bluuebunny/crossref_metadata_2025_split huggingface dataset:
Beyond quenching for singular reaction‐diffusion problems
Authors: Chan C. Y. , Ke Lan 
Published: November 2005

AbstractLet f(u) be twice continuously differentiable on [0, c]) for some constant c such that f(0) > 0,f′ ⩾ 0,f″ ⩾ 0, and limu→cf(u) = ∞. Also, let χ(S) be the characteristic function of the set S. This article studies all solutions u with non‐negative ut, in the region where u < c and with continuous ux for the problem: uxx – ut = − f(u)χ({u < c}), 0 < x < a, 0 < t < ∞, subject to zero initial and first boundary conditions. For any length a larger than the critical length, it is shown that if ∫f(u) du < ∞, then as t tends to infinity, all solutions tend to the unique steady‐state profile U(x), which can be computed by a derived formula; furthermore, increasing the length a increases the interval where U(x)  c by the same amount. For illustration, examples are given.
On boundary controllability of one‐dimensional vibrating systems by W, p‐controls for p ∈ [2, ∞]
Authors: Krabs W. , Leugering G. 
Published: November 2005

AbstractThis paper is concerned with boundary control of one‐dimensional vibrating media whose motion is governed by a wave equation with a 2n‐order spatial self‐adjoint and positive‐definite linear differential operator with respect to 2n boundary conditions. Control is applied to one of the boundary conditions and the control function is allowed to vary in the Sobolev space W, p for p∈[2, ∞] With the aid of Banach space theory of trigonometric moment problems, necessary and sufficient conditions for null‐controllability are derived and applied to vibrating strings and Euler beams.For vibrating strings also, null‐controllability by Lp‐controls on the boundary is shown by a direct method which makes use of d'Alembert's solution formula for the wave equation.
Stability and asymptotic behaviour in a reaction–diffusion system
Authors: Feng Wei 
Published: November 2005

AbstractThis paper is concerned with some qualitative analysis for a coupled system of five reaction–diffusion equations which arises from a physiology model. The uniform boundedness of the time‐dependent solution is obtained under various boundary conditions. Sufficient conditions are also given to ensure the asymptotic stability of the non‐negative steady‐state solutions under Dirichlet or Robin boundary condition for each component. Under homogeneous Neumann boundary condition for some components the time‐dependent solution is proven to converge to a constant steady state determined by the initial functions.
Guided waves by electromagnetic gratings and non‐uniqueness examples for the diffraction problem
Authors: Bonnet‐Bendhia Anne‐Sophie , Starling Felipe 
Published: November 2005

AbstractWe consider the two‐dimensional scalar problem of the diffraction of a plane wave by an infinite grating of conducting bodies immersed in a periodical dielectric medium. A Fredholm‐type formulation is derived and studied. The existence of a solution is proved and some uniqueness results are established. A detailed description of the guided modes of the grating is carried out. Finally, various non‐uniqueness examples for the diffraction problem are exhibited.
Solitary wave solutions and cnoidal wave solutions to the combined KdV and mKdV equation
Authors: Lou Sen‐Yue , Chen Li‐Li 
Published: November 2005

AbstractThis paper presents a mapping approach for the construction of exact solutions to the combined KdV and mKdV equation. There exist two types of soliton solutions which will reduce back to those of the KdV and mKdV equations in some appropriate limits. Four types of the general cnoidal wave solutions are also obtained.
A posteriori error analysis for linearization of nonlinear elliptic problems and their discretizations
Authors: Han Weimin 
Published: November 2005

AbstractThe paper is devoted to a posteriori quantitative analysis for errors caused by linearization of non‐linear elliptic boundary value problems and their finite element realizations. We employ duality theory in convex analysis to derive computable bounds on the difference between the solution of a non‐linear problem and the solution of the linearized problem, by using the solution of the linearized problem only. We also derive computable bounds on differences between finite element solutions of the nonlinear problem and finite element solutions of the linearized problem, by using finite element solutions of the linearized problem only. Numerical experiments show that our a posteriori error bounds are efficient.
Properties of simple model problems for reacting gas flows
Authors: Tegnér J. K. 
Published: November 2005

AbstractThe compressible Navier–Stokes equations for reacting gases are extremely complex. Simpler models have been considered, and for these completely non‐physical propagation speeds have been observed. These model problems are stiff, meaning that several different scales are present in the solution. Numerical solution of non‐reacting flows almost always involves addition of extra dissipation. It will be shown that this action will render a totally wrong propagation speed for a simple model equation of reacting flows. This problem will be accentuated by increasing stiffness of the problem. Existence and uniqueness of a solution to this model equation is proved. The dependence of the propagation speed on the viscosity and a term governing the stiffness (comparable to the reaction rate for a more complete model) is investigated. A remedy for the wrong propagation speed for this simple model equation is proposed such that the speed is correct although the front is smeared out.
Control problems with state constraints for shape memory alloys
Authors: Sokołowski J. , Sprekels J. 
Published: November 2005

AbstractIn this paper, two different control problems with state constraints for shape memory alloys are considered: in the non‐isothermal case, we study boundary control problems, and in the isothermal situation, a dynamical shape optimization problem is considered. In both cases, the transverse displacement is the constrained state variable. The first‐order conditions of optimality are derived.
Subsolutions and super solutions to systems of parabolic equations with applications to generalized Fujita‐type systems
Authors: Lu G. , Sleeman B. D. 
Published: November 2005

AbstractA constructive method for obtaining subsolutions and supersolutions to the Cauchy problem for systems of parabolic equations is discussed. Applications of the method to Fujita‐type systems are considered leading to global existence and finite time blow‐up results.
Large time asymptotics for a class of wave equations of higher order with a variable coefficient and time‐independent incitation
Authors: Winter Matthias 
Published: November 2005

AbstractWe consider the equation (−1)m∇m (p∇mu) + ∂u = ƒ in ℝn × [0, ∞] for arbitrary positive integers m and n and under the assumptions p −1, ƒ ϵ C and p > 0. Under the additional assumption that the differential operator (−1)m∇m (p∇mu) has no eigenvalues we derive an asymptotic expansion for u(x,t) as t → including all terms up to order o(1). In particular, we show that for 2m ≥ n terms of the orders tα, log t, (log t)2 and tβ·log t as t → ∞ may occur.
Thermal deformations of inhomogeneous elastic plates
Authors: Tiihonen Timo , Pietikäinen Reijo 
Published: November 2005

AbstractWe consider thermal deformations of transversally inhomogenous elastic plates. Thin plate equations are derived as limits of full three‐dimensional models both in the linear as well as in the non‐linear case with appropriate convergence proofs. In the non‐linear case also the corresponding von Kármán equations are formulated. It is obtained that the inhomogeneity leads to the loss of some symmetry properties at the von Kármán equations.
The identification problem for the exponential Radon transform
Authors: Solmon Donald C. 
Published: November 2005

AbstractThe exponential Radon transform, which arises in single photon emission computed tomography, is defined by ℛ ƒ(μ:ω,s) = ∫Rƒ(sω + tomega;⟂) eμt dtƒ. Here ƒ is a compactly supported distribution in the plane which represents the location and intensity of a radio‐pharmaceutical in a body of constant, but unknown, attenuation μ, and ω is a direction. The identification problem is to determine the attenuation μ from the data ℛƒ with ƒ unknown. We will show that μ can be determined from the data if and only if ƒ is not a radial distribution and give formulae for computing μ when ƒ is not radial.
On an initial boundary value problem for the equations of ideal magneto‐hydrodynamics
Authors: Secchi Paolo 
Published: November 2005

AbstractWe study an initial boundary value problem for the symmetric hyperbolic quasilinear system of the equations of ideal magneto‐hydrodynamics with a perfectly conducting wall boundary condition. Existence of a unique classical solution is proved inside a suitable class of functions of Sobolev type. Moreover, solutions inside the above class are shown to depend continuously in strong norm on the data.
On the one‐ and one‐half‐dimensional relativistic Vlasov‐Fokker‐Planck‐Maxwell system
Authors: Lai Raymond 
Published: November 2005

AbstractIn this paper, we study the relativistic Vlasov‐Fokker‐Planck‐Maxwell system in one space variable and two momentum variables. This non‐linear system of equations consists of a transport equation for the phase space distribution function combined with Maxwell's equations for the electric and magnetic fields. It is important in modelling distribution of charged particles in the kinetic theory of plasma. We prove the existence of a classical solution when the initial density decays fast enough with respect to the momentum variables. The solution which shares this same decay condition along with its first derivatives in the momentum variables is unique.
A finite element model for shells based on the discrete Kirchhoff hypothesis
Authors: Weeks George E. 
Published: November 2005

AbstractA ring type finite element model based on the discrete Kirchhoff hypothesis is developed and its feasibility for use in shell analysis is illustrated by determining the linear axisymmetric deformation behaviour of a conical shell loaded by lateral pressure. The displacement field is represented by a linear function of the meridional co‐ordinate. The effects of coupling between bending and extension are included and in this respect the analysis is an extension of earlier work by other investigators using this same model, where bending deformations only were considered. The results of the investigation indicate that the proposed model is capable of accurately described coupled bending and extension effects with a relatively small number of elements. In addition to the numerical results obtained several distinct advantages and disadvantages of this element are brought out. In particular, the element stiffness coefficients can be easily derived because of the simplicity of the assumed vector field. However, it appears that the price paid for such a simple vector field approximation is an undue amount of machine storage, even for a relatively small number of elements. Several suggestions are made for minimizing some of these difficulties.
The vibration of engine crankshafts—a fast numerical solution
Authors: Craven A. H. , Holmes R. 
Published: November 2005

AbstractThis paper describes a very fast numerical method for solving the full dynamical equations governing the motion of the crankshaft and, as an example, the method is used to calculate the effect of clearance tolerance on the performance of a typical bearing. It was found that the minimum film thickness is not greatly affected by the clearance tolerance, suggesting that a fair degree of variation of clearance can be allowed.
Numerical investigation of lake circulation around islands by the finite element method
Authors: Cheng Ralph T. 
Published: November 2005

AbstractLake circulations around island are calculated based on the shallow lake model using the finite element method. Wind stress, bottom friction, Coriolis force and shore line geometry are incorporated in the mathematical model and Lake Erie is used in the computations. A closure condition is derived for the multiply connected region of interest. The discussions are made in the light of accuracy and applicability of the numerical scheme used, and the influence of the circulation pattern due to the presence of islands.
Elasto‐plastic stress analysis. A generalization for various contitutive relations including strain softening
Authors: Nayak G. C. , Zienkiewicz O. C. 
Published: November 2005

AbstractSeveral iterative processes for solving elasto‐plastic problems are discussed in the context of a general formulation which includes:

Associated and non‐associated plasticity relations.
Strain hardening as well as strain softening behaviour.
Advantages of the ‘initial stress’ process are emphasized for a wide category of problems and the isoparametric formulation is used throughout.
Futher limitations on general hexahedron finite elements with derivative degrees of freedom
Authors: Rigby G. L. , McNeice G. M. 
Published: November 2005

AbstractIt is shown that isoparametric finite elements with derivative degrees of freedom of second order or higher in the local curvilinear space demand an excessive number of degrees of freedom in the global space. To illustrate this limitation as it pertains to the continued development of higher order elements, discussion is centered around the general hexahedron element.
Application of a pseudo‐viscous method to the calculation of the steady supersonic flow past a waisted body
Authors: Walkden F. , Caine P. 
Published: November 2005

AbstractA finite difference method for solving mixed initial and boundary value problems governed by hyperbolic partial differential equations is described. The method has been developed specifically to calculate the flow field associated with any arbitrary two‐dimensional or axi‐symmetric body placed in a uniform supersonic stream. In order to preserve accuracy in the neighborhood of the body surface, the equations governing the motion are formulated so that

Streamlines form one system of co‐ordinate curves.
Two of the equations of motion correspond to characteristic relations.
The boundary condition at the body is applied by omitting the equation associated with the characteristic curve reaching the body surface from inside. The method presented is a pseudo‐viscous method and flow fields which include shock waves can be treated with ease. The method has been used to calculate the flow past a particular axi‐symmetric waisted body. The shape of this body is such that a secondary internal shock wave is generated by coalescence of Mach lines behind the bow shock wave. The results obtained are compared with theoretical and experimental results obtained by other workers. The investigation has been carried out as part of a programme of work needed to validate the pseudo‐viscous method used.
A finite element analogue of the modified Rayleigh‐Ritz method for vibration problems
Authors: Parsad K. S. R. K. , Murty A. V. Krishna , Rao A. K. 
Published: November 2005

AbstractIn this paper finite element method for natural vibration problems, based on a modified Rayleigh‐Ritz method is presented. Numerical results of a few simple examples indicate that the method is promising.
Matrix analysis of local instability in plates, stiffened panels and columns
Authors: Przemieniecki J. S. 
Published: November 2005

AbstractA displacement method of matrix analysis for local instability of plates, stiffened panels and thin‐walled columns is presented. The analysis is applicable to stiffened panel and columns for which the cross‐section is made up of thin flat plates. For these cases it may be assumed that during buckling deformation no flat component of the cross‐section is translated in its own plane and the edge lines at the junctions between flats remain fixed in space. The analysis leads to the standard eigenvalue equation from which the buckling stress can be determined. The elastic and geometrical stiffness matrices derived for this analysis depend on the wavelength of the buckled pattern and this dependence is of a simple form since all coefficients in the resulting stiffness matrices contain the buckling wavelength only as a common factor allowing for considerable simplification in any numerical computations. With this new formulation of local instability analysis very few elements are required to obtain high accuracy for the buckling stress. Several examples illustrating typical applications of this new method have been included.
Bounds for eigenvalues in some vibration and stability problems
Authors: Rao G. Venkateswara , Murty A. V. Krishna , Rao A. Kameswara 
Published: November 2005

AbstractIn finite element displacement methods for vibration and stability problems, upper bounds to eigenvalues are ensured only if consistent and conforming elements arte used, whereas the use of other elements may yield an upper or a lower bound. Here a systematic perturbation of the mass (or geometric stiffness) matrix is used to generate two classes of eigenvalue sequences whose respective members tend to a common limit from opposite sides.
Convergence of consistently derived Timoshenko beam finite elements
Authors: Nickel R. E. , Secor G. A. 
Published: November 2005

AbstractThe accuracy and convergence properties of two new Timoshenko beam finite elements are compared to those now widely used. Both of the new elements are consistently derived from a variational principle written in terms of the transverse beam deflection and normal rotation. The deflection is expanded as a cubic and the rotation as a quadratic in the axial co‐ordinate of the beam, giving rise to a seven degrees of freedom element. The first element, called TIM7, includes all the degrees of freedom while the second, called TIM4, reduces this number to four through a constraint introduced by Egle. Both elements display monotonic covergence for beam natural frequencies as a function of the number of degrees of freedom and both will give the analyst some measure of confidence in response calculations for beams excited at high frequencies.
The optimum design of fluid distribution networks with particular reference to low pressure gas distribution networks
Authors: Boyne Grahame G. 
Published: November 2005

AbstractThis paper is concerned with the development of a computational algorithm to find the optimal solution to the fluid network distribution design problem. The problem is formulated as a non‐linear mathematical optimization problem and is solved using a sequential unconstrained minimization technique. Illustrative examples are included and the design solutions obtained compared with the solutions obtained using a parametric method.
Two hybrid elements for analysis of thick, thin and sandwich plates
Authors: Cook Robert D. 
Published: November 2005

AbstractTwo general quadrilateral elements for plate bending are developed. Each has 12 degrees of freedom and accounts for transverse shear deformation effects. Each is built from four triangular elements whose properties are derived by the assumed‐stress hybrid approach. Matrices needed to generate the stiffness properties of the triangular elements are explicitly stated so as to facilitate their use. Numerical test cases, in which shear deformation effects range from negligible to very important, are used to illustrate the behaviour of the elements. It is concluded that the simpler of the two quadrilaterals is one of the best plate elements currently available.
A finite element tensor approach to plate buckling and postbuckling
Authors: Vos Robert G. , Vann William P. 
Published: November 2005

AbstractA practical finite element method is presented for geometrically non‐linear (von Kármán) plate problems. Symmetric strain energy tensors provide an efficient formulation and solution, and allow the effects of initial imperfections to be considered. An unbalanced force iteration is employed, with the advantage that the time consuming Gauss decomposition needs to be performed only once. The convergence is controlled by an automatically computed relaxation factor, and this makes the method applicable in advanced stage of non‐linearity.Several different triangular elements are used in explicitly the required tensors. Buckling and post‐buckling solutions are outlined and demonstrated by numerical examples.
Comparison between sparse stiffness matrix and sub‐structure methods
Authors: Williams F. W. 
Published: November 2005

AbstractRecent publications have emphasized the advantages of the sparseness of the over‐all stiffness matrix of a structure. An alternative to setting up the over‐all stiffness matrix is to use sub‐structures. The main purpose of this paper is to show that there is equivalence between these two approaches when rows are not interchanged. It follows that a sparse matrix method can never be more efficient than the sub‐structure method, if a suitable choice of sub‐structures is assumed. However when identical sub‐structures are contained within a structure the repetition can be utilized by the sub‐structure method. In such cases the sub‐structure method will often be quicker than the best sparse matrix solution.
Flow of compressible fluid in porous elastic media
Authors: Ghaboussi J. , Wilson E. L. 
Published: November 2005

AbstractA finite element formulation for flow of fluid in a porous elastic media has been derived from a Gurtin type variational principle. Biot's field equations for porous media have been used in which the constitutive relations include the compressibility of the fluid. It has been shown that by proper choice of the form of the compressibility of the fluid as a function of the state variables, this option of the formulation can be used to treat the partially saturated soil. The method is general with respect to geometry, boundary conditions and material properties. Finally, the results of a series of examples have been presented and compared with exact results to demonstrate accuracy and applicability.
A compact Fortran sequence for limit analysis
Authors: Livesley R. K. 
Published: November 2005

AbstractThis note presents a FORTRAN sequence for solving a particular case of the ‘bounded variables’ problem.1 It is this problem, rather than the standard linear programming problem, which appears when systematic matrix methods are applied to the rigid‐plastic collapse analysis of a plane frame or truss The method uses considerably less storage than a standard simplex approach, and produces the collapse mode as a by‐product of the calculation. The sequence is part of a complete program for the plastic collapse analysis of frameworks, details of which may be obtained from the author.
Mathematical models of synchronous electrical machines
Authors: Rogers G. J. , Smith J. R. 
Published: November 2005

AbstractThis paper is concerned with developments in mathematical modelling of turbo‐generator units for use in the dynamic analysis of electrical power systems. Emphasis is placed on an over‐all reduction in computing time, whilst retaining a high order of accuracy of transient response. Accurate linear models are then derived and provide an alternative to the piecemeal formulations hitherto employed in small signal analysis. These equations form a practical basis for the synthesis of optimal control systems for large alternators.
Computer program for solution of large, sparse, unsymmetric systems of linear equations
Authors: Key John E. 
Published: November 2005

AbstractA computer program for the in‐core solution of large, sparse, unsymmetric systems of linear equations is presented in this paper. The program employs elimination techniques for solution of systems of linear equations. A limited number of zeros is stored and trivial arithmetic is by‐passed to preserve computer storage and to reduce the time required for solution. Several techniques for selecting the pivotal elements are discussed and their effect on accuracy and computational time are examined.