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  • 101
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 413-424 
    ISSN: 1069-8299
    Keywords: boundary integral equation ; necessary and sufficient condition ; plane elasticity problem ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: With respect to a given boundary value problem, the corresponding conventional boundary integral equation is shown to yield non-equivalent solutions, which are dependent upon Poisson's ratio and geometry. In the paper a systematic method for establishing a necessary and sufficient boundary integral formulation has been proposed for two-dimensional elastostatic problems. Numerical analyses show that the conventional boundary integral equation yields incorrect results when the scale in the fundamental solution approaches a degenerate scale value. However, the results of the necessary and sufficient boundary integral equation are in good agreement with analytical solutions of the boundary value problem.
    Additional Material: 8 Ill.
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  • 102
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 519-520 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 103
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996) 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 104
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 433-444 
    ISSN: 1069-8299
    Keywords: two-phase flow ; solute transport ; interphase exchange ; porous media ; finite element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The development of a numerical method for modelling two-phase flows and solute transport, particularly with interphase exchange in porous media, is presented. The governing equations are derived to describe two immiscible and compressible fluids flows such as water-air and two-phase solute transport with interphase exchange. Technically, the standard finite element method and a strongly implicit procedure are employed to solve the fully coupled governing equations. Pressures of two-phase fluids and solute concentrations in two-phase fluids are taken as the primary unknown variables, and the discretized equations are solved by a direct type of solver. Application examples are shown to confirm the applicability of the numerical method.
    Additional Material: 9 Ill.
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  • 105
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 447-454 
    ISSN: 1069-8299
    Keywords: inviscid drops ; coalescence ; boundary element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method is used to simulate the motion of inviscid drops colliding and coalescing at a solid surface. The equations of motion are solved by a boundary element method in which the free surface of the drop is represented by a moving grid. The numerical results include the configuration of the drop during coalescence and the kinetic and potential energies. A numerical example is used to demonstrate the way in which coalescence affects the configuration of the free surface.
    Additional Material: 3 Ill.
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  • 106
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 455-459 
    ISSN: 1069-8299
    Keywords: harmonic differential quadrature method ; computational complexity ; differential quadrature ; numerical method ; centrosymmetric matrix ; computational mechanics ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The structure of weighting coefficient matrices of harmonic differential quadrature (HDQ) is found to be either centrosymmetric or skew centrosymmetric, depending on the order of the corresponding derivatives. The properties of both matrices are briefly discussed in the paper. It is noted that the computational effort of the harmonic quadrature for some problems can be further reduced by up to 75 per cent by using the properties of the above-mentioned matrices.
    Additional Material: 1 Tab.
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  • 107
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 471-482 
    ISSN: 1069-8299
    Keywords: numerical methods ; constitutive equations ; composite ; mixing formulation ; anisotropic elastoplastic model ; mapping stress tensor space ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general constitutive model adequate for analysis of the thermomechanical response of composite materials is presented. The model is based on the mixture of the basic substances of the composite and allows the evaluation of the interdependence between the constitutive behaviour of different compounding materials. The behaviour of the each compound is modelled by a general anisotropic thermo-elasto-plastic model, termed the ‘base model’. The different base models for each compound are combined using mixing theory to simulate the behaviour of the multiphase material.
    Additional Material: 7 Ill.
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  • 108
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 483-495 
    ISSN: 1069-8299
    Keywords: finite element method ; solid modelling ; optimal interpolation ; a posteriori error estimation ; adaptive interpolation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem of approximating functions is considered in a general domain in one and two dimensions using piecewise polynomial interpolation. An error estimator is proposed which shows how to adaptively determine the interpolation degree. Numerical examples are given.
    Additional Material: 1 Ill.
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  • 109
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 461-470 
    ISSN: 1069-8299
    Keywords: linear polyhedra ; symbolic integration ; polynomial functions ; monomials ; tetrahedron ; hexahedron ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper concerns analytical integration of polynomial functions over linear polyhedra in three-dimensional space. To the authors' knowledge this is a first presentation of the analytical integration of monomials over a tetrahedral solid in 3D space. A linear polyhedron can be obtained by decomposing it into a set of solid tetrahedrons, but the division of a linear polyhedral solid in 3D space into tetrahedra sometimes presents difficulties of visualization and could easily lead to errors in nodal numbering, etc We have taken this into account and also the linearity property of integration to derive a symbolic integration formula for linear hexahedra in 3D space. We have also used yet another fact that a hexahedron could be built up in two, and only two, distinct ways from five tetrahedral shaped elements These symbolic integration formulas are then followed by an illustrative numerical example for a rectangular prism element, which clearly verifies the formulas derived for the tetrahedron and hexahedron elements.
    Additional Material: 5 Ill.
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  • 110
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 497-505 
    ISSN: 1069-8299
    Keywords: weight function approach ; edge crack problem ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A fundamental field for the edge crack problem is suggested, and the field is composed of the singular displacement field and the complementary regular field. The boundary displacement of the fundamental field plays the role of the weight function in the edge crack problem. After multiplying the boundary traction in the physical problem with the weight function and performing integration along the boundary, the stress intensity factor at the crack tip is obtainable. Numerical examples are given to demonstrate the use of the suggested weight function approach.
    Additional Material: 5 Ill.
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  • 111
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 543-555 
    ISSN: 1069-8299
    Keywords: control volume method ; finite element interpolation ; fluid flow ; upwind schemes ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Together with the finite element method (FEM), the control volume method (CVM) is of particular interest for the numerical solution of partial differential equations. The accuracy of computation of the CVM almost matches that of FEM in contour-adapted co-ordinates or block-structured meshes of a single element type. The CVM is superior to the FEM in terms of physical interpretation and ease of handling. The paper presents an interpretation of the FEM that allows it to be treated like a CVM. This formal CVM, which is based on FEM techniques, combines the advantages of both methods. The method is applied to the discretization of the Navier-Stokes equation.
    Additional Material: 12 Ill.
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  • 112
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 557-568 
    ISSN: 1069-8299
    Keywords: hyperbolic equations ; finite-difference methods ; Padé approximants ; sequential and parallel implementation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Techniques for two-time level difference schemes are presented for the numerical solution of first-order hyperbolic partial differential equations. The space derivative is approximated by (i) a low-order, and (ii) a higher-order backward difference replacement, resulting in a system of first-order ordinary differential equations, the solutions of which satisfy recurrence relations. The methods are obtained from the recurrence relations and are tested on three linear problems and one non-linear problem from the literature.
    Additional Material: 7 Tab.
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  • 113
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 507-517 
    ISSN: 1069-8299
    Keywords: non-linear constitutive model ; anisotropy ; finite strains ; axisymmetrical finite elements ; vascular biomechanics ; soft tissue biomechanics ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: To explore the mechanical non-linear behaviour of anisotropic arterial walls on a computational basis, the formulation of a continuum based elastic potential is a major task and challenge to the analyst. The present communication is concerned with the constitutive modelling and numerical analysis of vascular segments covering finite strains. Special attention is paid to a two term potential that constitutes an essential foundation for accurate simulation within the entire strain domain. Axisymmetrical membrane elements are assembled to match the geometry of blood vessels. Numerical results confirm the theoretical approach by referring to experimental data of different rat arteries.
    Additional Material: 6 Ill.
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  • 114
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 569-579 
    ISSN: 1069-8299
    Keywords: frictional contact ; large deformation ; one-pass approach ; master segment ; slave node ; contact constraint ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the context of large deformation analysis for metal forming processes a new one-pass approach for the frictional contact is proposed. This approach eliminates the short comings of traditional one-pass and two-pass approaches both from the constraint requirement and solution convergence points of view. Implemented in an updated Lagrangian framework with the Perturbed Lagrangian formulation of Ju and Taylor for non-linear frictional contact, a patch test and typical examples have been worked out to prove the validity of the proposed approach. It is observed that a finer surface discretization of the slave and master surfaces is no longer needed to enforce contact constraint.
    Additional Material: 9 Ill.
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  • 115
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 581-594 
    ISSN: 1069-8299
    Keywords: acoustics ; finite element method ; error estimation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A posteriori error estimation has become very popular, mainly in linear elasticity. A robust implementation of the superconvergent patch recovery technique of O. C. Zienkiewicz and J. Z. Zhu is presented for acoustic finite element analyses: the original concepts are extended to complex variables, and both local and global behaviours of the recovery procedure and the error estimation are studied. The numerical tests confirm the improvement of the rates of convergence for the recovered solution and also show the reliability of the error estimator except at frequencies corresponding either to the analytical or to the finite element eigenfrequencies.
    Additional Material: 13 Ill.
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  • 116
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 595-595 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 117
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996) 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 118
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 599-608 
    ISSN: 1069-8299
    Keywords: finite elements ; moving grids ; moving bodies ; mesh velocity ; ALE ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A Laplacian smoothing of the mesh velocities with variable diffusivity based on the distance from moving bodies is introduced. This variable diffusivity enforces a more uniform mesh velocity in the region close to the moving bodies. Given that in most applications these are regions where small elements are located, the new procedure decreases element distortion considerably, reducing the need for local or global remeshing, and in some cases avoiding it altogether.
    Additional Material: 11 Ill.
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  • 119
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 767-773 
    ISSN: 1069-8299
    Keywords: curved beam element ; membrane locking ; shear locking ; strain based element ; transformation matrix ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two curved beam elements with two nodes and three nodes are designed based on strain fields. At the element level, curvature and membrane strain fields are approximated independently and shear strain fields are incorporated into the formulation by the equilibrium equations. The displacement fields are obtained by integrating the assumed strain fields. Two examples are given to verify the formulations and demonstrate the numerical performance of the two curved beam elements. Analysis results obtained reveal that the elements describe the curved beam behaviour correctly and show exceptional accuracy throughout a wide slenderness range.
    Additional Material: 4 Ill.
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  • 120
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 775-785 
    ISSN: 1069-8299
    Keywords: membrane ; wrinkle ; non-linear ; elasticity ; finite-element method ; sail ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This is a presentation of a quadrilateral finite element for wrinkled curved elastic membranes. A modified form of the deformation gradient enables us to avoid the spurious compressive stresses generated by a classical model. It results in non-linear relations for the eigencomponents of the Cauchy stress tensor, which are solved by means of a secant method. The application of the element to sail design is presented in this paper.
    Additional Material: 8 Ill.
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  • 121
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 795-804 
    ISSN: 1069-8299
    Keywords: RLW equation ; finite element methods ; Petrov-Galerkin ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The RLW equation is solved by a least-squares technique using linear space-time finite elements. In simulations of the migration of a single solitary wave this algorithm is shown to have higher accuracy and better conservation than a recent difference scheme based on cubic spline interpolation functions. In addition, for very small amplitude waves (≤ 0.09) it has higher accuracy than an approach using quadratic B-spline finite elements within Galerkin's method. The development of an undular bore is modelled.
    Additional Material: 5 Ill.
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  • 122
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 787-793 
    ISSN: 1069-8299
    Keywords: regularization ; boundary integral equations ; hypersingular integrals ; Hadamard finite part ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Strongly singular integrals which are unbounded in the sense of Lebesgue appear naturally in boundary integral equations. Extending the analytic continuation method we derive finite part values for a class of singular integrals which arise frequently in practice. In connection with boundary integral operators we derive restrictions on the minimum smoothness of the density functions for the validity of the finite part results. Examples of applications of the results to boundary integral equations in potential theory are presented.
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  • 123
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996) 
    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 12 (1996), S. 805-805 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 125
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 827-834 
    ISSN: 1069-8299
    Keywords: stress-strain relationship ; monotonic loading ; failure stress ; failure strain ; initial modulus ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A function containing four parameters allowing close approximation of experimental stress-strain relationships is presented. The parameters are easily determined from corresponding conditions at the ends and inside of the total interval of the strain variation from zero stain up to failure stain. The family of curves obtained covers an area on the stress-strain plane where any acceptable stress-strain curve can pass. The softening behaviour of soils can also be taken into consideration.
    Additional Material: 3 Ill.
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  • 126
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    Communications in Numerical Methods in Engineering 12 (1996), S. 807-826 
    ISSN: 1069-8299
    Keywords: incompressible materials ; finite element method ; p-version ; elasticity ; stress extraction ; complementary energy ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Direct methods for computing the pointwise stresses for nearly incompressible elastic materials fail to provide meaningful results when applied to the displacement formulation of the finite element method (FEM). A new extraction method for accurate computation of pointwise stresses for nearly incompressible elastic materials is presented. It is based on the complementary energy principle applied over a local domain in the postprocessing phase in conjunction with the p-version finite element solution. It is shown that accurate pointwise stresses are obtained, that the relative error in the pointwise stresses converges at a rate which is as fast as the relative error measured in the energy norm or faster, and importantly, the extracted stresses are virtually independent of Poisson's ratio. Numerical results for two problems, one having a smooth solution and the other containing a singular point, are provided.
    Additional Material: 11 Ill.
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  • 127
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    Communications in Numerical Methods in Engineering 12 (1996), S. 835-847 
    ISSN: 1069-8299
    Keywords: superposition method ; perturbation of eigenvectors ; structural modification ; basis ofN-dimension Euclidean space ; orthogonalization of Schmit procedure ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The modal superposition method is often used for computing the perturbation of eigenvectors in structural modification and model correction. However, it will bring about significant errors in the solution when the high-frequency modes are truncated. This paper presents a new method, which uses known modes construct a new basis of the N-dimensional Euclidean space (say, the mixed-basis), to calculate the first and second order perturbations of the known eigenvectors. In the present method only the known modes are used. The accuracy of this method not only has no relation to number of the truncated modes but is better than the truncated modal superposition method, in which only the known modes are employed. A numerical example of a truss structure with 36 degrees of freedom is given to illustrate the effectiveness of the method.
    Additional Material: 1 Ill.
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  • 128
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    Communications in Numerical Methods in Engineering 12 (1996), S. 849-862 
    ISSN: 1069-8299
    Keywords: superconvergence ; isoparametric bilinear finite elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper the superconvergence property of isoparametric bilinear finite elements is considered. A new superconvergence recovery method for isoparametric bilinear finite elements is discovered on the four vertices and the four midpoints of the edges of the elements for piecewise strongly regular quadrilateral subdivisions.
    Additional Material: 4 Ill.
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  • 129
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    Communications in Numerical Methods in Engineering 12 (1996) 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 130
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    Communications in Numerical Methods in Engineering 12 (1996), S. 873-884 
    ISSN: 1069-8299
    Keywords: thin-walled beam ; finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new method for computing the deformation of thin-walled beams with closed cross-section under warping torsional loading is presented. In comparison to the classical theory (Umanski), the hypothesis of no deformation of the contour of the cross-section of the beam is maintained and the assumption of no distortion of the cross-section plane is modified. The new approach gives better results than the classical theory when both are compared to a standard finite element technique (using shell elements). The central idea of the new approach lies in the usage of a new finite element called a macro-element, which is especially well suited for thin-walled beam computations.
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  • 131
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    Communications in Numerical Methods in Engineering 12 (1996), S. 135-140 
    ISSN: 1069-8299
    Keywords: finite elements ; QUAD4 elements ; RBF corrections ; shear force predictions ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The residual bending flexibility correction is an extra-variational trick used to enhance the convergence rate of shear flexible beam and plate elements. In the paper we show how this can affect the shear deflection and shear force estimates in the QUAD4 element.
    Additional Material: 3 Ill.
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  • 132
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    Communications in Numerical Methods in Engineering 12 (1996), S. 597-597 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 133
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    Communications in Numerical Methods in Engineering 12 (1996), S. 521-529 
    ISSN: 1069-8299
    Keywords: bellows ; shell of revolution ; integral equation method ; compressed angle ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper a U-shaped bellows is treated as a flexible shell of revolution which consists of circular ring shells and truncated shallow conical shells; then the non-linear problem of U-shaped bellows under the action of axial compression force and internal pressure is solved by means of the non-linear theory of shells and the integral equation method. Numerical solutions obtained are compared with previous theoretical and experimental results. The present theory is more appropriate to the analysis of bellows in the light of real profile shape, and shows that the influence of compressed angle on the characteristic relation and peak stresses is noticeable.
    Additional Material: 6 Ill.
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  • 134
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    Communications in Numerical Methods in Engineering 12 (1996), S. 531-542 
    ISSN: 1069-8299
    Keywords: vibration ; inverse eigenvalue problem ; modal analysis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method for determining mass and stiffness modifications to achieve desired natural frequencies is presented. The given data are modal testing results, which consist of a truncated set of natural frequencies and mode shapes. The difficulty arising from the incompleteness of data is overcome by solving an optimization problem rather than seeking an exact solution. The obtained modifications are optimal in a Rayleigh-Ritz sense. The case where the mass and stiffness matrices are interrelated is also considered. Numerical examples demonstrating the various results and the sensitivity of the problem to perturbations are presented.
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  • 135
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    Communications in Numerical Methods in Engineering 12 (1996), S. 609-616 
    ISSN: 1069-8299
    Keywords: hybrid-Trefftz element ; plate ; transient analysis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a hybrid Trefftz (HT) element approach for the numerical solution of transient plate bending problems. In the proposed method, the dynamic plate equation is first discretized with respect to time and then the resulting set of elliptic equations is solved by the corresponding time independent hybrid Trefftz element approach. Two examples are considered to assess the effectiveness of the numerical method.
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  • 136
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    Communications in Numerical Methods in Engineering 12 (1996), S. 617-630 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Three different solution methods for the finite-volume discretized incompressible Navier-Stokes equations have been tested: segregated approaches, built around coupling methods such as SIMPLE, SIMPLER and PISO plus a line Gauss-Seidel linear solver; coupled methods, incorporating a penalty formulation to eliminate zero diagonal elements in the coefficient matrices, plus preconditioned GMRES as a linear solver;- and a FAS-full multigrid algorithm accelerating a classical segregated method based upon SIMPLE and the line Gauss-Seidel solver. Results demonstrate that the coupled method compares favourably to the segregated technique at small grid sizes but becomes too expensive for large problems. The FAS-full multigrid algorithm outperforms the other two methods when large numbers of nodes are employed in the simulation.
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  • 137
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    Communications in Numerical Methods in Engineering 12 (1996), S. 631-641 
    ISSN: 1069-8299
    Keywords: numerical analysis ; fast direct method ; elliptic problems ; finite difference methods ; eigenvalue problems ; harmonic ; biharmonic ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A high accuracy finite difference scheme has been developed for solving some elliptic problems which appear in engineering and applied sciences. These include Laplace, Poisson, Helmholtz and related equations. The second- and fourth-order problems dealing with vibration of membranes and plates have also been examined. Numerically, the problem reduces to a block tridiagonal system which can be solved by suitably modifying the fast direct method developed by Hockney. Comparison has been made with results obtained from some alternative numerical methods or analytical methods whenever available
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  • 138
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    Communications in Numerical Methods in Engineering 12 (1996), S. 643-655 
    ISSN: 1069-8299
    Keywords: viscoelastic flows ; sphere ; annular flow ; adaptive meshing ; finite elements ; error analysis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This work describes the implementation of an adaptive procedure for viscoelastic flows. Finite element simulations are conducted using a Taylor-Galerkin/pressure correction scheme. The constitutive equations considered are those for an Oldroyd-B and a Phan-Thien/Tanner model. The adaptive meshing technique is h-refined by grid remeshing, based on a Delaunay procedure. Results are presented for two benchmark problems, namely flow past a sphere in a cylindrical tube and flow in an annular converging tube. It is concluded from the results that the use of an adaptive procedure with mesh regeneration enables an optimized mesh to be devised and a predicted accuracy to be attained.
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  • 139
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    Communications in Numerical Methods in Engineering 12 (1996), S. 657-671 
    ISSN: 1069-8299
    Keywords: continuous casting ; free boundary problem ; co-ordinate transformation ; solidification front ; non-orthogonal control volume ; temperature profile ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient computational simulation scheme based on non-orthogonal control volume discretization and co-ordinate transformation techniques has been developed for solving the thermal transport phenomena, which involves tracking of the interface between solid and liquid phases (solidification front) and evaluation of the temperature profile during continuous casting operation. Conservation equations are reformulated in differential-integral form in terms of the transformed co-ordinates. All the terms arising from the non-orthogonality of the control volume have been retained in the numerical solution methodology, and a front tracking procedure has been formulated based on an iterative solution scheme. The formulation has been applied to solve the thermal transport phenomena in solidification processing of an A1-Mg alloy cylindrical ingot during continuous casting, which also includes axial conduction of heat. Theoretical evaluation of the solidification front and temperature distribution in the ingot are in good agreement with the experimentally measured data.
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  • 140
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    Communications in Numerical Methods in Engineering 12 (1996) 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 141
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    Communications in Numerical Methods in Engineering 12 (1996), S. 673-682 
    ISSN: 1069-8299
    Keywords: temperature field ; heat source ; IBEM ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The fundamental solution of the temperature field in an infinite three-dimensional body under the periodic unit thermal source is given in the present paper. According to the indirect boundary element method (IBEM) with fictitious heat sources, the problem of 3-D periodic heat conduction in a finite body is solved. By use of a quadratic inharmonic element, the problem of the corner region and the indetermination of the normal direction at boundary points can be solved in the numerical process. The validity of the present method is checked with two examples of which analytical solutions exist. It offers a useful method for the actual simulated calculation of the 3-D temperature field in engineering.
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  • 142
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    Communications in Numerical Methods in Engineering 12 (1996), S. 703-703 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 143
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    Communications in Numerical Methods in Engineering 12 (1996), S. 705-705 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 144
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    Communications in Numerical Methods in Engineering 12 (1996), S. 707-717 
    ISSN: 1069-8299
    Keywords: hybrid element ; shear locking ; penalty-equilibrating approach ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a penalty-equilibrating approach which is used to enforce the equilibrium constraints to individual hybrid elements so as to optimize the element performance. The approach has been applied successfully to improve the 4-noded hybrid stress membrane element (P-S) by Pian and Sumihara. It turns out that some defects of the P-S element, e.g. the shear locking phenomenon and the inability to pass the MacNeal's bending test, can be overcome and the element performance is significantly improved, without having to add any extra variables to the P-S element or to modify its stress fields.
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  • 145
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    Communications in Numerical Methods in Engineering 12 (1996), S. 683-702 
    ISSN: 1069-8299
    Keywords: unstructured grid generation ; finite elements ; advancing front ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We describe extensions and improvements to the advancing front grid generation technique that have proven useful over the years. The following areas are treated in detail: situations with thin or crossing surfaces, meshing of surfaces defined by triangulations, and ease of user input to define the desired element size in space. The first extension is important if one considers the generation of volumetric grids around shells, membranes, fabrics, or CAD-data that exhibit cusps. Traditional advancing front generators are likely to fail in these situations. We propose the introduction of a crossing environment variable attached to faces and points in order to filter out undesired or incorrect information during the grid generation process. The second extension is required for situations where the surfaces to be gridded are not defined analytically, but via a triangulation. Typical cases where such triangulations are used to define the domain are geophysical problems, climate modelling and medical problems. The third topic deals with the reduction of manual labour to specify element size in space. Sources, element size attached directly to CAD-data, and adaptive background grids are discussed. Adaptive background grids, in combination with surface deviation tolerances, are used to obtain surface triangulations that represent the geometry faithfully, and at the same time enable a smooth transition to volumetric meshes.
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  • 146
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    Communications in Numerical Methods in Engineering 12 (1996), S. 731-743 
    ISSN: 1069-8299
    Keywords: explicit integration ; finite elements ; stiffness matrix ; symbolic manipulation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper deals with the symbolic integration of a 4-noded isoparametric finite element for plane elasticity. An efficient approach to generate explicit formulas for computing the elementary stiffness matrix is discussed. The procedure is based on the use of the Derive symbolic manipulation code as well as in a posteriori manipulation of the expressions obtained. The accuracy of the results is tested in extremely distorted and geometrically ill-conditioned elements. Three practical engineering models are presented and the accuracy of the results is discussed. A computer time comparison between both numerical and symbolic integration approaches is also included, showing that relevant CPU savings are obtained when applying symbolic integration.
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  • 147
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    Communications in Numerical Methods in Engineering 12 (1996), S. 719-729 
    ISSN: 1069-8299
    Keywords: air humidification process ; experiments ; predictions with finite-difference technique ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper deals with a numerical and an experimental analysis of the humidification process of air in a nearly horizontal tube. The numerical analysis is based on a finite-difference solution of the three-dimensional momentum, heat and mass transfer differential equations within the tube for the evaporation process of a water stream of circular meniscus cross-section counterflowing to an air stream. In order to provide reliable, high-accuracy data to assist in the development of the theoretical model, tests have been conducted using specially constructed apparatus to measure temperature and velocity profiles within the tube. The proposed computer algorithm was validated by evaluating its ability to predict the measurements of temperatures and velocities along the stream's flow. The theoretical predictions agree well with the experimental data. The model may be used to give performance characteristics for a wide range of humidification processes with different working fluids and state conditions.
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  • 148
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    Communications in Numerical Methods in Engineering 12 (1996), S. 745-753 
    ISSN: 1069-8299
    Keywords: boundary element method ; foundations ; soil-structure interaction ; contact problem ; optimal solutions ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem of providing settlement uniformity of a rigid foundation on a non-uniformly compressible base has been reduced to the contact problem from elasticity theory, with controlling parameters which allow one to select either co-ordinates of the point of application of the vertical load resultant or contours in plan at which the foundation slope will be equal to zero. The solution of the problem is illustrated by numerical examples.
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  • 149
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    Communications in Numerical Methods in Engineering 12 (1996), S. 755-766 
    ISSN: 1069-8299
    Keywords: finite elements ; isoparametric ; Jacobian ; transformation ; valid ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Isoparametric elements are only valid if the Jacobian determinant of the transformation between a given element and a master element does not change sign within or on the element boundary. Some algorithms are known which analyse Jacobians for various element types. Some necessary conditions are presented for determining the validity of an element.
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  • 150
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    Communications in Numerical Methods in Engineering 12 (1996), S. 885-896 
    ISSN: 1069-8299
    Keywords: interfaces ; sliding ; contact ; impact ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an automatic sliding interface algorithm for intense impulsive loading computations due to high velocity impact and explosive detonation. This algorithm allows the user to perform computations involving complex sliding interfaces without having to predetermine the sliding interfaces; everything is automated. The interface determination algorithm, the searching algorithm and the contact algorithm are included.
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  • 151
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    Communications in Numerical Methods in Engineering 12 (1996), S. 863-871 
    ISSN: 1069-8299
    Keywords: objectivity ; kinematics ; computational mechanics ; large deformations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, an example problem is presented that illustrates the importance of strong objectivity in kinematic algorithms for large-deformation finite element applications. The example problem involves cyclic simple shearing of a hypoelastic material, wherein the increments of stretch and of rotation are of comparable magnitude. It is demonstrated that two kinematic algorithms that are in common use, and which are only weakly objective, give rise to an accumulative error in the normal stress components. The error is surprisingly large, even for very small strain increments. This behaviour arises due to a coupling between the stretch and rotation increments that is exhibited by weakly objective algorithms, and is perhaps especially serious in the context of models for jointed rock and other frictional materials, in which the shear response may depend strongly on the normal components of stress.
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  • 152
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    Communications in Numerical Methods in Engineering 12 (1996), S. 905-905 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 153
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    Communications in Numerical Methods in Engineering 12 (1996), S. 897-903 
    ISSN: 1069-8299
    Keywords: finite element analysis ; reinforced concrete element ; embedded reinforcement ; stress analysis ; brick element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper a mathematical formulation for embedding reinforcements in 3D brick concrete elements is presented. The computational aspects and the implementation process of the model have been discussed. The proposed algorithm may be implemented in 3D finite element programs for stress analysis of reinforced concrete structures.
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  • 154
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    International Journal of Quantum Chemistry 57 (1996), S. 7-15 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The solution of the Schrödinger equation for the d-dimensional hydrogen atom in a d-dependent potential defined by Gauss' law has been studied by the shifted 1/d method and the δ expansion. These methods provide analytical formulas for the eigenvalues and eigenfunctions which have been tested against “exact” numerical values obtained recently. The comparison shows that the results obtained with the analytical expressions are in excellent accord with the numerical ones and, on the other hand, provide a theoretical justification for a proposed empirical expression for the energies of the two-dimensional hydrogen atom with a logarithmic potential energy function. © 1996 John Wiley & Sons, Inc.
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  • 155
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    International Journal of Quantum Chemistry 57 (1996), S. 17-33 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An analysis of the structure of the optimized effective Kohn-Sham exchange potential vx and its gradient approximations is presented. The potential is decomposed into the Slater potential vs and the response of vs to density variations, vresp. The latter exhibits peaks that reflect the atomic shell structure. Kohn - Sham exchange potentials derived from current gradient approaches for the exchange energy are shown to be quite reasonable for the Slater potential, but they fail to approximate the response part, which leads to poor overall potentials. Improved potentials are constructed by a direct fit of vx with a gradient-dependent Padé approximant form. The potentials obtained possess proper asymptotic and scaling properties and reproduce the shell structure of the exact vx. © 1996 John Wiley & Sons, Inc.
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  • 156
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    International Journal of Quantum Chemistry 57 (1996), S. 43-51 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Analytical exact expressions are obtained for matrix elements of the modified Pöschl-Teller oscillator over different operators including powers of the hyperbolic functions sinh(α x), cosh(α x), and tanh(α x) and the differential operators d/dx and d2/dx2. These expressions are derived using explicitly the Pöschl-Teller eigenfunctions. In addition, several recursion relations connecting different Pöschl-Teller matrix elements are obtained using the factorization and hypervirial techniques. It is shown that these relations can be used to make easier the computation of the matrix elements. © 1996 John Wiley & Sons, Inc.
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  • 157
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    International Journal of Quantum Chemistry 57 (1996), S. 53-61 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The D-dimensional Coulomb system serves as a starting point for generating generalized atomic shells. These shells are ordered according to a generalized Madelung rule in D dimensions. This rule together with an Aufbau Prinzip is applied to produce a D-dimensional periodic table. A model is developed to rationalize the ordering of the shells predicted by the generalized Madelung rule. This model is based on the introduction of a Hamiltonian, invariant under the q-deformed algebra Uq(so(D)), that breaks down the SO(D + 1) dynamical symmetry of the hydrogen atom in D dimensions. The D = 2 case (Flatland) is investigated in some detail. It is shown that the neutral atoms and the (moderately) positive ions correspond to the values q = 0.8 and q = 1, respectively, of the deformation parameter q. © John Wiley & Sons, Inc.
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    International Journal of Quantum Chemistry 57 (1996), S. 137-137 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 159
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    International Journal of Quantum Chemistry 57 (1996), S. 1-2 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 160
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    International Journal of Quantum Chemistry 57 (1996), S. 123-135 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Ab initio calculations at the scf level were carried out to compute the polarization potential map (mpp) of the nucleic acid bases: cytosine, thymine, uracil, adedine, and guanine. For this purpose, the Dunning's 9s5p basis set contracted to a split-valence, was selected to perform the calculations. The molecular polarization potential (mpp) at each point was evaluated by the difference between the interaction energy of the molecule with a unit point charge and the molecular electrostatic potential (mep) at that point. meps and mpps for the different molecules were computed with a density of 5 points/Å2 on the van der Waals surface of each molecule, defined using the van der Waals radii. Due to the symmetry of the molecules, only half the points were computed. The total number of points calculated was 558 for cytosine, 621 for thymine, 526 for uracil, 666 for adenine, and 699 for guanine. The results of these calculations are analyzed in terms of their implications on the molecular interactions between pairs of nucleic acid bases. © 1996 John Wiley & Sons, Inc.
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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  • 162
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    International Journal of Quantum Chemistry 57 (1996), S. 139-139 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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  • 163
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    International Journal of Quantum Chemistry 57 (1996), S. 141-155 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The matrix differential calculus is applied for the first time to a quantum chemical problem via new matrix derivations of integral formulas and gradients for Hamiltonian matrix elements in a basis of correlated Gaussian functions. Requisite mathematical background material on Kronecker products, Hadamard products, the vec and vech operators, linear structures, and matrix differential calculus is presented. New matrix forms for the kinetic and potential energy operators are presented. Integrals for overlap, kinetic energy, and potential energy matrix elements are derived in matrix form using matrix calculus. The gradient of the energy functional with respect to the correlated Gaussian exponent matrices is derived. Burdensome summation notation is entirely replaced with a compact matrix notation that is both theoretically and computationally insightful. © 1996 John Wiley & Sons, Inc.
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  • 164
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    International Journal of Quantum Chemistry 57 (1996), S. 157-172 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The size-extensive quadratic CI method with single(s), double(D), and triple (T) excitations, QCISDT, is compared with QCISD, QCISD(T), CCSDT-n, and CCSDT. It is shown that QCISDT results are more accurate than are either QCISD or QCISD(T) results. In particular, QCISDT turns out to be more stable than are QCISD and QCISD(T) in cases with considerable multireference character. QCISDT and CCSDT results are of similar accuracy with slight advantages for the former method. Since QCISDT is much easier to implement on a computer than is CCSDT, it is an attractive alternative to CCSDT. © 1996 John Wiley & Sons, Inc.
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  • 165
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    International Journal of Quantum Chemistry 57 (1996), S. 173-182 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: This article presents remarks on the meaning of stopping power and of its magnitude. More precisely, the first set of remarks concerns the connection of stopping power with elements of particle-transport theory, which describes particle transport and its consequences in full detail, including its stochastic aspects. The second set of remarks concerns the magnitude of the stopping power of a material and its relation with the material's electronic structure and other properties. © 1996 John Wiley & Sons, Inc.
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  • 166
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    International Journal of Quantum Chemistry 57 (1996), S. 219-227 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: For the first hydrogen bond of the guanine-cytosine (G-C) pair, the potential function V(r, R) is found for the nonequilibrium bond length R. A new form of the semiempirical potential function, Clementi's calculations for V(r, R0) and some experimental data are used. New wave functions and energy levels as a function of the H-bond length for the ground and several excited states are obtained. This allows one to obtain frequencies and amplitudes of some vibrations of the G-C pair side groups involved in the formation of the hydrogen bond when the latter is not excited and when it is excited to the first energy level. © 1996 John Wiley & Sons, Inc.
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  • 167
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    International Journal of Quantum Chemistry 57 (1996), S. 229-233 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Restricted open-shell Hartree-Fock and unrestricted Hartree-Fock calculations of the electric-field gradient in atoms B, N, O, Al, S, and Cl were performed by relieving the spherical symmetric constraint. The Sternheimer's core polarization effect is then automatically taken into account. The orbitals produced by the axial symmetric self-consistent field are found to have axial symmetry of s-d and p-f mixing types. However, the nonequivalence of the three p orbitals also gives rise to ambiguity. © 1996 John Wiley & Sons, Inc.
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  • 168
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    International Journal of Quantum Chemistry 57 (1996), S. 235-243 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The diagonalization of a class of lattice spin models of a particular structure is first reviewed and secular polynomials for these models are calculated explicitly from the corresponding secular matrices. The structure of the eigenvectors of the given secular matrices is investigated and used to determine the eigenvalues theoretically, and proofs which have not appeared are presented. These results can be compared to the results obtained from the full secular polynomials. © 1996 John Wiley & Sons, Inc.
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  • 169
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 170
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    International Journal of Quantum Chemistry 57 (1996), S. 259-259 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 171
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    International Journal of Quantum Chemistry 57 (1996), S. 263-263 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 172
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    International Journal of Quantum Chemistry 57 (1996), S. 377-389 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The recently introduced set of quadratic ionic and covalent valence indices from changes in the pair-diagonal part of the molecular (Hartree-Fock) two-electron density matrix, ΔΓ(2)(a, b) (orthogonal atomic orbital [OAO] basis set), relative to separated atoms limit (SAL), is extended to cubic valence numbers; they are calculated from the corresponding changes in the three-electron density matrix, ΔΓ(3)(a,b,c). The two- and three-electron indices are given by the corresponding contributions to ΔΓ(2), and ΔΓ(3), which are quadratic and cubic in terms of relevant changes in the one-electron density matrix. The new valence measures are partitioned into one-, two-, and three-center contributions comprising purely ionic (covalent) and mixed ionic-covalent terms. For integral OAO occupations in the SAL, the sum of all three-electron contributions vanishes exactly in the UHF approximation; for fractional occupations, they give rise to a rather small correction to the overall two-electron valence index. The properties of cubic valence numbers are tested on a model three-orbital description of a symmetric (ABA), collinear transition state and on the OQ2 (Q = 1,0, -1) and O2(bond)H+ systems. Preliminary results for B2H6 are also given. © 1996 John Wiley & Sons, Inc.
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  • 173
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    International Journal of Quantum Chemistry 60 (1996), S. 235-248 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Extremal pair functions for an n-electron wave function of a closed-shell state are defined as linear combinations of spin-orbital-product pair functions that make some functionals (e.g., r212 or r-112) extremal. They are related to the natural spin geminals in the uncorrelated limit and are useful both for an analysis of wave functions in view of an understanding of the chemical bond and for the treatment of electron correlation. Numerical examples are shown and discussed for He2 as well as the 10-electron systems Ne, HF, H2O, NH3, and CH4. © 1996 John Wiley & Sons, Inc.
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  • 174
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    International Journal of Quantum Chemistry 60 (1996), S. 287-295 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The generalized Langevin equations are presented by considering such microscopic motions of molecules described by the microscopic Hamiltonian whose potential function is quadratic and internal degree of freedom is multidimensional. Considering the long time behavior of the reactive mode, the Grote-Hynes equation has been derived from the generalized Langevin equations. Furthermore, we have proved that solving the Grote-Hynes equation is equivalent to solving the eigenvalue problem for the whole system, and then the Grote-Hynes treatment coincides with the transition-state theory for the whole system. © 1996 John Wiley & Sons, Inc.
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  • 175
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    International Journal of Quantum Chemistry 60 (1996), S. 307-320 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Motivated by McWeeny's pioneering work on the solution of the Schrödinger equation in momentum space and his early treatment of X-ray scattering factors from the electron distribution ρ(r) in both isolated and bonded atoms, the relation between momentum space moments 〈pn〉 and ρ(r) is first developed semiclassically, as in the forerunner of density functional theory, the Thomas-Fermi method. The relation between 〈p〉 and the Dirac-Slater exchange energy prompts the treatment of an exact nonlocal relation between kinetic and exchange energies in Hartree-Fock theory. The Hiller-Sucher-Feinberg identity serves then to introduce the differential form of the virial theorem in a many-electron system. Following very recent work of Holas and March, this is used to obtain the exact exchange-correlation potential as a path integral expressed in terms of low-order density matrices. © 1996 John Wiley & Sons, Inc.
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  • 176
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    International Journal of Quantum Chemistry 60 (1996), S. 359-372 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The realization of a Clifford algebra in laboratory space is considered and it is demonstrated that the elements of the algebra cannot, as often assumed, be directly identified with vectors in this space, but, rather, that they form the parametric space of the symmetry operations of the Euclidean group as performed in the laboratory space. Details of this parametrization are established and expressions are given that determine the action of the Euclidean-group operations (screws included) on laboratory-space vectors in terms of the elements of the Clifford algebra. A discussion of Clifford vectors, bivectors, and pseudoscalars and their relation to the Gibbs vectors is provided. The correct definition of axial and polar vectors within the Clifford algebra is carefully discussed. It is shown how simple it is to generate finite point groups in 4-dimensional space by means of the Clifford algebra. © 1996 John Wiley & Sons, Inc.
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  • 177
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    International Journal of Quantum Chemistry 60 (1996), S. 393-400 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Spin-coupled calculations are carried out for the nitryl halides FNO2 and CINO2. The picture that emerges suggests that the nitrogen atoms use all five valence electrons in covalent bonding. The description of the NO2 group appears to be essentially transferable between the two molecules. No evidence is found for active d-orbital participation in the bonding in either of these molecules or in FPO2. We assess the geometries, charge distributions, and dipole moments of various X3NO and X3PO species (X = H, CH3, or F). We propose a simple rationalization of the dipole moment data without invoking supposed dπ-pπ bonding. © 1996 John Wiley & Sons, Inc.
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  • 178
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    International Journal of Quantum Chemistry 60 (1996), S. 409-419 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The photoionization cross sections and asymmetry parameters of the three main valence ionization processes in HI, corresponding to the formation of, respectively, 6π, 11σ, and 10σ holes, were calculated in the random-phase approximation (RPA). Our particular computational procedure, based on solving the integral equation for the half on the shell K-matrix upon a grid of points supplied by an L2 basis set calculation, affords recovery of the electronic continuum degeneracy of the final states. This makes it possible to compute the differential ionization cross section at any energy up to the fourth ionization threshold, allowing for the interaction of the three channels considered. The total cross section obtained by applying the Stieltjes imaging procedure to the discrete spectrum yielded by the RPA is also reported. © 1996 John Wiley & Sons, Inc.
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  • 179
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    International Journal of Quantum Chemistry 60 (1996), S. 453-466 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An extended geminal model has been applied to determine the interatomic potential for the X1Σ+g state Be2. By adopting a [11s, 9p, 6d, 4f, 2g] contracted Gaussian-type basis, the following potential minimum parameters are obtained: Re = 4.67 a.u. (4.63 a.u.) and De = 3.70 mH (3.82 ± 0.05 mH), experimental values in parentheses. A calculation with a nuclei-centered [9s, 7p, 4d, 2f, 1g] GTO basis plus two sets of bond-type function, each set comprising diffuse (2s, 2p, 2d, 2f, 1g) GTOs, yielded -3.79 mH as the value of the potential at R = 4.63 a.u. On the basis of an error analysis the best theoretical estimate of the binding energy is determined to be 3.83 ± 0.08 mH. The calculated value for the fundamental vibrational frequency is v0→1 = 224.7 cm-1 (exp. = 224 ± 3 cm). © 1996 John Wiley & Sons, Inc.
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  • 180
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    International Journal of Quantum Chemistry 60 (1996), S. 487-492 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The second electric dipole hyperpolarizability of the lithium atom is calculated using a series of multiconfiguration SCF wave functions with an increasing number of active space orbitals. In agreement with other recent calculations, we find a very large correlation correction to the hyperpolarizability. We analyze the frequency dependence of the dc Kerr hyperpolarizability γK(ο) = γ (- ο ο, 0, 0) and observe very significant dispersion effects. © 1996 John Wiley & Sons, Inc.
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  • 181
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    International Journal of Quantum Chemistry 60 (1996), S. 505-512 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The S0 and S1 potential energy surfaces of pentalene were studied using MMVB - a hybrid force-field/parametrized valence bond (VB) method designed to simulate CASSCF calculations for ground and covalent excited states. The results were calibrated against full CASSCF calculations. Four distinct critical points were optimized: on S0, a C2h minimum (with alternating single and double bonds) and a D2h transition structure; and on S1, a D2h minimum and an adjacent S1/S0 conical intersection. A VB exchange density matrix (which is independent of the choice of the spin-coupled basis) was used to rationalize the S0 and S1 surface topologies. Craig defined pseudoaromatic molecules to be those with nontotally symmetric electronic ground states. For pentalene, this is true for both CASSCF and MMVB calculations: the CASSCF S0 transition structure is an open-shell B1x singlet, and the VB ground state is dominated by a spin-coupling which transforms as B1g. A C2v minimum and a D2h transition structure were located on the CASSCF S2 potential energy surface. This state cannot be represented by MMVB because of the importance of ionic configurations. The characters of the S1 S2 states of pentalene are shown to be reverse of the S1 and S2 states of benzene. © 1996 John Wiley & Sons, Inc.
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  • 182
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    International Journal of Quantum Chemistry 60 (1996), S. 579-592 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Position and momentum space plots are presented for localized molecular orbitals in hydrocarbons, boranes, a carborane, and two octahedral transition metal complexes. The p-space representation proves to be valuable for visualizing such orbitals since it highlights the differences in their character from one molecule to another. Factors influencing the form of the orbitals in p space, including the oscillatory behavior caused by contributions to an orbital from more than one center, are examined in detail. © 1996 John Wiley & Sons, Inc.
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  • 183
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 184
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    International Journal of Quantum Chemistry 60 (1996), S. 609-616 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Coupled Hartree-Fock theory is used to compute and map the current density induced in planar hydrocarbons by an external magnetic field. Results of useful accuracy can be obtained with modest (6-31G**) basis sets by employing a continuous gauge transformation. Maps are presented and discussed for benzene, naphthalene, anthracene, tetracene, pentacene, heptacene, and biphenylene. © 1996 John Wiley & Sons, Inc.
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  • 185
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    International Journal of Quantum Chemistry 60 (1996), S. 617-634 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The group-function theory, as proposed by McWeeny for the study of weak intermolecular interactions and developed by Huzinaga in the context of valence-electron methods, is shown to be applicable to the ab initio study of tunable solid-state laser materials made of defective ionic crystals. The applicability of the theory relies on the existence of local electronic states (to which the demonstrated/potential laser activity is ascribed), which are essentially localized in a small cluster of atoms including the defect and whose electron correlation interactions with the surrounding crystal components are negligible. According to the group-function formalism, it is possible (a) to neglect electron correlation effects beyond the defect cluster and (b) to define a quantum mechanical embedding potential which embodies the rest of the so-called host effects. Computationally, the theory becomes applicable as the embedding potential is approximated through ab initio model potentials (AIMP). The results of AIMP embedded-cluster calculations demonstrate that it is possible to calculate the local structure and spectroscopy of the active defect at an ab initio level, the attainable accuracy being comparable to the usual one in molecular ab initio studies in the gas phase. Also, in this article, we present a systematic study of the local distortions produced upon doping divalent first-series transition-metal ions in rock-salt oxides, MO:Me2+ (M=Mg, Ca, Sr; Me=Sc-Zn) and Tl+ in KMgF3 and KF hosts. This study leads to the calculation of the local structures of the defects in these materials, which have not been measured. The results suggest that the use of the mismatch of the empirical ionic radii of the impurity and the substituted ion in order to predict local distortions in doped ionic crystals is not significant when it is smaller than 0.1 Å, and when it is larger, it should be weighted by a reduction factor depending on the host. For the first-series divalent transition-metal ion impurities, this factor is shown to be 0.15 for SrO, 0.25 for CaO, and around 0.50 for MgO. © 1996 John Wiley & Sons, Inc.
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  • 186
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    International Journal of Quantum Chemistry 60 (1996), S. 649-655 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Using ab initio HF/6-31G** and MP2/6-31G** calculations alternative reactions HC(OH)3 → HCO2H + H2O and HC(OH)3 + H2O → HCO2H + 2H2O are investigated and the results are compared with relevant PM3, HF/3-21G, and HF/6-31G data. Reactant and product complexes as well as transition states are located on corresponding potential energy surfaces. © 1996 John Wiley & Sons, Inc.
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  • 187
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    International Journal of Quantum Chemistry 60 (1996), S. 681-687 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Molecular structure of 21 chromophores of indigoid dyes were studied by an ab initio MP2/6-31 + G*/ /HF/6-31 + G* method. Bond lengths and bond angles were affected by π-electron conjugation. The difference between molecular structures of chromophores and indigoid dyes indicated that benzene rings and five-membered rings in indigoid dyes are structurally important. Absorption maxima of chromophores were successfully calculated by the CI-singles-MP2/6-31 + G* theory. Like indigoid dyes, absorption maxima of the chromophores are affected by the positions of the donor and acceptor groups on the trimethine group. Bathochromic shifts of the absorption maxima were observed with the best donor group of (SINGLE BOND)NH among (SINGLE BOND)NH, (SINGLE BOND)O, and (SINGLE BOND)S groups. Appropriate substitution of longer-chain polymethines brought about chromophoric systems having hypsochromic shifts. From these calculations, the absorption maxima of some indigoid dyes could be explained by their chromophores qualitatively. © 1996 John Wiley & Sons, Inc.
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  • 188
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  • 189
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    International Journal of Quantum Chemistry 60 (1996), S. 789-789 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 190
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    International Journal of Quantum Chemistry 60 (1996), S. 793-801 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: It is shown that the conventional concepts based on the use of the HOMO and LUMO are founded on very questionable assumptions. In particular, it is shown both theoretically and computationally that the LUMO of almost all neutral atoms and molecules is a continuum function with energy zero. The LUMO of any SCF calculation is an artifact of the basis-expansion method. A proposal is made for the identification of the pair donor and pair acceptor orbitals which play the true role of the HOMO and LUMO. © 1996 John Wiley & Sons, Inc.
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    International Journal of Quantum Chemistry 60 (1996), S. 825-832 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The G and F matrices in the molecular vibration problem, the secular matrix in Hückel calculation including some nonneighbor interactions, and the Fock matrices at any stage of iteration in the Pariser-Parr-Pople (PPP) calculations on cis- and trans-butadiene, benzene, and s-triaminobenzene systems have been shown to be factorizable by representing them graphically and then applying the generalized technique of splitting of graphs with n-fold symmetry. © 1996 John Wiley & Sons, Inc.
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  • 192
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    International Journal of Quantum Chemistry 60 (1996), S. 959-969 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The Wiener index is a graphical invariant that has found extensive application in chemistry. We define a generating function, which we call the Wiener polynomial, whose derivative is a q-analog of the Wiener index. We study some of the elementary properties of this polynomial and compute it for some common graphs. We then find a formula for the Wiener polynomial of a dendrimer, a certain highly regular tree of interest to chemists, and show that it is unimodal. Finally, we point out a connection with the Poincaré polynomial of a finite Coxeter group. © 1996 John Wiley & Sons, Inc.
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  • 193
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    International Journal of Quantum Chemistry 60 (1996), S. 971-981 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A study of π-electron systems confined by impenetrable surfaces is presented. The study results in a nonempirical-based approach to obtain confinement-adapted semiempirical π-Hamiltonians including repulsive terms (PPP or Hubbard). The impenetrable surface confinement of a physical system involves changes in the boundary conditions that the eigenvectors of its differential Hamiltonian operator have to fulfill, while the Hamiltonian itself remains unchanged. However, if this Hamiltonian is written in second quantization language, then confinement only involves changes of the Hamiltonian scalar factors (integrals). Semiempirical Hamiltonian integrals are replaced by parameters; therefore, confinement involves only changes of these parameters. It is shown that confinement changes Coulomb (αi) and exchange (βij), while repulsion (γij) parameters remain unaffected. Next, the influence of confinement upon the electron correlation of (i) π-electron molecular systems, (ii) atoms, and (iii) an electron gas is discussed. The behaviour of the correlation energy vs. the confinement size is found to be different for each type of system. A neat explanation of this variety is given in terms of the Coulomb attractive fields of the systems. Some chemical confinement effects such as an increase in the reactivity of π-electron systems is also outlined. © 1996 John Wiley & Sons, Inc.
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  • 194
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    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The Cl2CO … Cl2 complex was studied using ab initio post-Hartree-Fock theory at the MP2 and MP4 levels and, for comparison, the DFT method with 6-311G(2d), 6-311 + G(2d), and Sadlej's medium-size polarized (MSPBS) basis sets. A potential energy search recovered a planar minimum-energy structure characterized by a bent conformation. For this weakly bound complex, the interaction energy corrected for the basis set superposition error amounted to - 0.88, - 1.09, - 1.43, and - 0.38 kcal/mol at the MP4(SDTQ)/6-311G(2d), MP4(SDTQ)/6-311 + G(2d), MP4(SDTQ)/MSPBS, and DFT(Becke3LYP)/6-311 + G(2d) levels of theory, respectively. Two highly symmetrical forms, linear and T-shaped, correspond to transition-state conformers. The analysis of harmonic vibrational frequencies and potential energy distribution was performed at the MP2 and DFT levels with the 6-311 + G(2d) basis set. © 1996 John Wiley & Sons, Inc.
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  • 195
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    International Journal of Quantum Chemistry 60 (1996), S. 1065-1068 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A discussion is presented for possible diamond-lattice-based structures containing holes that can be filled with metal atoms or ions. To allow the formation of coordinative bonds to the metal, some carbon atoms should be replaced by heteroatoms (with nitrogen preferred, but in some cases oxygen or other heteroatoms may be considered). Two types of holes that may lead to the formation of coordinative bonds are discussed in detail: tetrahedral holes for four such bonds and quasi-octahedral holes for six such bonds. In turn, when suitably arranged in a translationally symmetric manner, these holes may resemble open or closed pores in foams; when they are open, the “channels” may lead to interesting properties with regard to metallic conductivity or superconductivity. © 1996 John Wiley & Sons, Inc.
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    International Journal of Quantum Chemistry 60 (1996), S. 1081-1091 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Electrostatic and hydrophobic complementarities between chymotrypsin and its inhibitor, avian ovomucoid third domains, were evaluated for eight species, which have different amino acid sequences, using molecular electrostatic potential (MEP) and MEP correlation, and the enzyme-inhibitor interaction was analyzed. The changes in the electrostatic and hydrophobic complementarities caused by the amino acid replacements were reflected clearly in the calculated MEP correlation, and it explained the observed binding association constants correctly. The electrostatic complementarity due to arginine at P′3 strongly promotes the binding process of the inhibitor, while the hydrophobic complementarity in the P1 and P′2 positrons also affects the binding process. It was demonstrated that our method is an effective molecular modeling tool in drug design and protein engineering. © 1996 John Wiley & Sons, Inc.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 197
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 60 (1996), S. 1179-1187 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The interaction between solutes and simple solvents in dilute solutions is analyzed in a systematic way. Different theoretical methods to describe specific solute-solvent interactions and general solvation effects are presented. Finally, the importance of solvent-induced changes in solute properties is discussed through the use of mixed quantum mechanics/classical mechanics strategies. © 1996 John Wiley & Sons, Inc.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 198
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 60 (1996), S. 743-752 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Secular polynomials (SPs) have been constructed and studied for the adjacency matrices A(GaCh) and A(GbCh) corresponding to chemical graphs of alkanes in terms of atoms (GaCh) and in terms of bonds (GbCh). The three second-class Chebyshev polynomials Up(Q), Up - 1(Q), and Up - 2(Q), with respect to the variable Q proportional to the SP of an isolated CH2-like subgraph, have been shown to appear within both SPs P[A(GaCh)] and P[A(GbCh)] and to play the role of algebraic analogues of a (CH2)p-like subgraph. Common noncanonical algebraic expressions for both SPs reflecting the regular internal structure of alkanes have been constructed on this basis. Spectral properties of both graphs GaCh and GbCh have been shown to be determined by those of Up(Q), e.g., the band limits of spectra proved to be related to the orthogonality interval Q = [-1;1] for polynomials Up(Q). Since the adjacency matrices (AMs) A(GbCh), but not A(GaCh), are proportional to definite model Hamiltonian matrices, the obtained results serve to interpret the one-electron spectra of alkanes in terms of peculiarities of usual chemical structure. © 1996 John Wiley & Sons, Inc.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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  • 199
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 60 (1996), S. 779-788 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A computational study of substituent effects on methane activation and elimination by high-valent zirconium complexes is reported. Substituent (Z) effects (in a structural, electronic, and enthalpic sense) are substantially less important for the imido (LnZr(DOUBLE BOND)NZ) and imidolike TS than the amido (LnM(SINGLE BOND)NHZ). For the microscopic reverse reaction, methane CH activation, it suggests that tailoring imido reactivity through electronic modification of nitrogen substituents will be difficult. Analysis of the earliest part of the reaction coordinate for methane elimination entails structural deformation of the Zr - amido to assume an appropriate geometry for elimination, which, in some cases, is directly reflected in substantially higher elimination barriers. Lower elimination barriers correlate with stronger agostic bonding, providing further support for the crucial importance of agostic bonding in facilitating alpha-elimination processes for high-valent transition-metal complexes. © 1996 John Wiley & Sons, Inc.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 200
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    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 60 (1996), S. 791-791 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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