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  • Articles  (4)
  • Physics  (3)
  • Jordan blocks  (1)
  • Wiley-Blackwell  (4)
  • American Institute of Physics (AIP)
  • 1
    Electronic Resource
    Electronic Resource
    Determination of Jordan chains by extended matrices (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 879-893 
    Details
    ISSN: 1069-8299
    Keywords: derogatory eigenproblems ; Jordan blocks ; Jordan chains ; Segre characteristic ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The major obstacle to determination of the Jordan chains for a highly degenerated eigenproblem is that the triangular combinations of the principal vectors in a Jordan chain are also principal vectors and the linear combinations of the eigenvectors of all Jordan blocks associated with the same eigenvalue are also eigenvectors. These indeterminate constants will hide the Jordan block structure and make the analysis very difficult. We propose an extended matrix method to find the Jordan chains and eliminate the indeterminate constants so that the Jordan block structure can be computed sequentially. An example with the Segre characteristic [(321)11] is given. © 1998 John Wiley & Sons, Ltd.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 2
    Electronic Resource
    Electronic Resource
    Model calculation of the thermal conductivity of polymer crystals (1985)
    New York : Wiley-Blackwell
    Journal of Polymer Science: Polymer Physics Edition 23 (1985), S. 1495-1504 
    Details
    ISSN: 0098-1273
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A linear lattice model without adjustable parameters provides an accurate description of the magnitude and temperature dependence of the thermal conductivity of Kc of polyethylene crystals parallel (∥) and perpendicular (⊥) to the chain direction. The model shows that heat is transported principally by phonons polarized transverse (T) to the chain direction. Phonons polarized longitudinal (L) to the chain direction contribute about 20% to the heat transport along the chain direction, and negligibly to heat transport perpendicular to the chain direction. Thermal resistance is caused by LTT three-phonon umklapp scattering in the parallel direction, and by TTT scattering in the perpendicular direction. The calculated values for large crystals are Kc∥ = 465 W m-1 K-1, Kc∥ = 0.16 W m-1 K-1 at 300 K, in agreement with experimental estimates and implying an anisotropy ratio of Kc∥/Kc⊥ ≈ 3000. The axial thermal conductivity of polyethylene crystals is extremely high and comparable to that of copper. Comparison with experimental data on semicrystalline samples at lower temperature yields a crude value of mean free path for boundary scattering of about 50 nm, agreeing in order of magnitude with the size of crystalline blocks.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pol.1985.180230803
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  • 3
    Electronic Resource
    Electronic Resource
    Temperature dependence of the thermal expansivity of polymer crystals: Linear chain model (1984)
    New York : Wiley-Blackwell
    Journal of Polymer Science: Polymer Physics Edition 22 (1984), S. 979-991 
    Details
    ISSN: 0098-1273
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A linear chain model is used to calculate the thermal expansivities of polymer crystals from room temperature down to liquid-helium temperature. Because of restraint by strong covalent forces, vibrations along the chains give a negligible contribution. Vibrations transverse to the chains cause the length projected along the chain direction to decrease. The expansivity along the chain direction, αc∥ is therefore negative, and has temperature dependence characterized by the low Debye temperature of transverse vibrations. These vibrations, through a cubic term in the interchain van der Waals potential, also cause a positive expansivity, αc⊥ perpendicular to the chain direction. The theoretical predictions for αc∥ and αc⊥ agree quite well with experimental data over the wide temperature range under consideration.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pol.1984.180220604
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  • 4
    Electronic Resource
    Electronic Resource
    Negative thermal expansivity of polymer crystals: Planar zig-zag chain model (1981)
    New York : Wiley-Blackwell
    Journal of Polymer Science: Polymer Physics Edition 19 (1981), S. 971-981 
    Details
    ISSN: 0098-1273
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The thermal expansivity of polymer crystals in the direction parallel to the chain axis α∥ is studied in a planar zig-zag chain model. Using values of force constants for polyethylene, it was found that α∥ = -1.3 × 10-5 K-1, in good agreement with experimental results. Torsional modes are found to contribute slightly more than half α∥. The expansivity is independent of the mass of the atomic groups on the chain and only weakly dependent on the interchain van der Waals interaction.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pol.1981.180190606
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