bluuebunny/crossref_metadata_2025_split huggingface dataset:
Further studies of stern wavemaking
Authors: Farrow D. E. , Tuck E. O. 
Published: February 2009

AbstractA new numerical method is applied to the problem of inviscid irrotational flow past a semi-infinite stern-like body of general shape. Both smooth-detachment and stagnant-detachment flows are considered, in the context of varying the geometry of the stern to generate very small waves, with the eventual aim of eliminating waves altogether. The results of this work confirm previously published results for the smooth-detachment case, but cast doubt on the existence of waveless solutions for stagnant detachment.
Low frequency scattering of elastic waves by a cavity using a matched asymptotic expansion method
Authors: Bencheikh L. 
Published: February 2009

AbstractThis work deals with low-frequency asymptotic solutions using the method of matched asymptotic expansions. It is based on two papers by Buchwald [3] and Buchwald and Tran Cong [4] who studied the diffraction of elastic waves by a small circular cavity and a small elliptic cavity, respectively, in an otherwise unbounded domain. Here we clarify and systematize some aspects of their work and extend it to the diffraction of elastic waves by a small cylindrical cavity with a hypotrochoidal boundary. Results for the case of an incident P-wave are compared, in the special case of an elliptic boundary, with the results from the numerical solution of the boundary integral equation method.
On the topology of parametric optimal control
Authors: Weber Gerhard-W. 
Published: February 2009

AbstractWe will study one-parameter families of differentiable optimal control problems given by:Here, at given times t the inequality constraint functions are of semi-infinite nature, the objective functional may also be of max-type. For each s ∈ ℝ the problem is equivalent to a one-parameter family (Ps (t))t∈[a,b] of differentiable optimization problems. From these the consideration of generalized critical trajectories, such as a local minimum trajectory, comes into our investigation. According to a concept introduced by Hettich, Jongen and Stein in optimization, we distinguish eight types of generalized critical trajectories. Under suitable continuity, compactness and integrability assumptions, those problems, which exclusively have generalized critical points being of one of these eight types, are generic. We study normal forms and characteristic examples, locally around these trajectories.Moreover, we indicate the related concept of structural stability of optimal control problems due to the topological behaviour of the lower level sets under small data perturbations. Finally, we discuss the numerical consequences of our investigations for pathfollowing techniques with jumps.
A model for the free-surface flow due to a submerged source in water of infinite depth
Authors: Vanden-Broeck J.-M. 
Published: February 2009

AbstractWe consider a free-surface flow due to a source submerged in a fluid of infinite depth. It is assumed that there is a stagnation point on the free surface just above the source. The free-surface condition is linearized around the rigid-lid solution, and the resulting equations are solved numerically by a series truncation method with a nonuniform distribution of collocation points. Solutions are presented for various values of the Froude number. It is shown that for sufficiently large values of the Froude number, there is a train of waves on the free surface. The wavelength of these waves decreases as the distance from the source increases.
Linearised evaporation from a soil of finite depth above a water table
Authors: Buchwald V. T. , Viera F. 
Published: February 2009

AbstractThe quasi-linear infiltration problem of flow from a semi-infinite wetted region on a soil of finite depth above a horizontal water table is considered in the presence of linearised evaporative loss away from the region. The resulting equations are solved by the Wiener-Hopf technique in terms of certain infinite products. Expressions for the porosity and stream function are derived, and appropriately plotted throughout the layer.
On a periodically forced, weakly damped pendulum. Part 1: Applied torque
Authors: Bryant Peter J. , Miles John W. 
Published: February 2009

AbstractCoplanar forced oscillations of a mechanical system such as a seismometer or a fluid in a tank are modelled by the coplanar motion of periodically forced, weakly damped pendulum. We consider the phase-locked solutions of the differential equation governing planar motion of a weakly damped pendulum driven by a periodic torque. Sinusoidal approximations previously obtained for downward and inverted oscillations at small values of the dimensionless driving amplitude ε are continued into numerical solutions at larger values of ε. Resonance curves and stability boundaries are presented for downward and inverted oscillations of periods T, 2T, and 4T, where T(≡ 2π/ω) is the dimensionless forcing period. The symmetry-breaking, period-doubling sequences of oscillatory motion are found to occur in bands on the (ω, ε) plane, with the amplitudes of stable oscillations in one band differing by multiples of about π from those in the other bands, a structure similar to that of energy levels in wave mechanics. The sinusoidal approximations for symmetric T-periodic oscillations prove to be surprisingly accurate at the larger values of ε, the banded structure being related to the periodicity of the J0 Bessel function.
A minimum trapping time problem in optimal control theory
Authors: Fisher M. E. , Noakes J. L. , Teo K. L. 
Published: February 2009

AbstractIn this paper we consider a natural extension of the minimum time problem in optimal control theory which we refer to as the minimum trapping time problem. The minimum trapping time problem requires a fixed time interval [0, T], where T is finite. The aim is to determine a control for which the system trajectory not only reaches a specified target in minimum time but also remains trapped within the target until time T. Our aim is to devise a computational procedure for solving the minimum trapping time problem. The computational procedure we adopt uses control parametrisation in which the class of controls is approximated by a class of piecewise constant functions. The problem we are solving is therefore an approximation to the original minimum trapping time problem. Some properties for the approximate problem are then established. These lead to an extremely efficient iterative procedure for calculating the minimum trapping time.
On eigensolutions of the one-speed neutron transport equation in plane geometry
Authors: Haidar Nassar H. S. 
Published: February 2009

AbstractWe revisit the singular eigensolution to the steady state one-speed transport equation for an isotropically scattering and multiplying heterogeneous slab. It is proved that this solution is a sum of Stieltjes integrals over the resolvent set of only the operator of multiplication by the angular variable.
Centre manifolds of forced dynamical systems
Authors: Cox S. M. , Roberts A. J. 
Published: February 2009

AbstractCentre manifolds arise in a rational approach to the problem of forming low-dimensional models of dynamical systems with many degrees of freedom. When a dynamical system with a centre manifold is subject to a small forcing, F, there are two effects: to displace the centre manifold; and to alter the evolution thereon. We propose a formal scheme for calculating the centre manifold of such a forced dynamical system. Our formalism permits the calculation of these effects, with errors of order |F|2. We find that the displacement of the manifold allows a reparameterisation of its description, and we describe two “natural” ways in which this can be carried out. We give three examples: an introductory example; a five-mode model of the atmosphere to display the quasi-geostrophic approximation; and the forced Kuramoto-Sivashinsky equation.
Welfare policy and multi-national monopolies
Authors: Rickard John , Russell Allen , Martini Christine 
Published: February 2009

AbstractThis paper examines the role of import tariffs and consumption taxes when a product is supplied to a domestic market by a foreign monopoly via a subsidiary. It is assumed that there is no competition in the domestic market from internal suppliers. The home country is able to levy a profits tax on the subsidiary; the objective of our analysis is to determine the levels of tariff or consumption tax which maximise national welfare. Comparisons are made under the two alternative policies from the perspectives of national welfare, total national cost and average national cost. The major policy implication of the analysis is that a consumption tax is the more effective instrument for maximising national welfare provided the profits tax is less than a certain critical value; if the profits tax exceeds this value then a tariff, though in the form of a subsidy, is the most effective instrument. Our results complement, correct and extend an earlier analysis by Katrak (1977) [6].
A numerical algorithm for optimal control problems with switching costs
Authors: Stewart David E. 
Published: February 2009

AbstractOptimal control problems with switching costs arise in a number of applications, and are particularly important when standard control theory gives “chattering controls”. A numerical method is given for finding optimal controls for linear problems (linear dynamics, linear plus switching cost). This is used to develop an algorithm for finding sub-optimal control functions for nonlinear problems with switching costs. Numerical results are presented for an implementation of this method.
An analytical solution for critical withdrawal of layered fluid through a line sink in a porous medium
Authors: Zhang H. , Hocking G. C. , Barry D. A. 
Published: February 2009

AbstractFluid withdrawn through a line sink from a layered fluid in a vertically confined porous medium is considered. A hodograph method is used to obtain the shape of the interface for a given sink position at the critical flow rate. The analytical solution is compared with a more general numerical solution developed in earlier work. It was found that the surface profiles obtained by the two methods are in close agreement. However, the present work has the advantage that it gives a fully explicit solution.
A discrete method for the logarithmic-kernel integral equation on an open arc
Authors: Prössdorf S. , Saranen J. , Sloan I. H. 
Published: February 2009

AbstractHere we discuss the stability and convergence of a quadrature method for Symm's integral equation on an open smooth arc. The method is an adaptation of an approach considered by Sloan and Burn for closed curves. Before applying the quadrature scheme, we use a cosine substitution to remove the endpoint singularity of the solution. The family of methods includes schemes with any order O(hp) of convergence.
One-dimensional pattern formation in a model of burning
Authors: Forbes Lawrence K. 
Published: February 2009

AbstractWe discuss a model of a burning process, essentially due to Sal'nikov, in which a substrate undergoes a two-stage decay through some intermediate chemical to form a final product. The second stage of the process occurs at a temperature-sensitive rate, and is also responsible for the production of heat. The effects of thermal conduction are included, and the intermediate chemical is assumed to be capable of diffusion through the decomposing substrate. The governing equations thus form a reaction-diffusion system, and spatially inhomogeneous behaviour is therefore possible.This paper is concerned with stationary patterns of temperature and chemical concentration in the model. A numerical method for the solution of the governing equations is outlined, and makes use of a Fourier-series representation of the pattern. The question of the stability of these patterns is discussed in detail, and a linearised solution is presented, which is valid for patterns of very small amplitude. The results of accurate solutions to the fully non-linear equations are discussed, and compared with the predictions of the linearised theory. Parameter regions in which there exists genuine nonuniqueness of solutions are identified.
On the variational stability of a class of nonlinear parabolic optimal control problems
Authors: Papageorgiou Nikolaos S. 
Published: February 2009

AbstractIn this paper we study parametric optimal control problems governed by a nonlinear parabolic equation in divergence form. The parameter appears in all the data of the problem, including the partial differential operator. Using as tools the G-convergence of operators and the Γ-convergence of functionals, we show that the set-valued map of optimal pairs is upper semicontinuous with respect to the parameter and the optimal value function responds continuously to changes of the parameter. Finally in the case of semilinear systems we show that our framework can also incorporate systems with weakly convergent coefficients.
Multiple-term approximations for Appell's F1 function
Authors: El-Gabali Magdi A. 
Published: February 2009

AbstractIn this paper computational issues of Appell's F1 functionare addressed. A novel technique is used in the derivation of highly efficient multiple-term approximations of this function (including asymptotic ones). Simple structured single- and double-term approximations, as the first two candidates of this multiple-term representa-tion, are developed in closed form. Error analysis shows that- the developed algorithms are superior to existing approximations for the same number of terms. The formulation presented is highly efficient and could be extended to a wide class of special functions.
On wave motion in a two-layered liquid of infinite depth in the presence of surface and interfacial tension
Authors: Rhodes-Robinson P. F. 
Published: February 2009

AbstractIn this paper various two-dimensional motions are determined for waves in a stratified region of infinite total depth with a free surface containing two superposed liquids, allowing for the effects of surface and interfacial tension. The fundamental set of wave-source potentials for the two layers is used to construct the set of slope potentials that produce discontinuous free-surface and interface slopes. The latter potentials are then utilized to obtain the potentials for waves due to both heaving vertical plates and incident progressive waves against a vertical wall. The underlying assumption of small time-harmonic motion pertains, described by a pair of velocity potentials for the two layers satisfying coupled linearized boundary-value problems, and all solutions are obtained in terms of their matching basic solutions. The technique for applying Green's theorem in the two layers is developed for use with the wave-source potentials, which themselves are found to obey a generalised reciprocity principle. Familiar results for a single liquid of infinite depth are hereby extended, but the new feature emerges of there being two types of progressive waves in all solutions. For ease of presentation the solutions are obtained for a particular relationship between surface and interfacial tension.
Second harmonic resonance in magnetohydrodynamic jet
Authors: Khosla H. K. , Chhabra R. K. 
Published: February 2009

AbstractCoupled nonlinear partial differential equations, which describe a nonlinear resonant interaction between the fundamental and its first harmonic on a magnetohydro-dynamic jet, are derived by the derivative expansion method. We investigate the spatial behaviour of the amplitude and phases. It is shown that the fluid surface is unstable in the neighbourhood of the first resonant wavenumber. In the steady state, it is observed that the general motion consists of both amplitude and phase modulated waves.
Solution of the problem of scattering of water waves by a nearly vertical plate
Authors: Bharathi L. Vijaya , Chakrabarti A. , Mandal B. N. , Banerjee S. 
Published: February 2009

AbstractAn approximate solution is determined for the problem of scattering of water waves by a nearly vertical plate, by reducing it to two mixed boundary-value problems (BVP) for Laplace's equation, using perturbation techniques. While the solution of one of these BVP is well-known, the other BVPs is reduced to the problem of solving two uncoupled problems, and the complete solution of the problem under consideration up to first-order accuracy is derived with a special assumption on the shape of the plate and a related approximation. Known results involving the reflection and transmission coefficients are reproduced.
Bubbles rising in an inclined two-dimensional tube and jets falling along a wall
Authors: Lee J. , Vanden-Broeck J.-M. 
Published: February 2009

AbstractThe motion of a two-dimensional bubble rising at a constant velocity U in an inclined tube of width H is considered. The bubble extends downwards without limit, and is bounded on the right by a wall of the tube, and on the left by a free surface. The same flow configuration describes also a jet emerging from a nozzle and falling down along an inclined wall. The acceleration of gravity g and the surface tension T are included in the free surface condition. The problem is characterized by the Froude number the angle β between the left wall and the horizontal, and the angle γ between the free surface and the right wall at the separation point. Numerical solutions are obtained via series truncation for all values of 0 < β < π. The results extend previous calculations of Vanden-Broeck [12–14] for β = π/2 and of Couët and Strumolo [3] for 0 < β < π/2. It is found that the behavior of the solutions depends on whether 0 < β 2π/3 or 2π/3 ≤ β < π. When T = 0, it is shown that there is a critical value F of Froude number for each 0 < β 2π/3 such that solutions with γ = 0, π/3 and π - β occur for F > Fc F = Fc and F < Fc respectively, and that all solutions are characterized by γ = 0 for 2π/3 ≤ β < π. When a small amount of surface tension T is included in the free surface condition, it is found that for each 0 < β < π there exists an infinite discrete set of values of F for which γ = π - β. A particular value F* of the Froude number for which T = 0 and γ = π - β is selected by taking the limit as T approaches zero. The numerical values of F* and the corresponding free surface profiles are found to be in good agreement with experimental data for bubbles rising in an inclined tube when 0 < β < π/2.
An inequality for probability density functions arising from a distinguishability problem
Authors: Guljaš Boris , Pearce C. E. M. , Pečarić Josip 
Published: February 2009

AbstractAn integral inequality is established involving a probability density function on the real line and its first two derivatives. This generalizes an earlier result of Sato and Watari. If f denotes the probability density function concerned, the inequality we prove is thatunder the conditions β > α 1 and 1/(β+1) < γ ≤ 1.
On the generalized complementarity problem
Authors: Yao Jen-Chih 
Published: February 2009

AbstractIn this paper, the generalised complementarity problem studied by Parida and Sen [13] is further extended. The extended problem appears to be more general and unifying. Characterisations of solutions to this extended problem are given. Some existence results derived by these characterisations are presented. An application of the extended problem to the quasi-variational inequalities of obstacle type is considered.
Control in W2(1) of nonlinear interconnected systems of neutral type
Authors: Chukwu E. N. 
Published: February 2009

AbstractIn this paper we resolve the problem of controllability of nonlinear interconnected systems of neutral type. We consider two types of systems, a general one, and one in which some control appears linearly. In each case we insist that each isolated system of the interconnected problem is controlled by its own variables while taking into account the interacting effects. Controllability is proved by assuming some controllability criteria of each isolated system and some growth condition of the interconnecting function. Fixed point and open mapping theorems are used. Examples from economics and engineering are presented.
Models and algorithms for multiple criteria linear cost network programs
Authors: Yang X. Q. , Goh C. J. 
Published: February 2009

AbstractIn this paper, we discuss a general model for multiple criteria linear cost network flow problems. This model includes several classes of existing models in the operations research literature as special cases. Based on this model, a search algorithm for finding a feasible solution of the concurrent flow problem is suggested and illustrative numerical examples are given. This search algorithm is also extended to obtain a new algorithm for finding the efficient frontier of a multiple criteria linear program.
The Laplace transform of exp(et)
Authors: Deakin Michael A. B. 
Published: February 2009

AbstractIn an earlier paper [4], the author showed how Laplace transforms might be assigned to a class of superexponential functions for which the usual defining integral diverges. The present paper considers the case of the function exp(et), which arises in combinatorial contexts and whose Laplace transform may be assigned by means of an extension of techniques described in the previous paper.
A note on withdrawal through a point sink in fluid of finite depth
Authors: Forbes Lawrence K. , Hocking Graeme C. , Chandler Graeme A. 
Published: February 2009

AbstractWithdrawal flow through a point sink on the bottom of a fluid of finite depth is considered. The fluid is at rest at infinity, and a stagnation point is present at the free surface, directly above the point sink. Numerical solutions are computed by means of the method of fundamental solutions, and it is observed that flows of this type are apparently possible for Froude number less than about 1.5. Relationships to previous work are discussed.
Reflection of water waves by a nearly vertical porous wall
Authors: Chakrabarti A. , Sahoo T. 
Published: February 2009

AbstractThe problem of reflection of water waves by a nearly vertical porous wall has been investigated. A perturbational analysis has been applied for the first order correction to be employed to the corresponding vertical wall problem. The Green's function technique has been used to obtain the solution of the boundary value problem at hand, after utilising a mixed Fourier transform together with an idea involving the regularity of the transformed function along the real axis. The cases of fluid of finite as well as infinite depth have been taken into consideration. Particular shapes of the wall have been considered and numerical results are also discussed.
A note on oscillations in a simple model of a chemical reaction
Authors: Sexton M. Jane , Forbes Lawrence K. 
Published: February 2009

AbstractWe investigate oscillatory behaviour in the famous Belousov-Zhabotinskii chemical reaction, as described by the simple two-variable Oregonator model. It is shown that oscillations are possible only in certain parameter regions. Numerical results are presented, and the presence of fold bifurcations discussed.
A comparison of constraint qualifications in infinite-dimensional convex programming revisited
Authors: Zặlinescu C. 
Published: February 2009

In 1990 Gowda and Teboulle published the paper [16], making a comparison of several conditions ensuring the Fenchel-Rockafellar duality formulainf{f(x) + g(Ax) | x ∈ X} = max{−f*(A*y*) − g*(− y*) | y* ∈ Y*}.Probably the first comparison of different constraint qualification conditions was made by Hiriart-Urruty [17] in connection with ε-subdifferential calculus. Among them appears, as the basic sufficient condition, the formula for the conjugate of the corresponding function; such functions are: f1 + f2, g o A, max{fl,…, fn}, etc. In fact strong duality formulae (like the one above) and good formulae for conjugates are equivalent and they can be used to obtain formulae for ε-subdifferentials, using a technique developed in [17] and extensively used in [46].