bluuebunny/crossref_metadata_2025_split huggingface dataset:
Chaotic breakdown of a periodically forced, weakly damped pendulum
Authors: Bryant Peter J. 
Published: February 2009

AbstractAn 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.
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

AbstractTwo 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

AbstractThe 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

AbstractIn 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.
Variational principles, duality, Legendre transformations and mine shaft ventilation
Authors: Watts A. M. 
Published: February 2009

AbstractThe 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

AbstractBy 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

AbstractThe 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

AbstractThe 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

AbstractWhen 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

AbstractBrockett 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

AbstractThis 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

AbstractAn 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

AbstractIn 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 equationto 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

AbstractA 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

AbstractA 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

AbstractWe 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 spacewith the property that for each j = 1, …, 2rwhere mj are integers and . Then γ(s) is defined byfor 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

AbstractIn 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

AbstractIn 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

AbstractA 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

AbstractThis 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

AbstractWe consider the (n, p) boundary value problemwhere 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 a family of logarithmic and exponential integrals occurring in probability and reliability theory
Authors: Chaudhry M. Aslam 
Published: February 2009

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

AbstractA 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

AbstractThe 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

AbstractRonney 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

AbstractMethods 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

AbstractIf 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.