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    ABSTRACT: Corbard & Thompson analyzed quantitatively the strong radial differential rotation that exists in a thin layer near the solar surface. We investigate the role of this radial shear in driving a flux transport dynamo operating with such a rotation profile. We show that despite being strong, near-surface radial shear effectively contributes only ∼1 kG (∼30% of the total) to the toroidal fields produced there unless an abnormally high, surface a-effect is included. While 3 kG spot formation from ∼1–2 kG toroidal fields by convective collapse cannot be ruled out, the evolutionary pattern of these model fields indicates that the polarities of spots formed from the near-surface toroidal field would violate the observed polarity relationship with polar fields. This supports previous results that large-scale solar dynamos generate intense toroidal fields in the tachocline, from which buoyant magnetic loops rise to the photosphere to produce spots. Polar fields generated in flux transport models are commonly much higher than observed. We show here that by adding enhanced diffusion in the supergranulation layer (originally proposed by Leighton), near-surface toroidal fields undergo large diffusive decay preventing spot formation from them, as well as reducing polar fields closer to the observed values. However, the weaker polar fields lead to the regeneration of a toroidal field of less than ∼10 kG at the convection zone base, too weak to produce spots that emerge in low latitudes, unless an additional poloidal field is produced at the tachocline. This is achieved by a tachocline a-effect, previously shown to be necessary for coupling the north and south hemispheres to ensure toroidal and poloidal fields that are antisymmetric about the equator.
    The Astrophysical Journal 02/2016; 575(1):41-45. DOI:10.1086/342555
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    ABSTRACT: In this paper, we consider the use of an efficient null space algorithm for hydraulic analysis that employs preconditioned conjugate gradient (PCG) methods for solving the Newton linear equations. Since large water network models are inherently badly conditioned, a Jacobian regularization is employed to improve the condition number to some degree, this resulting in an inexact Newton method whose analyses is presented. Based on this analysis, constraint preconditioners are used to improve the condition number further for more efficient use of CG solvers. Operational networks are used to study the computational properties of the various approaches.
    Procedia Engineering 12/2015; 119(1):623-632. DOI:10.1016/j.proeng.2015.08.915
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    ABSTRACT: Hydraulic resilience can be formulated as a measure of the ability of a water distribution network to maintain a minimum level of service under operational and failure conditions. This paper explores a hybrid approach to bridge the gap between graph-theoretic and hydraulic measures of resilience. We extend the concept of geodesic distance of a pipeline by taking into account energy losses associated with flow. New random-walk algorithms evaluate hydraulically feasible routes and identify nodes with different levels of hydraulic resilience. The nodes with the lowest scores are further analysed by considering the availability and capacity of their supply routes.
    Procedia Engineering 12/2015; 119(1):1241-1248. DOI:10.1016/j.proeng.2015.08.985


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