IUCAA Preprints

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    Hyperdiffusion in non-linear, large and small-scale turbulent dynamos
    (2011-07-05) Subramanian, Kandaswamy
    The generation of large-scale magnetic fields is generically accompanied by the more rapid growth of small-scale fields. The growing Lorentz force due to these fields back reacts on the turbulence to saturate the mean-field and small-scale dynamos. For the mean-field dynamo, in a quasi-linear treatment of this saturation, it is generally thought that, while the alpha-effect gets renormalised and suppressed by non-linear effects, the turbulent diffusion is left unchanged. We show here that this is not true and the effect of the Lorentz forces, is also to generate additional non-linear hyperdiffusion of the mean field. A combination of such non-linear hyperdiffusion with diffusion at small scales, also arises in a similar treatment of small-scale dynamos, and is crucial to understand its saturation.
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    Non-linear behaviour of the black hole system GRS 1915+ 105
    (2006-02-05) Misra, Ranjeev; Harikrishnan, K. P.; Ambika, G.; et al.
    Using non-lin~ar ti?Ie seri.e~ analysis, along with surrogate data analysis, it is shown that the various types of lon~ t~rI? varla~lbty exhibited by the black hole system GRS 1915+105, can be explained in terms of a ~et~rmlmstlc.n?n-bnear system with some inherent stochastic noise. Evidence is provided for a non-linear limit cycle ongm of one of.the low f~eque~cy QPO detected in the source, while some other types of variability could. be due ~oan underlying low dimensional chaotic system. These results imply that the partial differential equanons which govern the magneto- ~drodynamic flow of the inner accretion disk, can be approximated by a by a small number ( ~ 3 - 5) of non-linear but ordinary differential equations. While this analysis does not reveal the exact nature of these approximate equations, they may be obtained in the future, after results of magneto-hydrodynamic simulation of realistic accretion disks become available.