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  • 1
    Electronic Resource
    Electronic Resource
    Closest Approach in Universal Variables (1997)
    Springer
    Celestial mechanics and dynamical astronomy 69 (1997), S. 331-346 
    Details
    ISSN: 1572-9478
    Keywords: closest approach ; universal Kepler's equation ; optimization technique
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this paper, universal formulations of the closest approach problem are established and solved by two methods. The first method uses the technique of one-dimensional unconstraint minimization and needs the solution of the universal Kepler's equation twice, while for the second method, a constraint minimization technique is developed and needs the solution of two nonlinear simultaneous equations. Flexible iterative schemes of quadratic up to any positive integer order are developed for the solution of the universal Kepler's equation. The two methods of the minimization process are applied for the closest approach of Hyakutake and Hale–Bopp comets, while the first method is applied to obtain the minimum angular separation of ADS 9159, ADS 2959 and ADS 11632 visual binaries as typical examples of elliptic, parabolic and hyperbolic orbits.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008223105130
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  • 2
    Electronic Resource
    Electronic Resource
    Unified Symbolic Algorithm of Gauss Method for Near-Parabolic Orbits (1998)
    Springer
    Celestial mechanics and dynamical astronomy 70 (1998), S. 201-214 
    Details
    ISSN: 1572-9478
    Keywords: near‐parabolic orbits ; Kepler's equatio
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this paper, a unified algorithm of Gauss method for near‐parabolic orbits that is valid for both elliptic and hyperbolic cases is established symbolically and numerically.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008339612666
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  • 3
    Electronic Resource
    Electronic Resource
    Transfer reactions to unbound states by the diffraction model (1972)
    Springer
    The European physical journal 253 (1972), S. 28-37 
    Details
    ISSN: 1434-601X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Transfer reactions leading to unbound states are studied by means of the diffraction model. The unbound state is described by a resonance scattering wave function. The radial integrals are evaluated using some reasonable approximations. Comparison with the experimental results is very satisfactory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01387167
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  • 4
    Electronic Resource
    Electronic Resource
    Prediction of satellites in Earth's gravitational field with axial symmetry using Burdet's regularized theory (1987)
    Springer
    Earth, moon and planets 38 (1987), S. 21-36 
    Details
    ISSN: 1573-0794
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract In this paper, economical and stable recurrence formulae for the Earth's zonal potential and its gradient for Burdet's regularized theory will be established for any number N of the zonal harmonic coefficients. A general recursive computational algorithm based on these formulae is also established for the initial value problem of Burdet oscillator for the prediction of artificial satellites in the Earth's gravitational field with axial symmetry. Applications of the algorithm for the problem of the final state prediction are illustrated by numerical examples of three test orbits each for two geopotential models corresponding to N = 2 and N = 36. A final state of any desired accuracy is obtained for each case study, a result which shows the flexibility of the algorithm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00115934
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  • 5
    Electronic Resource
    Electronic Resource
    Tables for the trigonometric series representations of the orbital inclination function (1987)
    Springer
    Astrophysics and space science 139 (1987), S. 199-231 
    Details
    ISSN: 1572-946X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this paper, tables for the trigonometric series representations of the orbital inclination functionF lmp (i) in multiples of cosines or sines will be represented forl=2(1)10;m=0(1)l;p=0(1)l.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00644351
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  • 6
    Electronic Resource
    Electronic Resource
    Elastomeric properties of end-linked networks of high cross-link functionality. Accounting for possible changes in effective functionality with extent of reaction and chain-length distribution (1994)
    Springer
    Colloid & polymer science 272 (1994), S. 504-515 
    Details
    ISSN: 1435-1536
    Keywords: Model networks ; bimodal networks ; poly(dimethylsiloxane) ; elastomers ; rubber elasticity ; mechanical properties ; elongation modulus ; stress-strain isotherms ; end-linking reactions ; Flory ; Erman theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract This study reanalyzes some elastomeric properties in elongation reported for poly(dimethylsiloxane) (PDMS) networks of high cross-link functionality which had been prepared by using multifunctional siloxane oligomers to end link vinyl-terminated PDMS chains. The extent of reaction of the vinyl end groupsP vi spanned the range of 0.40 to 0.95. These networks had elongation moduli that significantly exceeded the values predicted by the Flory-Erman theory, except at very low values ofP vi. Trends in their stress-strain isotherms, as characterized by the Mooney-Rivlin constants 2C 2 and the ratio 2C 2/C1, also appeared to be different from those predicted by theory. Neglected in such standard analyses, however, was the fact that the segments between cross-links along the junction precursor molecules can themselves act as short network chains, contributing to the modulus and giving a strongly bimodal distribution of both network chain lengths and cross-link functionalities. Of particular interest is the apparent change in functionality with extent of reaction and chain length distribution. The results thus obtained do suggest strong dependence of the observed values of the phantom modulus on the network chain-length distribution, particularly at very small values of the ratio of the length of the short chains to the long ones. Calculations based on recognition of these complications can be used to characterize more realistically the deformation of such networks. The results give much better agreement with experiment. Such behavior could be an important characteristic of elastomeric networks in general. Also, a preliminary attempt was made to bridge theory with experiment based on Kloczkowski, Mark, and Erman's recent theory of fluctuations of junctions in regular bimodal networks. The agreement between theory and experiment thus obtained is rather satisfactory and lends further support to assumptions that take into account the possibly bimodal nature of these high-functionality networks.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00653214
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  • 7
    Electronic Resource
    Electronic Resource
    Elastomers having high functionality cross links viewed as bimodal networks. An alternative interpretation in terms of bimodal chain-length distributions (1995)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 33 (1995), S. 1151-1165 
    Details
    ISSN: 0887-6266
    Keywords: elastomers ; high-functionality networks ; polydimethylsiloxane (PDMS) ; bimodal distributions ; Flory-Erman theory ; Fixman-Alben distribution ; Monte-Carlo ; non-Gaussian ; Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Several groups have now prepared poly(dimethylsiloxane) networks of high cross-link functionality by end-linking vinyl-terminated chains by means of Si—H groups in siloxane oligomers (CH3)3SiO[SiHCH3O]xSi(CH3)3. The elongation moduli of these networks were generally found to be considerably larger than the values predicted from the functionality and number density of the cross links (based on the stoichiometry of the end-linking reaction). Not all the Si—H groups in an oligomer are used in the end-linking reaction, however, and the segments between cross-links can themselves act as short network chains. The connectivity of these short chains to the long ones, in what is essentially a bimodal distribution, has been neglected in analyses to date. They are taken into account in the present analysis, giving much better agreement between experiment and theory. The stress-strain behavior for such very short chains can be characterized by the use of Monte Carlo methods and the Fixman-Alben non-Gaussian distribution. This alternative analysis seems useful in reproducing the experimental observations, but further experimental and theoretical will be required to remove some remaining ambiguities. © 1995 John Wiley & Sons, Inc.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/polb.1995.090330801
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  • 8
    Electronic Resource
    Electronic Resource
    Simulations on the reinforcement of poly(dimethylsiloxane) elastomers by randomly distributed filler particles (1996)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 34 (1996), S. 1647-1657 
    Details
    ISSN: 0887-6266
    Keywords: elastomers ; excluded volume effect ; fillers ; filler particle size ; moduli ; non-Gaussian effects ; poly(dimethylsiloxane) ; reinforcement ; rotational isomeric state (RIS) theory ; Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Monte Carlo computer simulations were carried out on filled networks of poly(dimethylsiloxane) (PDMS), which were modeled as composites of crosslinked chains and randomly arranged spherical filler particles. The primary concern of the investigation was the effect of the excluded volume of these particles on the elastomeric properties of the polymers. Calculations were carried out for PDMS chains with different molecular masses between crosslinks, and for filler particles with different sizes and at various volume percentages. Distributions of end-to-end vectors for both unfilled and filled networks were obtained using Monte Carlo simulations based on rotational isomeric state (RIS) theory. More extended configurations, with a higher end-to-end distance, were observed for networks filled with smaller particles. The nominal stress f* and the modulus or reduced nominal stress [f*] were calculated from the distributions of end-to-end vectors using the Mark-Curro approach. Relatively small filler particles were found to increase the non-Gaussian behavior and to increase the normalized moduli above the reference value of unity. Temperature effects on the stress were also investigated. © 1996 John Wiley & Sons, Inc.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 9
    Electronic Resource
    Electronic Resource
    Stress-Strain isotherms for stereoirregular and stereoblock cis-trans polybutadienes (1986)
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 26 (1986), S. 162-166 
    Details
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Gamma radiation and high-energy electrons were used to crosslink two types of polybutadiene (PBD), the first having random cis-trans-vinyl contents and the second consisting primarily of blocks of cis units and blocks of trans. The resulting elastomers were studied in elongation in the unswollen stale, generally at 5°C, and in swelling equilibrium in a thermodynamically good solvent. Stress-strain isotherms obtained for the random-PBD networks did not show upturns in the reduced stress [f*] at high elongations, which is consistent with their non-crystallizability. The stereoblock polymers were found to be crystalline, with melting points ranging from 14 to 65°C. Attempts to achieve strain-induced crystallization in the stereoblock networks by judicious choice of temperature were unsuccessful as judged by the absence of any significant upturns in [f*]. Values of the elasticity constants 2C1 and 2C2, and the molecular weight between crosslinks were similar to those obtained from the linear portions of the isotherms previously reported for high-cis and high-trans PBD, which readily undergo strain-induced crystallization.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pen.760260208
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  • 10
    Electronic Resource
    Electronic Resource
    Elastomeric properties of networks prepared from high-cis and high-trans 1,4-polybutadienes (1986)
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 26 (1986), S. 304-309 
    Details
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Networks were prepared from a sample of 1,4-polybutacliene having an extremely high cis content (98.5 mol percent) and from other samples having relatively high trans contents (72 to 80 mol percent). The cross-linking techniques employed were gamma irradiation, ultraviolet irradiation, and peroxide thermolysis. The resulting elastomers were studied in elongation in the unswollen state at several temperatures, to their rupture points, and in swelling equilibrium in a good solvent. Values of the elasticity constant 2C1 obtained from the stress-strain isotherms at low and moderate elongations gave values of the molecular weight M, between cross-links in at least approximate agreement with those obtained from the swelling equilibrium data. The other elasticity constant 2C2 generally had relatively large values, suggesting inhomogeneous cross-linking, but approached zero for small Mc as expected from reduced configurational interpenetration. At high elongations, the reduced stress for the high-cis polymer showed marked upturns due to strain-induced crystallization.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pen.760260408
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