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  • 1
    Electronic Resource
    Electronic Resource
    A new K-matrix approach to N-body scattering (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 3117-3124 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Chandler–Gibson theory of N-body scattering is used to define a new K matrix for N-body quantum scattering systems. The half-on-shell K matrix has the proper channel thresholds and may be computed using a K-matrix form of the CG equations. The on-shell K matrix is an Hermitian matrix for all energies and is related to a unitary scattering matrix via a Cayley transform. A B-spline solution method is developed and applied to a two-body and a three-body test problem. The three-body numerical calculations are within 0.5% of the exact solution both below and above the breakup threshold.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529059
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  • 2
    Electronic Resource
    Electronic Resource
    N-body quantum scattering theory in two Hilbert spaces. V. Computation strategy (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 1533-1544 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this paper the development of our previously published theory of approximations for the Chandler–Gibson (CG) equations is continued. In particular, our approximation theory is rigorously brought to the point where N-particle scattering calculations can begin. This is accomplished by mapping the CG operator equations into a function equation form, where the unknowns belong to a new (third!) computational Hilbert space L. This mapping is facilitated by rescaling the Jacobi momentum variables for the relative free motion of the asymptotic clusters so that surfaces of constant kinetic energy are hyperspheres. The input terms to the resulting equations are expanded in a basis on the surface of the kinetic energy hypersphere. This leads to a system of infinitely many coupled one-dimensional integral equations with the kinetic energy as the continuous variable. The half-on-shell variant of these equations is then transformed to a K-matrix form. Our approximations result from truncating this system to a finite number of equations, which is equivalent to using a finite basis approximation of the original input terms. The basis sets could be hyperspherical harmonics, but the use of hyperspherical spline functions is also proposed. Our method generalizes the well-known method of partial waves for channels with two clusters, and it accommodates breakup channels in a straightforward way.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528286
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  • 3
    Electronic Resource
    Electronic Resource
    Erratum: N-body quantum scattering theory in two Hilbert spaces. V. Computation strategy [J. Math. Phys. 30, 1533 (1989)] (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 886-886 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530231
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  • 4
    Electronic Resource
    Electronic Resource
    -Body Quantum Scattering Theory in Two Hilbert Spaces: -Body Integral Equations (1998)
    Springer
    Few body systems 23 (1998), S. 223-258 
    Details
    ISSN: 1432-5411
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract. Scattering for a nonrelativistic system of distinguishable and spinless particles interacting via short-range pair potentials is considered. Half-on-shell integral equations (the CG equations) are proposed, the solutions of which determine approximate scattering amplitudes that converge to the exact scattering amplitude. It is proved, under mild Hölder integrability assumptions, that these apparently singular equations actually have a compact kernel for real energies and, consequently, a unique solution. The CG equations have a structure that is much simpler than the Yakubovskii equations and similar to that of coupled-reaction-channel equations. The driving terms look like distorted-wave Born integrals and nonorthogonality integrals. However, there is no restriction to channels with only two asymptotic bound clusters and for all channels, no matter how many bound clusters, appropriate boundary conditions are exactly satisfied. This work completes the establishment of a rigorous mathematical link between the solutions of the half-on-shell CG equations and the on-shell transition operators defined in time-dependent multichannel scattering theory, and it provides for the first time a rigorous theoretical basis for practical calculations of scattering amplitudes for certain problems with .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s006010050072
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  • 5
    Electronic Resource
    Electronic Resource
    General N-Body Theory of Nonrelativistic Quantum Scattering (1999)
    Springer
    Few body systems 27 (1999), S. 207-249 
    Details
    ISSN: 1432-5411
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract.  The two-Hilbert-space theory of scattering is reviewed with particular reference to its application to nonrelativistic multichannel quantum- mechanical scattering theory. In Part I the abstract assumptions of the theory are collected, transition operators (both on- and off-energy-shell) are defined, the dynamical equations that determine the off-shell transition operators are presented and their real-energy limits examined, and the convergence of sequences of approximate transition operators is established. A section on how to incorporate group symmetries into the formalism reports new work. The material of Part I is relevant to a variety of both classical and quantum scattering systems. In Part II attention is directed specifically to N-body nonrelativistic quantum scattering systems in which the particles interact via short-range pair potentials. A method of constructing approximate transition operators is presented and shown to satisfy all the abstract assumptions of Part I. The dynamical equations that determine the half-on-shell approximate transition operators are shown to be coupled one-dimensional integral equations that have compact kernels and unique solutions when considered as operators on a Hilbert space of Hölder continuous functions. Moreover, the on-shell parts of those approximate transition amplitudes are shown to converge to the exact on-shell amplitudes as the order of the approximation increases. Detailed formulas for the kernels of the integral equations are written down for systems of particles that are distinguishable and for systems containing identical particles. Finally, some important open problems are described.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s006010050130
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  • 6
    Electronic Resource
    Electronic Resource
    An analysis of the mechanics of solid phase extrusion of polymers (1980)
    Springer
    Journal of materials science 15 (1980), S. 359-375 
    Details
    ISSN: 1573-4803
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract An analysis is presented for the mechanics of the hydrostatic extrusion of polymers in the solid phase through a conical die. The analysis starts with the lower bound solution proposed by Hoffman and Sachs and includes the effects of strain, strain rate and pressure on the deformation behaviour. It is proposed that this involves knowledge of the tensile stress-strain-strain rate relationships for each polymer, and it is shown how such information for polyethylene and polyoxymethylene can be used to explain the observed behaviour of these materials in the solid-phase extrusion process.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02396784
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  • 7
    Electronic Resource
    Electronic Resource
    An analysis of the mechanics of solid phase extrusion of polymers (1980)
    Springer
    Journal of materials science 15 (1980), S. 359-375 
    Details
    ISSN: 1573-4803
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract An analysis is presented for the mechanics of the hydrostatic extrusion of polymers in the solid phase through a conical die. The analysis starts with the lower bound solution proposed by Hoffman and Sachs and includes the effects of strain, strain rate and pressure on the deformation behaviour. It is proposed that this involves knowledge of the tensile stress-strain-strain rate relationships for each polymer, and it is shown how such information for polyethylene and polyoxymethylene can be used to explain the observed behaviour of these materials in the solid-phase extrusion process.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00551687
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  • 8
    Electronic Resource
    Electronic Resource
    Thermal expansion behaviour of hydrostatically extruded linear polyethylene (1979)
    Springer
    Journal of materials science 14 (1979), S. 1838-1842 
    Details
    ISSN: 1573-4803
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The thermal expansion behaviour of a series of oriented linear polyethylenes has been measured over the temperature range −180 to + 70° C. With increasing deformation ratio the axial thermal expansion coefficient approaches that of the crystal unit cell, and the transverse expansion coefficient approaches that of the average in the crystal a- and b-axis directions. The implications of these results are discussed in terms of present understanding of the structure of these materials.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00551022
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  • 9
    Electronic Resource
    Electronic Resource
    The manufacture of ultra-high modulus polyethylenes by drawing through a conical die (1980)
    Springer
    Journal of materials science 15 (1980), S. 979-986 
    Details
    ISSN: 1573-4803
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Various grades of linear polyethylene have been drawn through a heated conical die at 100° C. It was found that after a suitable start-up procedure, continuous drawing was possible in all cases with a stable neck region extending beyond the die exit. The degree of deformation attainable was found to depend strongly on the draw velocity. Very high deformation ratios could be obtained and the Young's moduli of the die-drawn products were comparable to those of similar products obtained by solid state extrusion and tensile drawing, reaching values as high as 60 GPa. The effects of molecular weight and co-polymerization are substantial, but not exactly analogous to those previously observed in hydrostatic extrusion and tensile drawing. This is probably due to the non-isothermal nature of the final stage of deformation in the case of die drawing.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00552111
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  • 10
    Electronic Resource
    Electronic Resource
    The hydrostatic extrusion of polymethylmethacrylate (1980)
    Springer
    Journal of materials science 15 (1980), S. 2207-2220 
    Details
    ISSN: 1573-4803
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The hydrostatic extrusion behaviour of two grades of polymethylmethacrylate (PMMA) is reported and an analysis of the mechanics of the extrusion process is presented. Although the maximum degree of deformation achieved is considerably lower than that obtained for crystalline polymers, the process mechanics are controlled by the same factors (i.e. the billet-die friction, and the effects of strain rate and pressure on the material flow stress). A method for equating the effects of pressure and friction is described, following the work of Tabor on the adhesive mechanism of friction in polymers. This method gives a friction coefficient in the range 0.1 to 0.2 for the hydrostatic extrusion of PMMA, compared to values in the region 0.03 to 0.08 for crystalline polymers, suggesting conditions of boundary lubrication. The relatively high values of friction for PMMA are consistent with the requirement for careful preparation of the billet surface prior to extrusion, and the observation of the ″stick-slip″ phenomenon during extrusion. The differences between the grades of PMMA in both extrusion behaviour and tensile drawing behaviour are explicable in terms of their different glass transition temperatures.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00552308
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