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  • 1
    Electronic Resource
    Electronic Resource
    Relations between universal scaling constants for the circle map near the golden mean (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1045-1051 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The two-frequency quasiperiodic route to chaos is believed to be modeled by the critical circle map and the universal behavior of the scaling constants α and δ is determined by the order z of the inflection point. We have numerically determined α(z) and δ(z) as a function of this order. Using the renormalization group equations, we have succeeded in obtaining approximate analytical relations for α and δ that agree quite well with the data. In the limit as z→∞, we argue that ||δ||→1/ρ3=4.236 and δ/αz→1, in good agreement with the numerical computations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529382
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  • 2
    Electronic Resource
    Electronic Resource
    Multidimensional phase space and sunset diagrams (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 5553-5564 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We derive expressions for the phase space of a particle of momentum p decaying into N particles, that are valid for any number of dimensions. These are the imaginary parts of so-called "sunset" diagrams, which we also obtain. The results are given as a series of hypergeometric functions, which terminate for odd dimensions and are also well suited for deriving the threshold behavior. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1416887
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  • 3
    Electronic Resource
    Electronic Resource
    Morphology of the period-doubling universal function (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 758-770 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Results are presented concerning the structure on the real line of the "universal function'' which is the fixed point solution of the Feigenbaum–Cvitanovic renormalization group equation associated with period-doubling chaos in quadratic maps. It is shown that the values which the function takes at its turning points can be algebraically characterized by relation to the infinite cycle associated with the original turning point of the map on the interval. These extrema become increasingly numerous as the argument increases, and their locations can be found progressively using knowledge of the previously determined extrema. As well as providing a simple understanding of the structure of the universal function these simple observations may be of assistance in investigating the convergence or asymptotic behavior of approximations to the universal function, and perhaps in providing a "corrector'' step to some of these schemes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529755
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  • 4
    Electronic Resource
    Electronic Resource
    Grassmann coordinates and Lie algebras for unified models (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 3616-3641 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A variety of Lie algebras and certain classes of representations can be constructed using Grassmann variables regarded as Lorentz scalar coordinates belonging to an internal space. The generators are realized as combinations of multilinear products of the coordinates and derivative operators, while the representations emerge as antisymmetric polynomials in the variables and are thus severely restricted. The nature of these realizations and the interconnections between various subalgebras, for N independent complex anticommuting coordinates, is explored. The addition of such Grassmann coordinates to the usual spacetime manifold provides a natural superfield setting for a unified theory of symmetries of elementary particles. The particle content can be further restricted by imposing discrete symmetries (Lie algebra automorphisms). For the case N=5 some anomaly free choices of multiplets are derived through the imposition of specific superfield duality conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530049
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  • 5
    Electronic Resource
    Electronic Resource
    Chiral and gravitational anomalies in any dimension (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1334-1336 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Gravitational contributions to the chiral anomaly in 4N space-time dimensions as well as the purely gravitational anomaly in 4N−2 dimensions are expressed in terms of the Riemann–Christoffel tensor. Using this formula, we give a simple proof that if N≥4 there is no way to cancel the gravitational anomalies using fields of spin- 1/2 , - 3/2 , and -1.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526941
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  • 6
    Electronic Resource
    Electronic Resource
    Islands of stability and complex universality relations (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 60-63 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: For complex mappings of the type z→λz(1−z), universality constants α and δ can be defined along islands of stability lying on filamentary sequences in the complex λ plane. As the end of the filament is approached, asymptotic values αN∼λN−1∞, δN/α2N∼1 are attained, where μ∞=λ∞(λ∞−2)/4, is associated with the limiting form of the universal function for that sequence, g(z)=1−μ∞z2. These results are complex generalizations of the real mapping case (applying to tangent bifurcations and windows of stability) where μ∞=2 and δ/α2→ (2)/(3) correspond to the filament running along the real axis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527808
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  • 7
    Electronic Resource
    Electronic Resource
    Inflammability Ranges of Propane – Air Mixtures under Reduced Pressure (1951)
    [s.l.] : Nature Publishing Group
    Nature 167 (1951), S. 985-986 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] Ignition in our case was obtained by a spark produced by an air condenser charged at 22,000 volts passing through two small platinum electrodes at the base of a closed tube 4 cm. in diameter and 80 cm. high. The device used allowed us to employ either a single spark, corresponding to a single ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/167985b0
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  • 8
    Electronic Resource
    Electronic Resource
    Renormalization of rational Lagrangians
    Amsterdam : Elsevier
    Annals of Physics 66 (1971), S. 1-19 
    Details
    ISSN: 0003-4916
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1016/0003-4916(71)90182-5
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  • 9
    Electronic Resource
    Electronic Resource
    On the dynamical origin of SU(6)
    Amsterdam : Elsevier
    Physics Letters 21 (1966), S. 455-457 
    Details
    ISSN: 0031-9163
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://linkinghub.elsevier.com/retrieve/pii/0031-9163(66)90529-4
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  • 10
    Electronic Resource
    Electronic Resource
    Multiple field relations
    Amsterdam : Elsevier
    Physics Letters 22 (1966), S. 680-683 
    Details
    ISSN: 0031-9163
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://linkinghub.elsevier.com/retrieve/pii/0031-9163(66)90703-7
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