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  • 1985-1989  (2)
Materialart
Erscheinungszeitraum
Jahr
  • 1
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 48 (1987), S. 231-254 
    ISSN: 1572-9613
    Schlagwort(e): Discrete dynamics ; circle maps ; noise ; mean first passage times ; metastability ; escape rates
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract The problem of escape from a domain of attraction is applied to the case of discrete dynamical systems possessing stable and unstable fixed points. In the presence of noise, the otherwise stable fixed point of a nonlinear map becomes metastable, due to noise-induced hopping events, which eventually pass the unstable fixed point. Exact integral equations for the moments of the first passage time variable are derived, as well as an upper bound for the first moment. In the limit of weak noise, the integral equation for the first moment, i.e., the mean first passage time (MFPT), is treated, both numerically and analytically. The exponential leading part of the MFPT is given by the ratio of the noise-induced invariant probability at the stable fixed point and unstable fixed point, respectively. The evaluation of the prefactor is more subtle: It is characterized by a jump at the exit boundaries, which is the result of a discontinuous boundary layer function obeying an inhomogeneous integral equation. The jump at the boundary is shown to be always less than one-half of the maximum value of the MFPT. On the basis of a clear-cut separation of time scales, the MFPT is related to the escape rate to leave the domain of attraction and other transport coefficients, such as the diffusion coefficient. Alternatively, the rate can also be obtained if one evaluates the current-carrying flux that results if particles are continuously injected into the domain of attraction and captured beyond the exit boundaries. The two methods are shown to yield identical results for the escape rate of the weak noise result for the MFPT, respectively. As a byproduct of this study, we obtain general analytic expressions for the invariant probability of noisy maps with a small amount of nonlinearity.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    ISSN: 1434-6079
    Schlagwort(e): 34.50
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract For 3.6 MeV He impact theL I andL III subshell ionization probabilities of Pt have been measured. Due to relativistic effects in the electron wave functions, theL I subshell ionization probabilityI LI (b) is strongly enhanced at small impact parameters exceeding evenI LIII (b) in nice agreement with the SCA theory.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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