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  • 1
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 10 (1976), S. 917-935 
    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 instabilities, especially the singlet instabilities, of the conventional Hartree-Fock (HF) solutions for a variety of alternant and nonalternant hydrocarbons, some of which have been known to show lattice instabilities (bond-length alterations), are examined. The HF solutions for nonalternant hydrocarbons in the pentalene series larger than heptalene and [4n + 2]-annulenes larger than C22H22 are found to be singlet unstable and there appear new solutions lower in energy than the conventional HF solutions and characterized by charge-density waves exhibiting bond-order alterations. It is found that such symmetry-breaking solutions are energetically further stabilized by distorting the nuclear framework so that it may match up with the distribution of bond-order matrix elements of the charge-density wave, which means that in conjugated systems the singlet instability of the HF solution is always accompanied with the lattice instability. Further, it is shown that in conjugated systems, even when the HF solution is singlet stable, if it is not sufficiently stable as, for example, in pentalene and heptalene, there is every possibility for the occurrence of lattice instability. It is also shown that the singlet instability as well as the lattice instability arises from the existence of a sufficiently low-lying singlet excited state.
    Additional Material: 5 Ill.
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  • 2
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 18 (1980), S. 655-659 
    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 optical reflectivity spectra of quasi-one-dimensional polymers (SN)x, trans-(CH)x, and polydiacetylene are investigated in an energy range from 1 to 25 eV by use of synchrotron radiation. Observed structures associated with π-electron states are interpreted in terms of the quasi-one-dimensional one-electron bands calculated by the LCAO-type model.
    Additional Material: 2 Ill.
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 22 (1982), S. 1049-1058 
    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: Some new properties of the Lagrange multiplier μ introduced through the normalization constraint on ρ in the variations of energy density functionals are determined. Through arguments concerning the homogeneity properties of these functionals with respect to μ, it is demonstrated that at the point of variation μ = μ0 = E0/N, where E0 is the ground state energy and N is the total particle number. It is also shown that the value of μ0 is independent of the normalization imposed on ρ. The interpretation of μ0 as a chemical potential is discussed in the light of these findings.
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 15 (1980), S. 87-96 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a general procedure for calculating the buckling of stiffened skew plates by the Rayleigh-Ritz method with B-spline functions as co-ordinate functions.Convergence of the solutions is investigated in a few typical cases and is found satisfactory. The results are compared with existing values based on other numerical methods and found to be in good agreement. Buckling characteristics of stiffened skew plates are also studies with varying stiffness parameters of stiffeners, skew angles and aspect ratios.
    Additional Material: 4 Ill.
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 299-317 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A computational algorithm is developed and applied for optimization of beam and plate structures, subject to constraints on transient dynamic response. A continuous design formulation is retained, with dynamic response governed by partial differential operator equations. Adjoint equations are employed for sensitivity analysis and a function space gradient projection optimization approach is presented. Finite element analysis methods are applied for solution of the system dynamic and adjoint differential equations. Displacement constrained beam and plate minimum weight examples are solved, with a variety of boundary conditions.
    Additional Material: 7 Ill.
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  • 6
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 39-52 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an algorithm for optimal design of elastic structures, subjected to dynamic loads. Finite element, modal analysis and a generalized steepest descent method are employed in developing a computational algorithm. Structural weight is minimized subject to constraints on displacement, stress, structural frequency, and member size. Optimum results for several example problems are presented and compared with those available in the literature.
    Additional Material: 5 Ill.
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  • 7
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 897-907 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A discrete approach using the B-spline functions and the concept of the point least square is presented. The general procedure, in which trial functions satisfy neither governing differential equations nor boundary conditions, is used in solving solid mechanics problems. No numerical integration is required in the formulation and the resulting matrix has the advantage of always being symmetrical.To demonstrate the accuracy and versatility of the present method, vibration of beams, skew plate problems, thick plates and a non-self-adjoint problem are analysed. A good accuracy is obtained with increase in the number of fitting points and of knots of B-spline functions.
    Additional Material: 1 Ill.
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  • 8
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 40 (1991), S. 479-487 
    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 UV photoelectron spectra of 2-halogenofurans, together with 3-iodo and 2,5-diiodofurans, have been studied. The assignment of the lower energy region of the spectra was based on correlation of the ring π- and halogen levels in the related compounds, resolved vibrational structure, and in case of 2- and 2,5-diiodofurans by considering the relative intensities of their He I/He II spectra.
    Additional Material: 5 Ill.
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  • 9
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 375-392 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this work we analyse a model for radiative heat transfer in materials that are conductive, grey and semitransparent. Such materials are for example glass, silicon, water and several gases. The most important feature of the model is the non-local interaction due to exchange of radiation. This, together with non-linearity arising from the well-known Stefan-Boltzmann law, makes the resulting heat equation non-monotone. By analysing the terms related to heat radiation we prove that the operator defining the problem is pseudomonotone. Hence, we can prove the existence of weak solution in the cases where coercivity can be obtained. In the general case, we prove the solvability of the system using the technique of sub and supersolutions. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
    Additional Material: 2 Ill.
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  • 10
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1599-1618 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element method based on the virtual work principle to determine the steady state response of frams in free or forced periodic vibration is introduced. The axial and flexural deformations are coupled by mean of the induced axial force along the element. The spatial discretization of the deformations is achieved by the usual finite element method and the time discretization by Fourier coefficients of the nodal displacements. No unconventional element matrices are needed. After applying the harmonic balance method, a set of non-linear algebraic equations of the Fourier coefficients is obtained. These equations are solved by the Newtonian iteration method in terms of the Fourier coefficient increments. Nodal damping can easily be included by a diagonal damping matrix. The direct numerical determination of the Fourier coefficient increments is difficult owing to the presence of peaks, loops and discontinuities of slope along the amplitude-frequency response curves. Parametric construction of the response curves using the phase difference between the response and excitation is recommended to provide more points during the rapid change of the phase (i.e. at resonance). For undamped natural vibration, the method of selective coefficients adopted.Numerical examples on the Duffing equation, a hinged-hinged beam, a clamped-hinged beam, a ring and a frame are given. For reasonably accurate results, it is shown that the number of finite elements must be sufficient to predict at least the linear mode at the frequency of interest and the number of harmones considered must satisfy the conditions of completeness and balanceability, which are discussed in detail.
    Additional Material: 11 Ill.
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