Detailed mathematical and numerical analysis of a dynamo model
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..., in parameterisations of transport coefficients in MHD simulations)” (Sood and Kim, 2014)....
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...We propose a dynamical model for the evolution of rotation rate and magnetic field in spindown by extending a previous nonlinear dynamo model (Sood & Kim, 2013, 2014; Weiss et al. 1984)....
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...In particular, Sood & Kim (2013, 2014) incorporated various nonlinear transport coefficients such as α-quenching and flux losses and took the control parameter D known as the dynamo number to scale with rotation rate as D ∝ Ω2....
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...The parameters ν, ν0, κ and λ1,2 are much the same as in our previous work (Sood & Kim 2013, 2014)....
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...We note that Sood & Kim (2013, 2014) have demonstrated that nonlinear feedback plays a vital role in the generation and destruction of magnetic fields as well as self-regulation of the dynamo....
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...To this end, we evolve the stellar rotation and magnetic field simultaneously over the stellar evolution time by extending our previous work (Sood & Kim 2013, 2014) which incorporates the nonlinear feedback mechanisms on rotation and magnetic fields via α-quenching and magnetic flux losses as well…...
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References
32 citations
"Detailed mathematical and numerical..." refers background or result in this paper
...The precise dependence of differential rotation on rotation is quite uncertain since ΔΩ ∝ Ωn where 0 < n < 1 (Fröhlich et al. 2009; Hotta & Yokoyama 2011; Donahue et al. 1996; Reiners & Schmitt 2003; Barnes et al. 2005)....
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...Furthermore, the time variation of differential rotation has been reported in recent work (e.g., Fröhlich et al. 2012; Hotta & Yokoyama 2011)....
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"Detailed mathematical and numerical..." refers background in this paper
...We note that a simple parameterized model has attracted a lot of attention for fusion plasmas as a useful model for understanding regulation and bifurcation (L-H transition), which is crucial for improving plasmas (Zhu et al. 2013; Malkov et al. 2009; Kim & Diamond 2003)....
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12 citations
"Detailed mathematical and numerical..." refers background in this paper
...…revealed that with a certain set of conditions, low-order models are able to capture the basic behaviour of solar and stellar magnetic fields (Tobias et al. 1995; Weiss et al. 2001; Mininni et al. 2001; Pontieri et al. 2003; Wilmot-Smith et al. 2005; Passos & Lopes 2008; Lopes & Passos 2009, 2011)....
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9 citations
"Detailed mathematical and numerical..." refers background or methods in this paper
...The nonlinear dynamo model under investigation is the dynamical system consisting of the seven coupled ordinary differential equations (ODE) (Sood & Kim 2013; Weiss et al. 1984), (∂t + F2)A = 2DB,where D = D0 F1 , (1) (∂t + F3)B = i(1 + w0)A − 12iA ∗w, (2) (∂t + ν0)w0 = 1 2 i(A∗B − AB∗), (3) (∂t + ν)w = −iAB, (4) which are given in a dimensionless form....
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...(1)−(4) by timestepping for all complex variable A, B, w, and w0 using ν = 0.5, ν0 = 35.0 for different values of D0 between 1−400 (See Sood & Kim 2013 for more details)....
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...The nonlinear dynamo model under investigation is the dynamical system consisting of the seven coupled ordinary differential equations (ODE) (Sood & Kim 2013; Weiss et al. 1984), (∂t + F2)A = 2DB,where D = D0 F1 , (1) (∂t + F3)B = i(1 + w0)A − 12iA ∗w, (2) (∂t + ν0)w0 = 1 2 i(A∗B − AB∗), (3) (∂t +…...
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...Therefore, dynamo number D0 is scaled with rotation rate Ω as D0 ∝ Ω2 (Sood & Kim 2013)....
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...Finally, we presented how this self-regulatory behaviour comes about in the seventh-order system in the presence of an equal combination of α-quenching, poloidal flux loss, and toroidal flux loss (Sood & Kim 2013), where α-quenching, toroidal flux loss and poloidal flux loss are equally important....
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