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  • 1
    Electronic Resource
    Electronic Resource
    Classical numerical integrators for wave-packet dynamics (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 104 (1996), S. 2349-2355 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Gray and Verosky have recently studied the reformulation of the N-state matrix representation of the time-dependent Schrödinger equation as an N-degrees of freedom classical Hamiltonian system. This opens the possibility of using in quantum dynamics numerical integrators originally devised for classical mechanics. When the Hamiltonian matrix is time-dependent, Gray and Verosky suggest the use of a Magnus approximation before reducing the quantum system to its classical format. We show that Magnus approximations are not necessary and suggest an alternative technique. With the new technique it is possible to obtain simple integrators of arbitrarily high orders of accuracy that can be applied to all matrix Schrödinger problems with a, possibly time-dependent, real Hamiltonian matrix. The connection between the new approach and high-order split-operator methods is studied. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.470930
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  • 2
    Electronic Resource
    Electronic Resource
    Soliton and antisoliton interactions in the "good'' Boussinesq equation (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1964-1968 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The solitary-wave interaction mechanism for the good Boussinesq equation is investigated and found to be far more complicated than was previously thought. Three salient features are that solitary waves only exist for a finite range of velocities, that large solitons can turn into so-called antisolitons, and that it is possible for solitons to merge and split. Small solitons, however, appear to be stable. The existence of a potential well is linked to the different behaviors observed between small and large initial conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527850
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  • 3
    Electronic Resource
    Electronic Resource
    Histological investigation on the ovarian cycle of the bluefin tuna in the western and central Mediterranean (2003)
    Oxford, UK : Blackwell Science Ltd
    Journal of fish biology 63 (2003), S. 0 
    Details
    ISSN: 1095-8649
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Biology
    Notes: The histological analysis of eastern Atlantic bluefin tuna Thunnus thynnus ovaries caught from February to September 1999–2000, made it possible to distinguish the presence of seven oocyte developmental stages and allowed the characterization of six time-dependent ovary maturity stages. The ovaries of mature (fork length, LF ≥ 110 cm) bluefin tuna were non-active from August (spent period) to March (quiescent period) when they contained only perinucleolar-stage oocytes. Ovary development started in April to early May (recrudescent period) with the appearance of oocytes at the lipid stage. Vitellogenesis appeared in mid-May (ripening period) and post-vitellogenesis occurred in late May to mid-June (pre-spawning period). In late June to early July, hydrated oocytes, a sign of imminent spawning, were found only in specimens caught in Balearic waters. Females ranging between 100 and 110 cm LF, captured during the recrudescent and ripening periods, had the largest oocytes at the lipid stage, most of which were degenerating. An extensive vitellogenic atresia was observed in the ovaries of five females caught during the spawning period in non-spawning areas.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1046/j.1095-8649.2003.00132.x
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  • 4
    Electronic Resource
    Electronic Resource
    Size and age at sexual maturity of female bluefin tuna (Thunnus thynnus L. 1758) from the Mediterranean Sea (2005)
    Berlin, Germany : Blackwell Verlag GmbH
    Journal of applied ichthyology 21 (2005), S. 0 
    Details
    ISSN: 1439-0426
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Biology , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: The ovaries of 501 female eastern Atlantic bluefin tuna (Thunnus thynnus Linnaeus, 1758) captured in the Mediterranean Sea from May to September between 1998 and 2004 were analysed histologically. Body size at median sexual maturity (L50) was 103.6 cm fork length (FL), while 100% maturity was reached above 135 cm FL. The age analysis, based on the count of the translucent zones of the first spiniform ray of the first dorsal fin, showed that most of the specimens with FL = L50 were 3 years old while 100% maturity was reached between 4 to 5 years. The reported evidence indicates that for the eastern Atlantic bluefin tuna stock, the size and age of first sexual maturity of females was lower than in the western Atlantic stock.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1439-0426.2005.00700.x
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  • 5
    Electronic Resource
    Electronic Resource
    The spectral accuracy of a fully-discrete scheme for a nonlinear third order equation (1990)
    Springer
    Computing 44 (1990), S. 187-196 
    Details
    ISSN: 1436-5057
    Keywords: 65M10 ; Spectral method ; stability ; stability threshold
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Zur numerischen Lösung einer nichtlinearen Differentialgleichung dritter Ordnung, herrührend aus einem Strömungsproblem bei Gasteilchen, wird ein zeitdiskreter Pseudo-spektral-Algorithmus vorgeschlagen. Stabilität und Konvergenz des neuen Differenzenverfahrens werden analysiert. Numerische Vergleiche mit bestehenden Differenzenschemata sprechen klar zugunsten des neuen Verfahrens.
    Notes: Abstract A time-discrete pseudospectral algorithm is suggested for the numerical solution of a nonlinear third order equation arising in fluidization. The nonlinear stability and convergence of the new scheme are analyzed. Numerical comparisons with available finite-difference methods are also reported which clearly indicate the superiority of the new scheme.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02262215
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  • 6
    Electronic Resource
    Electronic Resource
    Some aspects of the boundary locus method (1980)
    Springer
    BIT 20 (1980), S. 97-101 
    Details
    ISSN: 1572-9125
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The boundary locus method for determining the stability region of a linear multistep method is considered from several viewpoints. In particular we show how it is related to the order of the method. These ideas are extended to Runge-Kutta and other methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01933590
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  • 7
    Electronic Resource
    Electronic Resource
    Order conditions for canonical Runge-Kutta-Nyström methods (1992)
    Springer
    BIT 32 (1992), S. 131-142 
    Details
    ISSN: 1572-9125
    Keywords: Primary 65L05 ; Secondary 70H15 ; 05C05 ; Hamiltonian systems ; symplectic structures ; Runge-Kutta-Nyström methods ; order conditions ; trees
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We are concerned with Runge-Kutta-Nyström methods for the integration of second order systems of the special formd 2 y/dt 2=f(y). If the functionf is the gradient of a scalar field, then the system is Hamiltonian and it may be advantageous to integrate it by a so-called canonical Runge-Kutta-Nyström formula. We show that the equations that must be imposed on the coefficients of the method to ensure canonicity are simplifying assumptions that lower the number of independent order conditions. We count the number of order conditions, both for general and for canonical Runge-Kutta-Nyström formulae.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01995113
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  • 8
    Electronic Resource
    Electronic Resource
    Runge-kutta schemes for Hamiltonian systems (1988)
    Springer
    BIT 28 (1988), S. 877-883 
    Details
    ISSN: 1572-9125
    Keywords: AMS 65 L ; 70H ; Runge-Kutta methods ; Hamiltonian systems ; symplectic geometry ; conservation of energy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study the application of Runge-Kutta schemes to Hamiltonian systems of ordinary differential equations. We investigate which schemes possess the canonical property of the Hamiltonian flow. We also consider the issue of exact conservation in the time-discretization of the continuous invariants of motion.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01954907
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  • 9
    Electronic Resource
    Electronic Resource
    The non-existence of symplectic multi-derivative Runge-Kutta methods (1994)
    Springer
    BIT 34 (1994), S. 80-87 
    Details
    ISSN: 1572-9125
    Keywords: 65L06 ; 70H15 ; Multi-derivative Runge-Kutta methods ; symplectic methods ; irreducible methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A sufficient condition for the symplecticness ofq-derivative Runge-Kutta methods has been derived by F. M. Lasagni. In the present note we prove that this condition can only be satisfied for methods withq≤1, i.e., for standard Runge-Kutta methods. We further show that the conditions of Lasagni are also necessary for symplecticness so that no symplectic multi-derivative Runge-Kutta method can exist.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01935017
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  • 10
    Electronic Resource
    Electronic Resource
    Lack of dissipativity is not symplecticness (1995)
    Springer
    BIT 35 (1995), S. 269-276 
    Details
    ISSN: 1572-9125
    Keywords: Hamiltonian problems ; symplectic integrators ; nondissipative methods ; Runge-Kutta-Nyström procedures
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We show that, when numerically integrating Hamiltonian problems, nondissipative numerical methods do not in general share the advantages possessed by symplectic integrators. Here a numerical method is called nondissipative if, when applied with a small stepsize to the test equationdy/dt = iλy, λ real, has amplification factors of unit modulus. We construct a fourth order, nondissipative, explicit Runge-Kutta-Nyström procedure with small error constants. Numerical experiments show that this scheme does not perform efficiently in the numerical integration of Hamiltonian problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01737166
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