular then it experiences reflection in general. The present paper studies the case when the cylinder is not quite circular and derives expressions for reflection and transmission coefficients correct to order ∈, where ∈ is a measure of small departure of the cylinder cross-section from circularity. A simplified perturbation analysis is employed to derive two independent boundary value problems (BVP) up to first order in ∈. The first BVP corresponds to the problem of water wave scattering by a submerged circular cylinder. The reflection coefficient up to first order and the first order correction to the transmission coefficient arise in the second BVP in a natural way and are obtained by a suitable use of Green' integral theorem without solving the second BVP. Assuming a Fourier expansion of the shape function, these are evaluated approximately. It is noticed that for some particular shapes of the cylinder, these vanish. Also, the numerical results for the transmission coefficients up to first order for a nearly circular cylinder for which the reflection coefficients up to first order vanish, are given in tabular form. It is observed that for many other smooth cylinders, the result for a circular cylinder that the reflection coefficient vanishes, is also approximately valid.
Splash formation at the nose of a smoothly curved body in a stream
Authors: Tuck E. O. , Simakov S. T.
Published: February 2009

In two-dimensional flow past a body close to a free surface, the upwardly diverted portion may separate to form a splash. We model the nose of such a body by a semi-infinite obstacle of finite draft with a smoothly curved front face. This problem leads to a nonlinear integral equation with a side condition, a separation condition and an integral constraint requiring the far-upstream free surface to be asymptotically plane. The integral equation, called Villat's equation, connects a natural parametrisation of the curved front face with the parametrisation by the velocity potential near the body. The side condition fixes the position of the separation point, whereas the separation condition, known as the Brillouin-Villat condition, imposes a continuity relation to be satisfied at separation. For the described flow we derive the Brillouin-Villat condition in integral form and give a numerical solution to the problem using a polygonal approximation to the front face.
Wavelet multipliers and signals
Authors: He Z. , Wong M.W.
Published: February 2009

The Schatten-von Neumann property of a pseudo-differential operator is established by showing that the pseudo-differential operator is a multiplier defined by means of an admissible wavelet associated to a unitary representation of the additive group Rnon theC*-algebra of all bounded linear operators fromL2(Rn) intoL2(Rn). A bounded linear operator onL2(R) arising in the Landau, Pollak and Slepian model in signal analysis is shown to be a wavelet multiplier studied in this paper.
Fully nonlinear flow over successive obstacles: hydraulic fall and supercritical flows
Authors: Belward Shaun R.
Published: February 2009

In this paper we consider the flow of an incompressible, inviscid and homogeneous fluid over two obstacles in succession. The flow is assumed irrotational and solutions are sought in which a hydraulic fall occurs over the first obstacle with supercritical flow over the second. The method used to solve the problem is capable of calculating flows over topography of any shape.
On the square-root method for continuous-time algebraic Riccati equations
Authors: Lu Linzhang , Pearce C. E. M.
Published: February 2009

We give a simple and transparent proof for the square-root method of solving the continuous-time algebraic Riccati equation. We examine some benefits of combining the square-root method with other solution methods. The iterative square-root method is also discussed. Finally, paradigm numerical examples are given to compare the square-root method with the Schur method.
Observability-enhanced proportional navigation guidance with bearings-only measurements
Authors: Li Mingyan , Lim Cheng-Chew
Published: February 2009

We analyse the performance of the additive observable proportional navigation guidance system, which is well-suited for low-cost homing missiles with bearings-only measurements. Closed-form solutions are derived for both manoeuvring and non-manoeuvring targets. Guidelines on how to select the navigation constants of the control law are presented. We show that the additive observable proportional navigation guidance system can cover a larger capture area than can a conventional proportional navigation system.
Second-order time discretization with finite-element method for partial integro-differential equations with a weakly singular kernel
Authors: Kim Chang Ho , Choi U Jin
Published: February 2009

We propose the second-order time discretization scheme with the finite-element approximation for the partial integro-differential equations with a weakly singular kernel. The space discretization is based on the finite element method and the time discretization is based on the Crank-Nicolson scheme with a graded mesh. We show the stability of the scheme and obtain the second-order convergence result for the fully discretized scheme.
Synthesis of layered shells from a finite set of viscoelastic materials
Authors: Bondarev E. A. , Budugaeva V. A. , Gusev E. L.
Published: February 2009

The method suggested earlier for solving the problems of optimal design from a limited set of elastic materials is generalized to a viscoelasticity case. The computational experiment for the problem of free oscillations of a spherical shell shows that characteristics of a viscoelastic layered structure may be improved due to peculiarities of wave propagation through the boundaries of layers made of different materials.
On some inequalities for entropies of discrete probability distributions
Authors: Jardas Cvetan , Pečarić Josip , Roki Rajko , Sarapa Nikola
Published: February 2009

In this paper we prove some inequalities for finite sums and infinite series with positive terms. As an application of these results we obtain some inequalities for entropies of discrete probability distributions.
A nonmonotonic trust region method for constrained optimization problems
Authors: Zhang Jianzhong , Zhu Detong
Published: February 2009

In this paper we propose an easy-to-implement algorithm for solving general nonlinear optimization problems with nonlinear equality constraints. A nonmonotonic trust region strategy is suggested which does not require the merit function to reduce its value in every iteration. In order to deal with large problems, a reduced Hessian is used to replace a full Hessian matrix. To avoid solving quadratic trust region subproblems exactly which usually takes substantial computation, we only require an approximate solution which requires less computation. The calculation of correction steps, necessary from a theoretical view point to overcome the Maratos effect but which often brings in negative results in practice, is avoided in most cases by setting a criterion to judge its necessity. Global convergence and a local superlinear rate are then proved. This algorithm has a good performance.
A numerical method for friction problems with multiple contacts
Authors: Stewart David E.
Published: February 2009

Friction problems involving “dry” or “static” friction can be difficult to solve numerically due to the existence of discontinuities in the differential equations appearing in the right-hand side. Conventional methods only give first-order accuracy at best; some methods based on stiff solvers can obtain high order accuracy. The previous method of the author [16] is extended to deal with friction problems involving multiple contact surfaces.
Reaction waves and non-constant diffusivities
Authors: Watt S. D. , Weber R. O.
Published: February 2009

A reaction-diffusion equation with non-constant diffusivity,

ut = (D(x, t)ux)x + F(u),

is studied for D(x, t) a continuous function. The conditions under which the equation can be reduced to an equivalent constant diffusion equation are derived. Some exact forms for D(x, t) are given. For D(x, t) a stochastic function, an explicit finite difference method is used to numerically determine the effect of randomness in D(x, t) upon the speed of the reaction wave solution to Fisher's equation. The extension to two spatial dimensions is considered.
On two lemmas of Brown and Shepp having application to sum sets and fractals, II
Authors: Pearce C. E. M. , Pečarić J.
Published: February 2009

Simple proofs are given of improved results of Brown and Shepp which are useful in calculations with fractal sets. A new inequality for convex functions is also obtained.
Continuous-time quadratic cost flow problems with applications to water distribution networks
Authors: Ernst A. T.
Published: February 2009

This paper deals with a class of network optimization problems in which the flow is a function of time rather than static as in the classical network flow problem, and storage is permitted at the nodes. A solution method involving discretization will be presented as an application of the ASG algorithm. We furnish a proof that the discretized solution converges to the exact continuous solution. We also apply the method to a water distribution network where we minimize the cost of pumping water to meet supply and demand, subject to both linear and nonlinear constraints.
Solvability of generalized nonlinear symmetric variational inequalities
Authors: Adly S. , Oettli W.
Published: February 2009

This paper deals with the study of a general class of nonlinear variational inequalities. An existence result is given, and a perturbed iterative scheme is analyzed for solving such problems.
The control parameterization enhancing transform for constrained optimal control problems
Authors: Teo K. L. , Jennings L. S. , Lee H. W. J. , Rehbock V.
Published: February 2009

Consider a general class of constrained optimal control problems in canonical form. Using the classical control parameterization technique, the time (planning) horizon is partitioned into several subintervals. The control functions are approximated by piecewise constant or piecewise linear functions with pre-fixed switching times. However, if the optimal control functions to be obtained are piecewise continuous, the accuracy of this approximation process greatly depends on how fine the partition is. On the other hand, the performance of any optimization algorithm used is limited by the number of decision variables of the problem. Thus, the time horizon cannot be partitioned into arbitrarily many subintervals to reach the desired accuracy. To overcome this difficulty, the switching points should also be taken as decision variables. This is the main motivation of the paper. A novel transform, to be referred to as the control parameterization enhancing transform, is introduced to convert approximate optimal control problems with variable switching times into equivalent standard optimal control problems involving piecewise constant or piecewise linear control functions with pre-fixed switching times. The transformed problems are essentially optimal parameter selection problems and hence are solvable by various existing algorithms. For illustration, two non-trivial numerical examples are solved using the proposed method.
Strict lower subdifferentiability and applications
Authors: Xu H. , Rubinov A. M. , Glover B. M.
Published: February 2009

We investigate the strict lower subdifferentiability of a real-valued function on a closed convex subset of Rn. Relations between the strict lower subdifferential, lower subdifferential, and the usual convex subdifferential are established. Furthermore, we present necessary and sufficient optimality conditions for a class of quasiconvex minimization problems in terms of lower and strict lower subdifferentials. Finally, a descent direction method is proposed and global convergence results of the consequent algorithm are obtained.
Necessary optimality conditions for bicriterion discrete optimal control problems
Authors: Yang X. Q. , Teo K. L.
Published: February 2009

In management science and system engineering, problems with two incommensurate objectives are often detected. Bicriterion optimization finds an optimal solution for the problems. In this paper it is shown that bicriterion discrete optimal control problems can be solved by using a parametric optimization technique with relaxed convexity assumptions. Some necessary optimality conditions for discrete optimal control problems subject to a linear state difference equation are derived. It is shown that in this case no adjoint equation is required.