Quick search Find article
Quick search
Find article

Trace for the Loewner equation with singular forcing

FREE ARTICLE

L P Kadanoff and M Kleine Berkenbusch



CORRIGENDUM

This is a Corrigendum for the article 2004 Nonlinearity 17 R41

In the above invited article there was an error in the description of equation (17) which gives the behaviour of the trace close to the singularity in the case of square-root forcing β = 1/2. The equation is correct only in the limit as κ goes to infinity. The correct equation, valid for all κ > 4, is
        \gamma(s) - y_- = C \rme^{\rmi\phi} [\xi(s)]^{({2\sqrt{\kappa-4}})/({\sqrt{\kappa} + \sqrt{\kappa-4}})}.        (17)
Note that this change does not affect any of the subsequent derivations.

Figure 4 shows a comparison between numerical data and the form of the singularity for this β and κ = 16. The figure shows a good but not excellent fit to the asymptotic form.

The error mentioned here was originally detected by Panos Oikonomou, who then went on to extend the asymptotic analysis of the original article. The original invited article was devoted to the determination of the asymptotic form of the trace when there is a forcing of the form (−t)β for small negative t and β in the interval (0,1/2). The extended analysis related to negative values of β. The result of this was that the analysis of the earlier article apparently works quite well in the new regime, in which the trace asymptotes the real axis at infinity. For example, a good fit is obtained to equation (38) (without the correction term proportional to d) for β = −0.25.

The authors of this article would like to thank their colleague, Panos Oikonomou, for correcting their error and extending their work.


Dates

Issue 2 (March 2005)



  1. Trace for the Loewner equation with singular forcing

    L P Kadanoff and M Kleine Berkenbusch 2005 Nonlinearity 18 937

  2. Krein space quantization in curved and flat spacetimes

    T Garidi et al 2005 J. Phys. A: Math. Gen. 38 245

  3. Theory of symmetry for a rotational relativistic Birkhoff system

    Luo Shao-Kai et al 2002 Chinese Phys. 11 429

  4. First-order Dirac symmetry operators

    I M Benn and J M Kress 2004 Class. Quantum Grav. 21 427

  5. Projected spin networks for Lorentz connection: linking spin foams and loop gravity

    Etera R Livine 2002 Class. Quantum Grav. 19 5525

  6. A diffuse neutron scattering study of local atomic order and pair interaction potentials in disordered FCC γ-MnNi alloys

    O Moze and T J Hicks 1984 J. Phys. F: Met. Phys. 14 211

  7. A study of energy and effective atomic number dependence of the exposure build-up factors in biological samples

    G S Sidhu et al 2000 J. Radiol. Prot. 20 53

  8. Instabilities in an inductively coupled oxygen plasma

    C S Corr et al 2003 Plasma Sources Sci. Technol. 12 265

  9. A broadband controller for shunt piezoelectric damping of structural vibration

    S Behrens et al 2003 Smart Mater. Struct. 12 18

  10. Self-organization effects and light amplification of collective atomic recoil motion in a harmonic trap

    Lin Zhang et al 2005 J. Opt. B: Quantum Semiclass. Opt. 7 355

View by subject




Export







Please login to access our web services, or create an account if you don't yet have one.

You must have cookies enabled in your web browser to be able to login.

Username
Password

Forgotten your password? Get a new one here.