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  • Articles: DFG German National Licenses  (7,599)
  • 1990-1994  (4,441)
  • 1985-1989  (3,158)
  • Engineering  (5,851)
  • Physical Chemistry  (1,748)
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  • Articles: DFG German National Licenses  (7,599)
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  • 101
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 717-735 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Sheet metal forming is simulated by finite element methods using a stress resultant constitutive law in this paper. A Lagrangian description of axisymmetric and plane-strain shell deformation is first reviewed. Then a stress resultant constitutive law in rate form is presented, where the effect of thickness reduction due to large plastic deformation is considered. A finite element formulation in terms of stress resultants and their work-conjugate generalized strain rates is derived based on the virtual work principle. A hemispherical punch stretching operation and a plane-strain draw operation are simulated by a finite element program based on the finite element formulation. The results of these finite element simulations are in good-agreement with those using the through-the-thickness integration method. The results of the hemispherical punch stretching simulation suggest that the coupling term of moments and membrane forces of the modified Ilyushin yield function should be eliminated to avoid numerical instability under stretching-dominated conditions for this rate-independent plasticity formulation. Further, the results suggest that the hardening rule in a power-law form based on the small-strain approach must be modified to take account for finite deformation effects of combined stretching and bending. Under the plane-strain draw operation, the sheet experiences a large amount of bending before the final stretching. The simulation based on the stress resultant constitutive law can produce this essential aspect of deformation pattern as that of the through-the-thickness integration method, whereas a simulation based on a membrane theory cannot. In conclusion, the results of these simulations indicate that a finite element program based on the stress resultant constitutive law can simulate sheet-forming processes with much shorter computational time than that based on the through-the-thickness integration method.
    Additional Material: 11 Ill.
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  • 102
    Electronic Resource
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 813-826 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A return mapping algorithm is presented for the numerical time integration of the constitutive equations for elastoplasticity with isotropic yield surfaces, constructed from all three invariants of the stress tensor. Based on the first-order backward Euler difference formula (BDF), the governing equations for the stresses are solved in the space of the invariants and the discretized persistence parameter. The stresses are recovered afterwards. The solution concept is applied to a pressure-independent yield function, expressed in terms of the second and third invariant of the stress tensor. The numerical performance of the method is demonstrated with two examples.
    Additional Material: 3 Ill.
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  • 103
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 793-812 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A technique for refining three-dimensional tetrahedral meshes is proposed in this paper. The proposed technique is capable of treating arbitrary unstructured tetrahedral meshes, convex or non-convex with multiple regions resulting in high quality constrained Delaunay triangulations. The tetrahedra generated are of high quality (nearly equilateral). Sliver tetrahedra, which present a real problem to many algorithms are not produced with the new method. The key to the generation of high quality tetrahedra is the iterative application of a set of topological transformations based on the Voronoi-Delaunay theory and a reposition of nodes technique. The computational requirements of the proposed technique are in linear relationship with the number of nodes and tetrahedra, making it ideal for direct employment in a fully automatic finite element analysis system for 3-D adaptive mesh refinement. Application to some test problems is presented to show the effectiveness and applicability of the new method.
    Additional Material: 15 Ill.
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  • 104
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 1027-1038 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The stiffness matrix of a plane four-node quadrilateral finite element is given in closed form. When expressed as a FORTRAN subroutine and compared with the classical method of forming the stiffness matrix using Gaussian integration, the approach gives a CPU time speed-up of the order of 2-3 on a vector machine and of the order of 4-5 on a scalar machine. The technique used to generate the terms of the stiffness matrix made use of a computer algebra system which could clearly be extended to generate the matrices for other elements types.
    Additional Material: 2 Ill.
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  • 105
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    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 75-101 
    ISSN: 1070-5325
    Keywords: Variable-step preconditioners ; Nonlinear preconditioning ; Generalized conjugate gradient method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: When solving large size systems of equations by preconditioned iterative solution methods, one normally uses a fixed preconditioner which may be defined by some eigenvalue information, such as in a Chebyshev iteration method. In many problems, however, it may be more effective to use variable preconditioners, in particular when the eigenvalue information is not available.In the present paper, a recursive way of constructing variable-step of, in general, nonlinear multilevel preconditioners for selfadjoint and coercive second-order elliptic problems, discretized by the finite element method is proposed. The preconditioner is constructed recursively from the coarsest to finer and finer levels. Each preconditioning step requires only block-diagonal solvers at all levels except at every k0, k0 ≥ 1 level where we perform a sufficient number ν, ν ≥ 1 of GCG-type variable-step iterations that involve the use again of a variable-step preconditioning for that level.It turns out that for any sufficiently large value of k0 and, asymptotically, for ν sufficiently large, but not too large, the method has both an optimal rate of convergence and an optimal order of computational complexity, both for two and three space dimensional problem domains.The method requires no parameter estimates and the convergence results do not depend on the regularity of the elliptic problem.
    Additional Material: 8 Tab.
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  • 106
    Electronic Resource
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    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 65-74 
    ISSN: 1070-5325
    Keywords: Elasticity ; Finite elements ; preconditioning ; Multilevel ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The basic theory of the strengthened Cauchy-Buniakowskii-Schwarz (C.B.S.) inequality is the main tool in the convergence analysis of the recently proposed algebraic multilevel iterative methods. An upper bound of the constant γ in the strengthened C.B.S. inequality for the case of the finite element solution of 2D elasticity problems is obtained. It is assumed that linear triangle finite elements are used, the initial mesh consisting of right isosceles triangles and the mesh refinement procedure being uniform. For the resulting linear algebraic systems we have proved that γ2〈0.75 uniformly on the mesh parameter and on Poisson's ratio ν ∊ (0, 1/2). Furthermore, the presented numerical tests show that the same relation holds for arbitrary initial right triangulations, even in the case of degeneracy of triangles.The theoretical results obtained are practically important for successful implementation of the finite element method to large-scale modeling of complicated structures. They allow us to construct optimal order algebraic multilevel iterative solvers for a wide class of real-life elasticity problems.
    Additional Material: 1 Ill.
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  • 107
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    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 247-263 
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper presents a row relaxation method for solving the regularized ℓp least norm problem \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm minimize}P({\rm x}) = \frac{1}{2}\varepsilon \parallel {\rm x}\parallel _{\rm 2}^{\rm 2} + \parallel A{\rm x} - {\rm b}\parallel _p^p /p $$\end{document} where e and p are positive constants, 1〈p〈∞ The interest that we have in this problem lies in the observation that for small values of E the minimizer of P (X ) is a good substitute for a minimizer of the unregularized problem \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm minimize }U({\rm x}) = \parallel A{\rm x} - {\rm b}\parallel _p^p /p $$\end{document} It is shown that the dual of the regularized problem has the form \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm minimize }D({\rm y}) = {\rm b}^T {\rm y} - \frac{1}{2}\varepsilon \parallel A^T {\rm y/}\varepsilon \parallel _2^2 - \parallel {\rm y}\parallel _q^q /q $$\end{document} where q = p /(p - 1). Moreover, if y solves the dual problem then X = ATy/∊ solves the primal problem and P(ATy/∊) = D(y). Maximizing the dual objective function by changing one variable at a time results in a row relaxation method that resembles Kaczmarz's method. This feature makes the new method suitable for solving large sparse C, problems that arise in computerized tomography, geophysics, and groundwater hydrology. Numerical experiments illustrate the feasibility of our ideas.
    Additional Material: 5 Tab.
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  • 108
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    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 331-333 
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 109
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    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 313-329 
    ISSN: 1070-5325
    Keywords: Discretization method ; Nonlinear ABS class ; Newton-type method ; Quadratic convergence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we give a class of algorithms for solving nonlinear algebraic equations using difference approximations of derivatives. The class is a modification of the original ABS class with the advantage of requiring less function evaluations. Special cases include the methods of Brown and Brent and the discretized Newton method, which is formulated in a way requiring fewer function evaluations per iteration.
    Additional Material: 1 Tab.
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  • 110
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    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 287-311 
    ISSN: 1070-5325
    Keywords: Linear systems ; Incomplete factorizations ; Parallel computation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper two new implementations of SSOR and incomplete factorization preconditioners are given, for shared memory and distributed memory parallel computers respectively. These new implementations give increased solution speeds for matrix problems such as those arising from discretized partial differential equations with natural ordering of the grid points, for which it is well-known that the standard implementation of these preconditioners is difficult to parallelize effectively. For shared memory machines, a new technique is presented here which decreases the number of synchronization points in each preconditioning step and thus allows better parallel speedups. For distributed memory machines, an implementation based on block cyclic reduction is given which circumvents the problem of idle processors during the preconditioning phase. Descriptions of the implementations are given, and numerical comparisons are given for a model diffusion problem on the Cray Y-MP and the CM-2 Connection Machine.
    Additional Material: 5 Ill.
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  • 111
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    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 511-532 
    ISSN: 1070-5325
    Keywords: Iterative methods for linear systems ; Acceleration of convergence ; Preconditioning ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A new incomplete factorization method is proposed, differing from previous ones by the way in which the diagonal entries of the triangular factors are defined. A comparison is given with the dynamic modified incomplete factorization methods of Axelsson-Barker and Beauwens, and with the relaxed incomplete Cholesky method of Axelsson and Lindskog. Theoretical arguments show that the new method is at least as robust as both previous ones, while numerical experiments made in the discrete PDE context show an effective improvement in many practical circumstances, particularly for anisotropic problems.
    Additional Material: 5 Tab.
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  • 112
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    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 571-581 
    ISSN: 1070-5325
    Keywords: GMRES ; GMRES(m) ; Large-scale nonsymmetric linear systems ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The generalized minimal residual (GMRES) method is widely used for solving very large, nonsymmetric linear systems, particularly those that arise through discretization of continuous mathematical models in science and engineering. By shifting the Arnoldi process to begin with Ar0 instead of r0, we obtain simpler Gram-Schmidt and Householder implementations of the GMRES method that do not require upper Hessenberg factorization. The Gram-Schmidt implementation also maintains the residual vector at each iteration, which allows cheaper restarts of GMRES(m) and may otherwise be useful.
    Additional Material: 4 Ill.
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  • 113
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    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 555-570 
    ISSN: 1070-5325
    Keywords: Linear system of equations ; Iterative method ; Fast algorithm ; Arnoldi process ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A new iterative scheme is described for the solution of large linear systems of equations with a matrix of the form A = ρU + ζI, where ρ and ζ are constants, U is a unitary matrix and I is the identity matrix. We show that for such matrices a Krylov subspace basis can be generated by recursion formulas with few terms. This leads to a minimal residual algorithm that requires little storage and makes it possible to determine each iterate with fairly little arithmetic work. This algorithm provides a model for iterative methods for non-Hermitian linear systems of equations, in a similar way to the conjugate gradient and conjugate residual algorithms. Our iterative scheme illustrates that results by Faber and Manteuffel [3,4] on the existence of conjugate gradient algorithms with short recurrence relations, and related results by Joubert and Young [13], can be extended.
    Additional Material: 3 Ill.
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  • 114
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    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 583-587 
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 115
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 373-384 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper demonstrates an approach to generate three-dimensional boundary-fitted computational meshes efficiently. One basic idea underlying the present study is that often similar geometries have to be meshed, and therefore an efficient mesh-adaption method, which allows adaptation of the topological mesh to the specific geometry, would be more efficient than generating all new meshes. On the other hand the mesh generation for Cartesian topologies has been shown to be a very simple task. It can be executed by connecting and removing brick elements to a basic cube. In connection with a so-called ‘Macro Command Language’, a high degree of automation can be reached when adapting topologically defined meshes to a surface. Furthermore, a high mesh quality has proved to be the key to good simulation results. During the mesh generation it is important to provide the possibility of modifiying the mesh quality and also the mesh density at any time of the meshing process. Using this generation method the meshing time is reduced - e.g. a computational mesh for a two-valve cylinder head can be generated within a few hours.
    Additional Material: 11 Ill.
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  • 116
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    Communications in Numerical Methods in Engineering 10 (1994), S. 393-401 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we present numerical experiments made to investigate the behaviour of the Newmark time-stepping scheme applied to non-linear dynamic systems. Our attention is focused on the instability and chaos in the Newmark scheme when it is applied to the equation ü + P(u) = 0, representing a non-linear elastic spring. Some unusual modes of behaviour, which are of substantial interest, have been observed. In the first case, a stable but chaotic solution is found. In the second case, while a stable solution is obtained with a certain time step, an unstable solution is found by decreasing the time step. In the third case, instability is triggered by neglecting the initial acceleration. A simple modification of the Newmark scheme is proposed which keeps the energy constant for the equation ü + P(u) = 0 and thereby guarantees unconditional stability. Numerical examples in support of such an energy-conserving scheme are presented.
    Additional Material: 6 Ill.
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  • 117
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    Communications in Numerical Methods in Engineering 10 (1994), S. 421-423 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A note on the effects of a weak discontinuity in the forcing function g(x) of a singular, integral equation of the first kind and the resulting strong discontinuity that can appear in the solution f(x) is presented.
    Additional Material: 1 Ill.
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  • 118
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    Communications in Numerical Methods in Engineering 10 (1994), S. 427-435 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a new method for the numerical solution of transient linear heat conduction problems. In the proposed method, the transient linear heat conduction equation is first integrated with respect to time over subsequent intervals. Then the resulting set of elliptic equations is discretized in space according to a finite-element procedure. The method is unconditionally stable. At the end of the paper, the effectiveness of the proposed method is assessed through some numerical examples.
    Additional Material: 4 Tab.
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  • 119
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    Communications in Numerical Methods in Engineering 10 (1994), S. 453-460 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In finite-element analysis of transient heat conduction, oscillatory results are quite common. Several criteria for eliminating oscillation which permit choice of time step length and/or element mesh and type are sensibly derived and proved with a different methodology from those of previous work. Numerical examples are presented to show their validity and usefulness.
    Additional Material: 3 Tab.
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  • 120
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    Communications in Numerical Methods in Engineering 10 (1994), S. 437-451 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper a computation code based on the finite-element method for temperature evolutions in composite elements with internal cavities is presented. It is suitable for the analysis of various thermal problems encountered in mechanical and civil engineering such as fire risk assessment. It is based on a plane isoparametric triangular element with six nodes allowing the modelling of curved boundaries. In order to analyse composite steel-concrete elements and to take into account the non-linearities coming from the temperature-dependent material properties and from the boundary conditions, an implicit integration scheme is used. Another advantage of the program is the possibility of describing internal cavities with convection and radiation exchanges. In order to show the capacity of the program two examples are presented. Comparisons have been made with experimental and other numerical results, exhibiting very good agreement.
    Additional Material: 15 Ill.
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  • 121
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    Communications in Numerical Methods in Engineering 10 (1994), S. 461-468 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A speculation is presented to explain in physical terms the biblical story in which the withdrawal and return of the sea saved the Hebrews but drowned the army of Pharaoh. The explosion of the volcano on the island of Thira (Santorini) is speculated to be connected with this biblical story.To support our proposition concerning depression and flooding waves, we have made a numerical calculation with a highly accurate computer code and provided an outline of the PLIM method (piecewise linear interpolation method) used. This calculation is numerically very challenging because the volcano is located far from the shore and hence detailed discretization is not practical. In addition, we show that if a less accurate numerical method is used, the whole phenomenon is lost because of numerical errors.Our simple approach provides a withdrawal and return of the water to the shore that is sufficiently large, but the duration of this occurence is only a few minutes. The opportunity for a much longer duration as a consequence of other phenomena has not been excluded, however.
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  • 122
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    Communications in Numerical Methods in Engineering 10 (1994), S. 489-496 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The possibility of improving heat transfer rates by the imposition of a wavy boundary led to this extension of direct simulation of heat transfer in turbulent flow in a channel. This part of the paper shows how a pattern of micro-riblets on the surface and parallel to the flow is incorporated into the solution of the Navier-Stokes and temperature equations. The channel is two-dimensional with walls at different but uniform temperatures, and the fluid properties are constant. The presence of the patterns presents a considerable computational problem that can be largely overcome by the use of a discrete Green function technique. The method is illustrated by making short-time calculations of the velocity and temperature fields for a Prandtl number of 0.72, a Reynolds number based on channel half-width and bulk velocity of 2800, and a sinusoidal pattern with a height of 5 wall units.
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  • 123
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    Communications in Numerical Methods in Engineering 10 (1994) 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 124
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    Communications in Numerical Methods in Engineering 10 (1994), S. 511-521 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the present study a hybrid boundary-element and finite-element method is developed for the non-linear analysis of two-dimensional elastic media with inclusions, and it is utilized in defining the micro-mechanical stress field in composite materials. The linear elastic, isotropic and homogeneous matrix is treated with the BEM, while the non-linear elastic and orthotropic inclusions (fibres) are treated with the FEM.
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  • 125
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    Communications in Numerical Methods in Engineering 10 (1994), S. 501-510 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite-element solution for elastohydrodynamic lubrication (EHL) of spherical bodies undergoing elastic deformation is presented. The Galerkin finite-element approach is employed and the domain under investigation is discretized using isoparametric quadrilateral elements. Isothermal conditions are assumed and the generation of the pressure is assumed to be governed by the Reynolds equation. The viscosity and the density of the oil are assumed to be functions of the pressure. It is assumed that the underlying surface deforms elastically under the hydrodynamic pressure distribution. The accuracy of the technique is illustrated in particular examples.
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  • 126
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    Communications in Numerical Methods in Engineering 10 (1994), S. 523-530 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient algorithm is developed for the formation of a minimal cycle basis of a graph. This method reduces the number of cycles to be considered as candidates for being the elements of a minimal basis and makes practical use of the Greedy algorithm feasible. A comparison is made between the existing methods and the present algorithm. A counter-example is presented for Kaveh's algorithm from planar graphs.
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  • 127
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    Communications in Numerical Methods in Engineering 10 (1994) 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 128
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    Communications in Numerical Methods in Engineering 10 (1994), S. 711-716 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We derive explicit expressions of shape functions for the 8-node serendipity element with bilinear element geometry, which is modified so that it can represent any quadratic fields in Cartesian co-ordinates. The modification is similar to the one by MacNeal and Harder, but is slightly different and based on our own idea. We also show that the usual 6-node triangular element can be obtained by applying the node degeneration technique to this modified element.
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  • 129
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    Communications in Numerical Methods in Engineering 10 (1994), S. 673-681 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Timoshenko beam elements have been the subject of numerous publications. The difficulty was that of arriving at a superconvergent element with four degrees of freedom, as is the case for the Bernuli-Euler classical beam element. Two different approaches are presented here for the derivation of the shape functions. The first is based on the flexibility matrix, where utilizing the unit load method, including the term that accounts for the shear deformations in the virtual work expression, the stiffness matrix is derived. Then, a second method is presented to derive the exact shape functions, directly from the differential equations of the Timoshenko beam theory. The resulting shape functions are the same in both methods.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 683-697 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The convergence of stress maxima, computed directly from finite element solutions, is investigated with respect to a family of exact solutions characterized by varying degrees of smoothness. The performances of h- and p-extensions and the product and trunk spaces are evaluated and documented with respect to a family of benchmark problems. In uniform p-extensions a characteristic pattern in the convergence of stress maxima was observed. There does not appear to be a clear-cut advantage of the product space over the trunk space in this respect. The much faster convergence of stress maxima in the case of p-extensions, as compared with h-extensions, is evident from the results.
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  • 131
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    Communications in Numerical Methods in Engineering 10 (1994), S. 699-709 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Enhanced 8-node three-dimensional solid and 4-node shell elements are proposed in the paper. Improvement of the response of the 3-D solid is achieved through additional strains corresponding to generalized displacements incompatible between elements. In the case of the 4-node shell, the membrane behaviour is improved through addition of incompatible membrane strains.Some linear and geometrically non-linear examples demonstrate significant improvements of the elements. Results are compared with solutions obtained with the standard, displacement-based elements and with results available in the literature.
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  • 132
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    Communications in Numerical Methods in Engineering 10 (1994), S. 717-730 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Factorization procedures for the efficient solution of large sparse linear finite difference systems have been introduced recently. In these procedures the large sparse symmetric coefficient matrix of a certain structure is factorized exactly, yielding a direct solution method. Furthermore, approximate factorization procedures yeild implicit preconditioning iterative methods for the finite difference solution. The numerical implementation of these algorithms is presented and Fortran subroutines for the efficient solution of the resulting sparse symmetric linear system of algebraic equations are given.
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  • 133
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    Communications in Numerical Methods in Engineering 10 (1994), S. 731-734 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is well known that the finite element discretization with a distributed mass matrix gives overstimates of the natural frequencies of a system. The note shows that these do not necessarily become progressively worse as the frequency increases.
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  • 134
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    Communications in Numerical Methods in Engineering 10 (1994), S. 751-758 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Semi-discretization methods with iterated corrections are considered for solving the heat equation with boundary conditions containing integrals over the interior of the interval. The given problem is transformed into an ordinary differential system of equations, when we substitute the spatial derivative by finite differences. Such a system is then solved with an implicit integrator together with a quadrature method for the boundary integrals and, for each time step, the numerical scheme - implicit integrator and quadrature method - is repeated iteratively in order to achieve a given accuracy. The extra work we need with the iterated corrections enables us to take care of the interrelation of the solution u(x, t) at the interior and at the boundary points and also to start the numerical process with rough approximations of u(0, t) and u(1, t).An improvement of the results is achieved when we estimate the local spatial truncation error and make the injection of that estimation into the ordinary differential system. Numerical experiments are presented.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 735-742 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A technique is presented whereby numerical calculations of vibration modes can be improved. The paper looks at the classical two-dimensional wave equation using finite difference approximations. Analysis of the numerical dispersion of the approximations is used to develop a correction method. In general the numerical dispersion is dependent upon both the frequency and the direction of a wave, but if a 9-point formula is used the directional dependence is much reduced. This enables correction factors to be obtained using only the frequency of a vibration mode. The method was tested on the vibration of a square membrane and of an L-shaped region; in both cases a marked improvement in accuracy was obtained, at very little computational cost.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 773-783 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper describes a method for generating triangulations of two-dimensional domains. Firstly, a description is given of a reliable algorithm that creates a constrained Delaunay triangulation for a multiply-connected planer domain, without performing any explicit visibility computations. Then, several techniques to improve an existing triangulation are discussed. It turned out that a new variant of mesh relaxation was most effective in improving an existing triangulation. Several examples are included to illustrate the method's overall behaviour.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 785-790 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Second- and fourth-order-accurate spatial discretization methods give rise to discretization errors which are large than the corresponding subgrid terms in large eddy simulation of compressible shear layers in 2D, if the ratio between the filter width and the grid spacing is close to one. Even if an exact representation for the subgrid-scale contributions is assumed, large eddy simulation is accurate only if this ratio is sufficiently larger than one. In that regime fourth-order methods are more accurate than second-order methods. An analysis of the data obtained from two-dimensional direct numerical simulations of compressible shear layers substantiates these assertions.
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  • 138
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    Communications in Numerical Methods in Engineering 10 (1994), S. 763-771 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper considers the solution of the Fokker-Planck-Kolmogorov equation by the finite element method (FEM). The problem is set in a variational formulation suitable for the FEM. Some theoretical aspects related to applying the method are discussed. Discretization of the problem is carried out and questions of convergence and order of the method are also addressed. A numerical example is given to verify the validity of the approach.
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  • 139
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    Communications in Numerical Methods in Engineering 10 (1994), S. 791-797 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We present in this paper a nine-point, fourth-order difference scheme for the numerical solution of the quasilinear Poisson equation in polar co-ordinates, \documentclass{article}\pagestyle{empty}\begin{document}$$ Au_{rr} + \frac{1}{r}u_r + \frac{1}{{r^2 }}u_{\theta \theta } = f\left({r,\theta,u,u_{r,} u_\theta} \right) $$\end{document} with appropriate boundary conditions. A separate difference scheme of order four valid at r = 0 has also been obtained. The method is based on five evaluations of the function f. The numerical results of two problems obtained using this scheme are listed. The numerical results demonstrate the fourth-order accuracy of the scheme.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 809-814 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a probabilistic boundary element method for analysis of structural responses to static loading, when the shape parameters of structures are considered as random variables. We can use this method to evaluate the mean values and standard deviations of the responses, and estimate the stochastic errors of structural character resulting from manufacturing errors.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 815-825 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In the paper we address the problem of 2D adaptive quadrilateral mesh generation by using the variational principles. We first find the variational integral which generates the known grid system of curve-by-curve error equidistributions. We then use the same intergral to generate a new adaptive grid system which is superior to the known system in that the new system produces smoother meshes. Moreover, the new integral may be combined linearly with existing smoothness control integrals to yield more robust adaptive grid systems. Numerical results and comparisons are reported.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 799-808 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The diffraction of waves due to the presence of submerged objects in the ocean environment is solved by a relatively novel approach involving the direct boundary integration method (DBIM). Firstly, the method is tested for the case of a submerged circular cylinder and compared with the conventional boundary element method (BEM) results. The agreement between the results using this method and the BEM is good. Further, the DBIM has been applied to the case of a submerged horizontal plate for which the horizontal and vertical force coefficients are computed and compared with a semi-analytical solution using the matched eigenfunction expansion method (EFEM). It is found that the computed results using DBIM are in good agreement with those of EFEM and BEM. Further, the DBIM is found to be computationally more efficient than the BEM for the water wave diffraction problems presented in this paper.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 837-844 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A scheme is presented that automatically determines the magnitude of the time step in quasistatic boundary value problems discretized via some customary method (finite elements, finite differences). The basic idea stems from the path-following techniques widely employed in purely static analyses in the sense that the incremental displacements, measured in some suitable norm, are constrained to a prefixed value. Examples of trusses composed of a viscoelastic material are included to demonstrate the effectiveness of the method.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 827-835 
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    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The generalized integral transform technique is used to reduce eigenvalue problems described by partial differential equations to algebraic ones, that can be solved by existing codes for matrix eigensystem analysis. The method is illustrated for the operators that correspond to heat and mass diffusion, but can be employed in different fields. Three examples demonstrate the potential of the method.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 857-858 
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    Communications in Numerical Methods in Engineering 10 (1994), S. 859-860 
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    Communications in Numerical Methods in Engineering 10 (1994) 
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    Communications in Numerical Methods in Engineering 10 (1994), S. 845-856 
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    Topics: Mathematics , Technology
    Notes: Use of upwind finite element methods was so far confined to forced convection problems. The present work is devoted to the application of false diffusion techniques to phenomena involving natural convection. A range of Rayleigh numbers in which the discretization by the conventional Galerkin scheme fails is considered. A false diffusion method similar to the Streamline upwind technique has been employed to avoid cross-wind diffusion. The upwind parameter is changed continually until a true solution is obtained. The present scheme provides convenient means for obtaining gradually improved guesses from which a more accurate solution can be obtained using the conventional Galerkin method. The criterion for the determination of a true solution is established, and hot-wall Nusselt number values are documented in tabular form.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 869-878 
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    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An approach is presented for the formulation of the unilateral contact constraint in the presence of contact surface discontinuities. Such discontinuities may be due to physical corners on the surfaces of contacting bodies, or may be introduced by a discretization process (e.g. finite elements). It is asserted that a strong analogy exists between this problem and the one describing inelastic evolution in the presence of a discontinuous yield surface. This analogy is exploited to produce an effective treatment of the frictionless corner problem, complete with an effective augmented Lagrangian implementation for accurate constraint enforcement.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 861-867 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The paper deals with a B-type strain projection method with specific reference to axisymmetric incompressible solids. Essentially the \documentclass{article}\pagestyle{empty}\begin{document}$ \overline{\overline {\rm{B}}} $\end{document} (B double bar) method, which is reported in the present study, is based on Hughes' B-bar approach utilizing modified shape functions to represent the radial displacement and geometry. As a consequence of adopting these procedures the \documentclass{article}\pagestyle{empty}\begin{document}$ \overline{\overline {\rm{B}}} $\end{document} method results in an exact satisfaction of incompressibility constraints. The rationale of the \documentclass{article}\pagestyle{empty}\begin{document}$ \overline{\overline {\rm{B}}} $\end{document} method leads to the modified mean-dilatation approach for the case of an axisymmetric incompressible problem. It is interesting to note in the present work that the explicit influence of enhanced hoop strain is eliminated from the discrete divergence condition.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 879-893 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An interface finite element for non-linear analysis of frictionless contact problems is presented. A constitutive equation relates stresses in the interface layer to the deformation gradient with respect to an imaginary reference configuration where the layer thickness is constant and finite. The equation of equilibrium is written in the same configuration, while the boundary conditions involve stresses related to an actual reference configuration used in the formulation for the contacting bodies. Finite element discretization is introduced for the layer in order to calculate the unknown field of displacements. Computational examples demonstrate properties of the contact element and its range of applicability in the analysis of large deformation contact problems including relative sliding of curved surfaces.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 895-906 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents boundary integral equation to two-dimensional elasticity with the stress component σijtitj as one of the boundary values, where ti are direction cosines of the tangent on the boundary. This form of BEM has an advantage in that the stress component σijtitj on the boundary can be calculated directly from the numerical solution. The present formulation for planar problems uses two kernels, one of which is logarithmic singular and the other is 1/r singular. The effectiveness of the approach is also discussed through some test examples.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 907-911 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A finite difference scheme is derived to solve for the probability density that a moving point, whose velocity is continually pertubed by Gaussian white noise, reaches a given target within a given time period. The numerical scheme is applied to the problem of finding the probability that two moving spheres collide.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 943-948 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A sixth-order and a ninth-order method are developed for the numerical solution of special non-linear third-order boundary value problems y‴ = ø(x,y), a〈 x 〈 b, y(a) = A1, y″(a) = B2 and y(b) = A2. The method arise from a four-point recurrence relation. Convergence analysis of the sixth-order method is discussed. The methods are tested on a problem. Modification to these methods are obtained for problems with boundary conditions of the form y(a) = A1, y'(a) = B1 and y(b) = A2.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 927-931 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Numerical viscosities of finite-difference schemes are usually obtained from truncation-error analyses based on Taylor series expansions. Here we observe that numerical viscosities can also be obtained very simply and directly from the growth factor ξ in a conventional Fourier stability analysis. A general formula is derived for the numerical viscosity in terms of the first and second derivatives of ξ with respect to the wavenumber k, evaluated at k = 0. A single Fourier analysis therefore suffices to determine both stability limits and numerical viscosities.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 913-926 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Based on the concept of the Laplacian matrix of a graph, this paper presents the SGPD (spectral graph pseudoperipheral and pseudodiameter) algorithm for finding a pseudoperipheral vertex or the end-points of a pseudodiameter in a graph. This algorithm is compared with the ones by Grimes et al. (1990), George and Liu (1979), and Gibbs et al. (1976). Numerical results from a collection of benchmark test problems show the effectiveness of the proposed algorithm. Moreover, it is shown that this algorithm can be efficiently used in conjunction with heuristic algorithms for ordering sparse matrix equations. Such heuristic algorithms, of course, must be the ones which use the pseudoperipheral vertex or pseudodiameter concepts.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 933-941 
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    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element program is developed as a tool to analyse shells of revolution with local non-linearities. In reality, shells of revolution often exhibit local deviations, like a cut-out, a junction and/or an imperfection. The stress concentration around a local deviation may produce plasticity and/or geometric non-linearities in the surrounding region. The analytical model consists of three different types of elements: rotational, transitional and general. The rotational shell elements are used in the region where the shell is axisymmetrical and linear, while the two-dimensional general shell elements are deployed in the deviation region where non-linearities may occur. Transitional shell elements connect the two distinctively different types of elements to achieve displacement field continuities. The solution using the local-global system with appropriate condensation and a predicted stress incremental procedure is suggested. It is shown that the technique is a very attractive alternative to the entirely general element style analysis for axisymetric shell structures with local deviations.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 949-953 
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    Communications in Numerical Methods in Engineering 10 (1994), S. 955-956 
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    Communications in Numerical Methods in Engineering 10 (1994), S. 957-959 
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    Communications in Numerical Methods in Engineering 10 (1994), S. 961-970 
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    Notes: New developments of describing the theoretical basis towards an effective virtual-pulse (VIP) time integral methodology are proposed for general non-linear transient heat transfer problems. Primarily to validate the proposed methodology of computation, simple numerical test cases are provided and comparisons are also drawn with the implicit second-order-accurate Crank-Nicolson method. For the models tested, the proposed method has comparable or improved accuracy and stability characteristics. The VIP methodology introduced here for tackling non-linear thermal problems offers attractive features and is a viable alternative to traditional time-stepping practices. Efforts are underway to demonstrate the practical applicability to multi-dimensional thermal analysis.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 983-992 
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    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper describes an optimized computational implementation of a basic ‘building block’ for non-linear structural dynamic analysis programs: the combination of the modified Newton-Raphson iterative technique with an implicit time integration operator (in this case a member of the Newmark family), working in an incremental--iterative formulation for the equations of motion. The objective of this implementation is to attain improved computational efficiency, regarding both CPU time and memory requirements. The basic formulation and derivation are presented, along with the implementation details; the positive aspects related to the computational optimization are highlighted.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 1005-1012 
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    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A mixed variational principle is presented for the geometrically linear micropolar continuum. Then a suitable discretization and its implementation are discussed, resulting in an improved element behaviour for micropolar localization analysis. The intriguing element performance is demonstrated for the case of localization within a compression problem.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 971-981 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element models based on discrete-layer theories are presented for the coupled-field analysis of laminated plates containing piezoelectric layers. The three displacements and the electrostatic potential are treated as unknowns in this formulation, which allows for piece-wise approximations of the variables through the thickness of each layer. Two specific models are demonstrated in which the transverse displacement is either variable or constant, and the in-plane displacements and potential take piece-wise linear approximations through the thickness. The models are applied to example problems with applied surface tractions and specified surface potentials. Good agreement is found with exact solutions.
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  • 166
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    Communications in Numerical Methods in Engineering 10 (1994), S. 993-1003 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: On the basis of simple one-dimensional finite element analyses, comparison in simulations of uniaxial tension using explicit dynamic and implicit static tonnulations has been made. Results show that for materials having a Hollomon-type constitutive law with power-law strain rate sensitivity, the explicit dynamic method can be employed for the quasistatic simulations of tensile tests only below the critical test velocities or critical normalized material densities. These critical values are determined numerically as a function of material parameters.
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  • 167
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    Communications in Numerical Methods in Engineering 10 (1994), S. 1013-1020 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new type of B3-spline interpolation is presented. This new formulation allows the user to introduce interior point and line supports in much the same way as in a conventional finite element formulation. The bandedness and efficiency of the standard B3-spline interpolation are retained. The new formulation can be incorporated into existing B3-spline formulations with very little effort. Several examples are presented to demonstrate the versatility of the new approach.
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  • 168
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    Communications in Numerical Methods in Engineering 10 (1994), S. 1045-1046 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 169
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    Communications in Numerical Methods in Engineering 10 (1994), S. 1047-1048 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 170
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    Communications in Numerical Methods in Engineering 10 (1994), S. 1021-1025 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A comparison is made of implementations of consistent tangent operators that arise in implicit integration of Von Mises and Drucker-Prager yield criteria. When computing the consistent tangent operator a matrix inversion has to be performed at integration point level. The consequences of different formulations of the consistent tangent operator on the numerical accuracy are assessed.
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  • 171
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    Communications in Numerical Methods in Engineering 10 (1994), S. 1027-1043 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper describes a procedure to generate boundary characteristic orthogonal polynomials (BCOPs) over a domain in Rn. The method is based upon the Gram-Schmidt process of orthogonalization. The orthogonal polynomial sequence (OPS) is generated from a set of linearly independent functions which satisfy the given boundary conditions. The procedure is illustrated by taking several examples in R2, the most important case from the application point of view. Extensive numerical work has been carried out for simple domains like the circle, square and isosceles right-angled triangle. The following cases have been considered: (a) when the BCOPs vanish on the boundary; (b) when they and their normal derivatives vanish on the boundary; (c) when no conditions have been imposed on the boundary. The results for other geometries such as an ellipse, a parallelogram and an arbitrary triangle follow by some simple transformations. The procedure is also applicable to one-dimensional problems and can be easily extended to R3.
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  • 172
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    Journal of Physical Organic Chemistry 7 (1994), S. 63-67 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The relative basicities of six monosubstituted dipolar trimethylamines (XCH2NMe2) were determined in nine different solvents from potentiometric titration. Solvation effects on basicity variations were analyzed by the solvatochromic parameters (π*, α and β). Non-specific solvation of the substituted dimethylammonium ions is not reflected adequately by the solvent's dipolarity-polarizability constant, π*. A better representation of non-specific interaction between solvents and the monosubstituted dipolar trimethylammonium ions is gained from the product of π* and the solvent dipole moment (μ). For these ions where the dipolar substituents are separated from the reaction center by one methylene unit, there is an interaction between the charge of the ammonium ion and the dipolar substituent. As a result, solvent molecules must not only solvate the dipolar substituents, but must also gain access between the lines of force of the dipolar substituent and the charge. Bulky solvents, such as nitrobenzene, cannot access adequately the region between the dipolar substituents and the reaction center to accomplish similar solvation as less bulky solvents.
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  • 173
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    Journal of Physical Organic Chemistry 7 (1994), S. 80-89 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Measured pseudo-first-order rate constants for intramolecular formation of tetrahedral intermediates from N-2-hydroxyethylphthalimide, N-2-aminoethylphthalimide and N-2-thioethylphthalimide at pH 〉 6 are reported. The reaction is specific and general base catalysed, with β(Brønsted) values 0·44, 0·52 and 0·52 respectively. From a plot of log kb (general base rate constants) vs γ′ [the affinities of EtXH (X = O, NH, S) toward the carbonylic carbon], β′nuc values of 0·01 (with OH- as specific base), 0·25 (with imdidazole as general base) and 0·27 (with HPO42- as general base were obtained). The observed relationships pxy = ϑβ′/ - ϑpKa = -ϑ(Brønsted)/ϑγ′ = 0·03 is supported by the predictions of an energy contour diagram, which, on extrapolation to a non-stable tetrahedral intermediate, predicts a late and slightly protonated transition state for the cleavage process. At pH 〈 3, these intermediates cleave to yield only the corresponding diacylimides. These reactions are general base and acid catalysed with β 〉 0·3 and α 〈 0·1. A fast equilibrium between the intermediate and its N-protonated (amide) form is reached. The general base rupture of the latter is faster than that of the corresponding non-protonated intermediate by a factor of ca 109 - 1010-fold.
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  • 174
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    Journal of Physical Organic Chemistry 7 (1994), S. 96-104 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A rigorous procedure was developed for measuring the relative rates of addition of bromine atoms to eleven substituted α-methylstyrenes (1-Y, with Y = CF3, NO2, F, CN, Cl, Br, CO2Me, Me, COMe, OMe and SMe). The reaction was run in tetrahydrofuran in the presence of HBr, O2 and dibutyl peroxyoxalate at 30°C. All products were derived from the YC6H4CMeCH2Br adduct radicals, which were immediately intercepted by O2. Correlation analysis of all the data confirmed the proposition that in the absence of measurable steric effects, the relative rates for radical additions can be correlated only by a dual-parameter equation and not by a single-parameter equation. Among various combinations of σ* and σx, the (σJJ* + σmb) combination yields the best correlation.
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  • 175
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    Journal of Physical Organic Chemistry 7 (1994), S. 90-95 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Transfer of the cobalt-bound methyl in MeCo(III)Pc to thiophenoxide ion was studied (H2Pc is the planar macrocyclic phthalocyanine; the cobalt is held in the center in this plane). In dimethylacetamide solution, the reaction is rapid, requiring stopped flow for the kinetics, and yielding MeSPh and Co(I)Pc- in good yield. The kinetics are not simple second order, but instead approach a constant rate at high [PhS-], attributed to the reversible formation of an inert complex with PhS- occupying the vacant octahedral site in MeCo(III)Pc, on the other side of the phthalocyanine plane from the methyl group. The kinetics allow the estimation of the equilibrium constant, K, and the SN2 rate constant, k, which at 25°C have values of ca. 9·4 × 103 l mol-1 and 1·8 × 104 l mol-1, respectively. Although these values are rough, the ratio k/K is firm at 1·91 ± 0·02 s-1; this is the limit of the rate at high [PhS-]. An alternative mechanism, which is entirely consistent with the kinetics, involves a rate-determining homolysis of the Co—S bond of the same complex. The mechanism is not favored because the product yields are high for a radical combination process and alternative chain processes are kinetically unacceptable. Further, the rate constant is about what would be expected from the reactivity of other nucleophiles in SN2 reactions. Further arguments in favor of the SN2 mechanism are presented. This transfer of the methyl group from Co to S is part of the possible analogy to the vitamin B12-promoted methionine synthesis in nature. The other step in the biological, enzymatic process is the transfer of methyl from the nitrogen of N-methyltetrahydrofolate to cobalt. An attempt to model this with the very reactive N-methyl-2,6-dichloropyridinium ion was unsuccessful; the reaction took an entirely different course, presumably initiated by electron transfer, but leading to substantial loss of Cl- from the pyridine. No more than 0.5% methyl transfer took place. This system does mimic well the complete natural enzymatic process.
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  • 176
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    Journal of Physical Organic Chemistry 7 (1994), S. 116-116 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
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  • 177
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    Journal of Physical Organic Chemistry 7 (1994) 
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    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 178
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    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Protonation of tetrafluoro-2,11-dithia [3·3]paracyclophane and tetrafluoro-2,11-dithia [3·3]metaparacyclophane in high-acidity super acid media, namely FSO3H.SbF5 (1:1) ‘magic acid’-SO2CIF, gave their corresponding acidic disulfonium ions. Additional ring protonation to give a disulfonium-monoarenium trication was not observed. With the non-fluorinated 2,11-dithia [3·3] cyclophanes, the disulfonium ions can be ring protonated in equilibrium to give a dynamic disulfonium-monoarenium trication. Tetrafluoro [2·2]-metaparacyclophane is monoprotonated at the meta ring and gives a complex mixture of conformational isomers. Multinuclear magnetic resonance data on the cyclophane precursors and their derived cations are compared and analysed. The energies, conformations and charge distributions of the isometric fluorinated and non-fluorinated [2·2] - and dithia [3·3] cyclophanes were calculated by the AM1 and PM3 methods, respectively. In all but one case the cyclophane arenium ions predicted by theory to be energetically most favoured are those observed in solution under stable ion conditions. In agreement with experiment, the instabilities of S,S,C-cyclophane trications are also theoretically predicted.
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  • 179
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    Journal of Physical Organic Chemistry 7 (1994), S. I 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 180
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    Journal of Physical Organic Chemistry 7 (1994), S. 117-121 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The kinetics of oxidation of metol (N-methyl-p-aminophenol) by thallium(III) have been studied in a perchloric acid medium. This organic compound is employed extensively in photographic work. The stoichiometry of the reaction is represented by: C6H4(OH)NHCH3 + TIIII → C6H4(O)NCH3 + TII + 2H+The kinetics indicate the rate law: \documentclass{article}\pagestyle{empty}\begin{document}$$k' = \frac{{Kk\left[{metal} \right]}}{{1 + K\left[{metal} \right]}}$$\end{document} where k′ is the pseudo-first-order rate constant. The rate constants and thermodynamic parameters for the rate-limiting step have been evaluated.
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  • 181
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    Journal of Physical Organic Chemistry 7 (1994), S. 178-180 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The volumes of activation and of reaction were measured for the reaction between sulphur dioxide and 2,3-dimethylbuta-1,3-diene to form 3,4-dimethylsulpholene. Values of ΔV and ΔV* are -33 and -35 cm3 mol-1, respectively in accordance with a concerted reaction having a very product-like transition state.
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  • 182
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    Journal of Physical Organic Chemistry 7 (1994), S. 192-195 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The secondary α-deuterium isotpe effect on the equiliburium constant (KD/KH) for the hydration of p-nitrobenzaldehyde is 1·39 ± 0·05. The Kinetic secondary α-deuterium isotope effect (KD/KH) for the addition of water to p-nitrobenzaldehyde is 1·18 ± 0·07. This result demonstrates that there is extensive carbon-oxygen bond formation in the transition state for addition of water to the carbonyl group of p-nitrobezaldehyde.
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  • 183
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    Journal of Physical Organic Chemistry 7 (1994) 
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    Keywords: Organic Chemistry ; Physical Chemistry
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  • 184
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    Journal of Physical Organic Chemistry 7 (1994), S. 218-220 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: In the hydride transfer of Leuco Crystal Violet to form the Crystal Violet, cation, the role of cyanomethylene acceptors was found to be essentially different from that of p-benzoquinones, both previously believed to act as π-acceptors in the same manner.
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  • 185
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    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: In constrast with recent molecular orbital calculations on the decarboxylation of O-protonated 2-oxetanone, this experimental work indicates that no decarboxylation of this cation occurs in sulphuric acid solution up to 150°C, but instead a clean isomerization to protonated acrylic acid takes place. Parallel theoretical work shows that the gas-phase model is too crude to account successfully for the experimental facts obtained in acidic media. However, the latter are well reproduced when the effect of the solvent is taken into account. The present findings do not necessarily invalidate the reaction mechanism currently accepted to explain the rate enhancement and change of stereochemistry accompanying the decarboxylation of 3,4-disubstituted 2-oxetanones under acid catalysis.
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  • 186
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    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The enol-keto tautomerism of the Schiff bases formed by pyridoxal 5'-phosphate (PLP) with ethylenediamine (Etd) and ethylamine (Et) was studied by electrochemical and spectrophotometric methods. The spectroscopic results revealed differences between the two reactions, i.e. the enolimine/ketoenamine ratio observed in PLP-Etd mixture is higher than that of PLP-Et. The differences observed in the electroreduction mechanism and stability of the Schiff bases formed provide additional evidence for an unusually high concentration of enolimine in PLP-Etd in buffered aqueous solutions.The results are consistent with a cyclic structure such as that previously proposed by Robitaille et al. [J. Am. Chem. Soc. 111, 3034-3047 (1989)] on the basis of spectroscopic data. Protonation of the terminal amino group of the Etd moiety in the Schiff base involves the formation of the cyclic species. The low basicity of ethylenediamine favours the formation of similar concentrations of the enol and keto tautomers of the Schiff base at neutral pH. This behaviour, also observed in the Schiff base formed by PLP and polylysine, may be involved in coenzyme-protein linkages.
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  • 187
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    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: 2,2-Dimethyl-1-(p-methoxyphenyl)propyl p-nitrobenzoate (ROPNB) was subjected to solvolysis in phenol in the presence of tetrabutylammonium [carboxy-13C]-p-nitrobenzoate, in which the ‘common ion rate depression’ was confirmed to arise at the stage of the second ion-pair intermediate (Int-2). The unchanged substrate recovered at 46% reaction contained the isotopically labelled leaving group, indicating the occurrence of common ion exchange to the extent of 41-46%. In the solvolysis of the optically active substrate under identical conditions, the unchanged substrate was recovered with 51·4% racemization and ROPh was produced with slightly (1·56%) retained configuration, similarly to the solvolysis in the absence of the common ion salt. These isotope-tracer and stereochemical outcomes indicate that the common ion exchange in this solvolysis system should be attributable to the retentive nucleophilic attack on Int-2 by the common ion salt via a quadrupole (four-centre ion pair) transition state, accompanying the common ion rate depression, and they suggest that the special salt effect also should proceed by an analogous anion-exchange mechanism to that for the common ion effects.
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  • 188
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    Journal of Physical Organic Chemistry 7 (1994), S. 256-258 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The relative thermodynamic stabilities of 2-propenylbenzene (allylbenzene), and the E and Z forms of 1-propenylbenzene were determined over the temperature range 50-170°C by chemical equilibration in DMSO solution with t-BuOK as catalyst. The values of the thermodynamic parameters ΔG⊖, ΔH⊖ and ΔS⊖ at 298·15 K for each isomerization reaction between the title compounds were evaluated.
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  • 189
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    Journal of Physical Organic Chemistry 7 (1994), S. 309-315 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The hydride transfer reactions of 4,4′-bis(dimethylaminophenyl)methane (Michler's hydride) with p-benzoquinones were studied. The rate of formation of Michler's Hydrol Blue was followed spectrophotometrically. The second-order rate constants and the activation parameters were estimated. The formation of a charge-transfer complex was observed at low temperatures. Stable and unstable paramagnetic species formed during the reactions were assigned by ESR spectroscopy. The observed kinetic behaviour and the stoichiometry were in line with those previously obtained for the systems involving Leuco Crystal Violet, Leuco Malachite Green and Leuco Bindschedler's Green. Hence the reaction is considered to proceed according to the so-far accepted multi-step mechanism. However, when tetracyano-p-quinodimethane or tetracyanoethylene was used as a π-acceptor, a comparatively stable radical ion pair was formed as a result of a one-electron transfer, followed by the gradual formation of Michler's Hydrol Blue. The kinetic behaviour and the stoichiometry of the reaction were examined, together with the enhanced kinetic effects of added triethylamine. A modified mechanism for these systems is proposed. The role of cyanomethylenes was found to be essentially different from that of p-benzoquinones, and therefore π-acceptors are divided into two groups of cyanomethylenes and p-benzoquinones.
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  • 190
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    Journal of Physical Organic Chemistry 7 (1994), S. 316-322 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Rates of hydrolysis of the vinyl ether functional groups of (Z)- and (E)-β-methoxyacrylic acid and (Z)-and (E)-β-methoxymethacrylic acid and their methyl esters were measured in aqueous perchloric acid solution. Additional rate measurements were also made for one substrate, (Z)-β-methoxymethacrylic acid, in buffer solutions down to pH 7, and a rate profile was constructed. The results show that the β-carboxy and β-carbomethoxy substituents produce strong rate retardations, ranging from 2000- to 25 000-fold, for both Z- and E-isomers in both the acrylic and methacrylic acid series. The rate profile for (Z)-β-methoxymethacrylic acid indicates that ionization of this substrate to the carboxylate ion form rises the rate of hydrolysis by a factor of 240. It is argued that this difference in reactivity of ionized and non-ionized forms of the substrate is due to conjugative and inductive effects of the substituents, rather than β-lactone formation as suggested in an earlier observation of the same phenomenon in a different system.
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  • 191
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    Keywords: Organic Chemistry ; Physical Chemistry
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  • 192
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    Journal of Physical Organic Chemistry 7 (1994), S. ii 
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    Keywords: Organic Chemistry ; Physical Chemistry
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  • 193
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    Journal of Physical Organic Chemistry 7 (1994), S. 325-351 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Aromatic nitration is effectively carried out by the deliberate irradiation of the charge-transfer absorption band (hvCT) of the transient electron donor-acceptor complex [ArH, NO2Y+], where NO2Y+ represents common nitrating agents. Time-resolved spectroscopy demonstrates that the charge-transfer nitration effected in this way proceeds via an electron-transfer mechanism, in which the collapse of the reactive triad, [ArH+ ·, NO2·, Y] is critical to the formation of the Wheland intermediate. Comparative product analyses of toluene and anisole nitrations together with the ‘non-conventional’ products arising from NO+ catalysis, ipso attack and addition/elimination show that the activation process leading to charge-transfer (photochemical) nitration is indistinguishable from that leading to electrophilic (thermal) aromatic nitration.
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  • 194
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    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The stereochemistry and kinetics of the methoxide ion substitution reactions (Z)- and (E)-methylbenzohydroximoyl cyanidc [PhC(CN)=NOCH3] were investigated. The reaction of the (Z)-hydroximoyl cyanide with sodium methoxide in DMSO-methanol (9:1) solution at 44·8°C gives a mixture of methyl (Z)-O-methylbenzohydroximate [PhC(OCH3)=NOCH3] and the O-methyloxime of α-ketophenylacetamide PhC(CONH2)=NOCH3. The (E)-hydroximoyl cyanide undergoes methoxide ion-catalyzed isomerization to the E-isomer faster than it undergoes nucleophilic substitution. These observations were interpreted in terms of an addition-elimination mechanism in which the rate-limiting step is elimination of the nucleofuge (AN + DN#).
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    Journal of Physical Organic Chemistry 7 (1994), S. 359-363 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Nucleophilic substitution reactions of 1-(trimethylsilyl)ethyl arenesulphonates with anilines and benzylamines in acetonitrile and methanol at 65·0°C were studied. The cross-interaction constants, ρXZ, between substituents in the nucleophile (X) and leaving group (Z) are relatively small (0·10 for XC6H4NH2 in MeCN) but similar to those for other SN2 processes at a secondary carbon atom. This provides further evidence for an approximately constant, loose SN2 transition state at a secondary carbon regardless of the size of the Cα substituent. The transition-state variations with substituents X and Z are in accord with that expected from the positive ρXZ value observed: a stronger nucleophile and/or nucleofuge leads to an earlier transition state, i.e. a lower degree of bond making and breaking.
    Additional Material: 3 Tab.
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  • 196
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 7 (1994), S. 420-430 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The MM3 force field has been extended to cover alkyl iodides. Structures, vibrational spectra and heats of formation have been well fitted to available experimental data. The experimental and ab initio conformational relationships are also satisfactorily reproduced.
    Additional Material: 2 Ill.
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  • 197
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 7 (1994), S. 431-436 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Imidazole (Imz)-catalysed hydrolysis of benzoate esters proceeds via the intermediate formation of N-benzoylimidazoles. This paper considers the second step of this reaction, viz., Imz-catalysed hydrolysis of N-(4-X-benzoyl)imidazoles, X = CH3, H, Cl, CN and NO2, and N-(disubstituted benzoyl)imidazoles, 2-chloro-4-nitro, 2, 4-dinitro and 3,5-dinitro, in water-acetonitrile mixtures (10% or 14%, v/v, in organic solvent). On the basis of catalytic rate constants and the kinetic solvent isotope effect, it is shown that catalysis by Imz is of the general-base type. Unexpectedly, the hydrolysis of N-(2,4-dinitrobenzoyl)imidazole was found to be slower than that of N-(4-nitrobenzoyl)imidazole. It is shown that this reactivity order is due to a combination of a steric effect and stabilization of the reactant state due to a donor-acceptor interaction between the Imz moiety and the 2,4-dinitrophenyl ring.
    Additional Material: 2 Tab.
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  • 198
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The critical micelle concentration of solutions of cetyltrimethylammonium bromide and of tetradecyltrimethylammonium bromides were determined by a kinetic method. This involved the determination of the rates of the hydroxydehalogenation of some activated aromatic substrates over a wide range of detergent concentrations. Measurements were made in solutions containing significant quantities of added hydroxyl ion and substrates which were themselves amphiphilic. Conventional methods cannot be applied with confidence to such systems. The effects of changing hydroxyl ion concentrations, added sodium bromide, changing the nature of the aromatic substrate (whether neutral or charged), the identity of the micellar counterion and the temperature were investigated. It was wound that added bromide or hydroxyl ions resulted in a lower CMC whereas increased temperature led to an increase in the CMC. The nature of the micellar counterion (Br, F, OH, SO4) had little effect on the CMC. The presence of a charged aromatic substrate led to a considerable lowering of the CMC, whereas the neutral aromatic substrate used showed very little effect.
    Additional Material: 5 Tab.
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  • 199
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 7 (1994), S. 555-560 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Kinetic studies on the reversible reactions of benzyl bromides with N, N-dimethylanilines were carried out for both the forward (kf) and reverse (kr) directions. The equilibrium constants, K were calculated using the ratio kf/kr and the equilibrium cross-interaction constant, ρeXY was determined. The ρeXY value was shown to represent a maximum intensity of interactions between substituents X and Y through covalent bonds within a molecule. The normalized values of ρX (ρnuc) and ρXY indicate that in the transition state the fractional development or loss of polar and resonance interactions in the benzyl system are imbalanced or non-perfectly synchronized. In the forward reaction the fractional loss of resonance interaction becomes enhanced, whereas in the reverse reaction the fractional development of resonance interaction lags behind the corresponding changes of polar interactions by ca 45%.
    Additional Material: 1 Ill.
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  • 200
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 7 (1994), S. 578-584 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The acid-catalysed solvolysis of 9-(2-phenoxy-2-propyl)fluorene in mixtures of water with acetonitrile or methanol at 25°C provides 9-(2-hydroxy-2-propyl)fluorene, 9-(2-propenyl)fluorene, and 9-(2-acetamido-2-propyl)fluorene or 9-(2-methoxy-2-propyl)fluorene, respectively. The overall kinetic deuterium isotope effects for the reactions of the hexadeuterated analogue 9-(1,1,1,3,3,3-2H6)-9-(2-phenoxy-2-propyl)fluorene in 90 vol.% acetonitrile in water were measured as (kEH + kSH)/(kED6 + kSD6) = 1·54 ± 0·05, which is composed of the isotope effect kSH/kSD6 = 1·4 ± 0·1 for formation of the substitution products and kEH/kED6 = 4·0 ± 0·2 for production of 9-(2-methoxy-2-propyl)fluorene. Similar isotope effects were measured in other solvent mixtures. The results strongly indicate a branched mechanism involving rate-limiting formation of a common carbocation-molecule pair (with a secondary isotope effect of 1·54), which either undergoes nucleophilic attack by a solvent molecule (with a secondary isotope effect of ca 1), or is dehydronated (isotope effect ca 2·8) by the leaving group or by the solvent. The ion-molecule pair shows very low selectivities. Thus, in 50 vol.% acetonitrile in water, an acetonitrile molecule is as efficient as a water molecule as a nucleophile towards the ion-molecule pair, kMeCN/kHOH ≥ 1 (ratio of second-order rate constants). The discrimination between methanol and water is anomalously small, kMeOH/kHOH = 0·7.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
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