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  • ATOMIC AND MOLECULAR PHYSICS  (5)
  • 65D30  (3)
  • Interdisciplinary physics  (3)
  • 1
    Electronic Resource
    Electronic Resource
    On the Smolyak cubature error for analytic functions (2000)
    Springer
    Advances in computational mathematics 12 (2000), S. 71-93 
    Details
    ISSN: 1572-9044
    Keywords: cubature ; Smolyak algorithm ; error bounds ; analytic functions ; Clenshaw–Curtis quadrature ; Kronrod–Patterson quadrature ; 65D30 ; 41A55 ; 41A63 ; 65D32
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider Smolyak's construction for the numerical integration over the d‐dimensional unit cube. The underlying class of integrands is a tensor product space consisting of functions that are analytic in the Cartesian product of ellipses. The Kronrod–Patterson quadrature formulae are proposed as the corresponding basic sequence and this choice is compared with Clenshaw–Curtis quadrature formulae. First, error bounds are derived for the one‐dimensional case, which lead by a recursion formula to error bounds for higher dimensional integration. The applicability of these bounds is shown by examples from frequently used test packages. Finally, numerical experiments are reported.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018904816230
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Asymptotics for the remainder of a class of positive quadratures for integrands with an interior singularity (1993)
    Springer
    Numerische Mathematik 65 (1993), S. 121-133 
    Details
    ISSN: 0945-3245
    Keywords: 65D30 ; 41A55
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary For functions with an interior singularity, the errors of a class of positive quadrature formulae with high algebraic degree are reduced to those of the much simpler ‘Euler-Maclaurin type formulae’. Applying this method to certain classes of functions, such as, for example,f(x)=h(x)|x-u| β , where β〉−1, with a sufficiently smooth functionh, we obtain the main term of the error expansion for quadrature rules of ultraspherical type.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385744
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Gaussian integration of Chebyshev polynomials and analytic functions (1995)
    Springer
    Numerical algorithms 10 (1995), S. 187-202 
    Details
    ISSN: 1572-9265
    Keywords: Gaussian integration ; Chebyshev polynomials ; error bounds ; analytic functions ; 65D30 ; 41A55
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Explicit bounds for the quadrature error of thenth Gauss-Legendre quadrature rule applied to themth Chebyshev polynomial are derived. They are precise up to the orderO(m 4 n −6). As an application, error constants for classes of functions which are analytic in the interior of an ellipse are estimated. The location of the maxima of the corresponding kernel function is investigated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02198303
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  • 4
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    Local dynamics of a randomly pinned crack front during creep and forced propagation: An experimental study (2011)
    American Physical Society (APS)
    Details
    Publication Date: 2011-04-15
    Description: Author(s): Ken Tore Tallakstad, Renaud Toussaint, Stephane Santucci, Jean Schmittbuhl, and Knut Jørgen Måløy We have studied the propagation of a crack front along the heterogeneous weak plane of a transparent poly(methyl methacrylate) (PMMA) block using two different loading conditions: imposed constant velocity and creep relaxation. We have focused on the intermittent local dynamics of the fracture front... [Phys. Rev. E 83, 046108] Published Thu Apr 14, 2011
    Keywords: Interdisciplinary physics
    Print ISSN: 1539-3755
    Electronic ISSN: 1550-2376
    Topics: Physics
    Published by American Physical Society (APS)
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  • 5
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    Average crack-front velocity during subcritical fracture propagation in a heterogeneous medium (2011)
    American Physical Society (APS)
    Details
    Publication Date: 2011-09-10
    Description: Author(s): Olivier Lengliné, Renaud Toussaint, Jean Schmittbuhl, Jean E. Elkhoury, J. P. Ampuero, Ken Tore Tallakstad, Stéphane Santucci, and Knut Jørgen Måløy We study the average velocity of crack fronts during stable interfacial fracture experiments in a heterogeneous quasibrittle material under constant loading rates and during long relaxation tests. The transparency of the material (polymethylmethacrylate) allows continuous tracking of the front posit... [Phys. Rev. E 84, 036104] Published Fri Sep 09, 2011
    Keywords: Interdisciplinary physics
    Print ISSN: 1539-3755
    Electronic ISSN: 1550-2376
    Topics: Physics
    Published by American Physical Society (APS)
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  • 6
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    Onset of localization in heterogeneous interfacial failure (2012)
    American Physical Society (APS)
    Details
    Publication Date: 2012-08-11
    Description: Author(s): Arne Stormo, Knut Skogstrand Gjerden, and Alex Hansen We study numerically the failure of an interface joining two elastic materials under load using a fiber bundle model connected to an elastic half space. We find that the breakdown process follows the equal load sharing fiber bundle model without any detectable spatial correlations between the positi... [Phys. Rev. E 86, 025101] Published Fri Aug 10, 2012
    Keywords: Interdisciplinary physics
    Print ISSN: 1539-3755
    Electronic ISSN: 1550-2376
    Topics: Physics
    Published by American Physical Society (APS)
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  • 7
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    Heteronuclear transition metal diatomics - The bonding and electronic structure of ScNi, YNi, ScPd, and YPd (1991)
    In:  Other Sources
    Details
    Publication Date: 2011-08-24
    Description: High quality ab initio calculations show that ScNi, YNi, ScPd, and YPd all have 2Sigma(+) ground states in agreement with electron spin resonance experiments. For ScNi and YNi, this is expected based on the lowest atomic asymptote. For ScPd and YPd, the lowest atomic asymptote would give the order of stability 2Delta greater than 2Pi equal to about 2Sigma(+), but the calculations show that mixing in of the excited asymptotes preferentially lowers the 2Sigma(+) state. The calculations show that the quartet states are about 20-30 kcal/mol above the ground state, and therefore probably do not contribute significantly to the unexpected g(vertical) values found in experiment. Calculations of excited states for YPd reveal some strong transitions that should be amenable to spectroscopic studies.
    Keywords: ATOMIC AND MOLECULAR PHYSICS
    Type: Chemical Physics (ISSN 0301-0104); 153; 399-408
    Format: text
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  • 8
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    Polyatomic molecular Dirac-Hartree-Fock calculations with Gaussian basis sets (1990)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: Numerical methods have been used successfully in atomic Dirac-Hartree-Fock (DHF) calculations for many years. Some DHF calculations using numerical methods have been done on diatomic molecules, but while these serve a useful purpose for calibration, the computational effort in extending this approach to polyatomic molecules is prohibitive. An alternative more in line with traditional quantum chemistry is to use an analytical basis set expansion of the wave function. This approach fell into disrepute in the early 1980's due to problems with variational collapse and intruder states, but has recently been put on firm theoretical foundations. In particular, the problems of variational collapse are well understood, and prescriptions for avoiding the most serious failures have been developed. Consequently, it is now possible to develop reliable molecular programs using basis set methods. This paper describes such a program and reports results of test calculations to demonstrate the convergence and stability of the method.
    Keywords: ATOMIC AND MOLECULAR PHYSICS
    Type: NASA-CR-187854 , NAS 1.26:187854
    Format: application/pdf
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  • 9
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    Finite nucleus effects on relativistic energy corrections (1993)
    In:  Other Sources
    Details
    Publication Date: 2019-07-13
    Description: The effect of using a finite nucleus model in quantum-chemical calculations is examined. Relativistic corrections from the first order Foldy-Wouthuysen terms are affected indirectly by the change in wavefunction, but also directly as a result of revised expressions for the Darwin and spin-orbit terms due to the change in nuclear potential. A calculation for the Rn atom indicates that the mass-velocity and Darwin corrections are much more sensitive to the finite nucleus than the non-relativistic total energy, but that the total contribution for these two terms is quite stable provided the revised form of the Darwin term is used. The spin-orbit interaction is not greatly affected by the choice of nuclear model.
    Keywords: ATOMIC AND MOLECULAR PHYSICS
    Type: Chemical Physics Letters (ISSN 0009-2614); 201; 4-Jan; p. 27-32.
    Format: text
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  • 10
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    All-electron molecular Dirac-Hartree-Fock calculations - The group IV tetrahydrides CH4, SiH4, GeH4, SnH4, and PbH4 (1991)
    In:  Other Sources
    Details
    Publication Date: 2019-07-12
    Description: A basis-set-expansion Dirac-Hartree-Fock program for molecules is described. Bond lengths and harmonic frequencies are presented for the ground states of the group 4 tetrahydrides, CH4, SiH4, GeH4, SnH4, and PbH4. The results are compared with relativistic effective core potential (RECP) calculations, first-order perturbation theory (PT) calculations and with experimental data. The bond lengths are well predicted by first-order perturbation theory for all molecules, but none of the RECP's considered provides a consistent prediction. Perturbation theory overestimates the relativistic correction to the harmonic frequencies; the RECP calculations underestimate the correction.
    Keywords: ATOMIC AND MOLECULAR PHYSICS
    Type: Journal of Chemical Physics (ISSN 0021-9606); 95; 2583-259
    Format: text
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