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Published in Carl W. Hall, Laws and Models, 2018
LUMINOSITY PERIOD FOR CEPHEIDS, LAW OF Cepheid variables (stars that have a regular period of light pulsation) have an absolute brightness or luminosity, which is connected by a fixed law to the period of their light variation, with the relative distance related to their apparent brightness, m: M = m + 5 – 5 log d where M = brightness or luminosity m = apparent brightness d = relative distance Keywords: brightness, cepheid, light, luminosity Source: Thewlis, J. 1961-1964. LUNDQUIST NUMBER, Lu OR NLu A dimensionless group in magnetohydrodynamics used to characterize unidirectional Alfvn waves: Lu = L (/)1/2 where = magnetic flux density = electrical conductivity L = fluid layer thickness = magnetic permeability = mass density Keyword: electrical, magnetic, magnetohydrodynamics Sources: Bolz, R. E. and Tuve, G. L. 1970; Chemical Engineering Progress 59(8):75, 1963; Jerrard, H. G. and McNeill, D. B. 1992; Land, N. S. 1972; Lerner, R. G. and Trigg, G. L. 1991; Parker, S. P. 1992; Potter, J. H. 1967. See also ALFVN LUSSER PRODUCT LAW OF RELIABILITIES When the reliability of components is Rn, the reliability of the system, Rsystem, is the product of the reliabilities of the components, which points to the need for high reliabilities of components if the system reliability is to be high: Rsystem = R1 R2 R3 ... Rn Keywords: components, reliability, system LUSSER, Robert, German space scientist during WWII Source: Bazovsky, I. 1961; See also EXPONENTIAL FAILURE; PRODUCT LAW; RELIABILITY LYASHCHENKO NUMBER, Ly OR NLy (c. 1964) A dimensionless group in fluidization: Ly = NRe3/NAr where NRe = Reynolds number NAr = Archimedes number Keywords: dimensionless group, fluidization Sources: Bolz, R. E. and Tuve, G. L. 1970; Parker, S. P. 1992; Potter, J. H. 1967. See also ARCHIMEDES; REYNOLDS
The DRESDYN project: liquid metal experiments on dynamo action and magnetorotational instability
Published in Geophysical & Astrophysical Fluid Dynamics, 2019
F. Stefani, A. Gailitis, G. Gerbeth, A. Giesecke, Th. Gundrum, G. Rüdiger, M. Seilmayer, T. Vogt
The construction of the liquid-sodium MRI/TI experiment (figure 6) relies on our experience with HMRI and AMRI gained at the PROMISE facility, and with the TI experiment. One of the main constructional challenges of the new device is to combine a sophisticated mechanical configuration of split end-rings (which is necessary for the MRI part) with appropriate electrical contacts for applying the internal currents that are needed for the TI. As shown by Rüdiger et al. (2003), MRI for liquid sodium starts at a magnetic Reynolds number of Rm=21 and a Lundquist number of Lu=4.4 (both values correspond to the more conservative estimate for different electrical boundary conditions). With a height of the active Tayler–Couette cell of 2 m (figure 2(b)), and an outer radius of 0.4 m, we plan to reach a rotation rate of the inner cylinder of 20 Hz and an axial field of 130 mT, which is in either case more than double the critical value. With view on the safety issues when dealing with one ton of liquid sodium, one of the most critical aspects is the driving of the inner cylinder. For that purpose, a sophisticated magnetic coupler (figure 6(c)) has been developed and already tested, which ensures a hermetic seal of the entire experiment. Another critical part of the experiment is the large coil for generating the axial magnetic field. Great effort was spent to make this field as homogeneous as possible. The resulting construction weighs 5 tons, and will require around 120 kW of electrical power.
Magnetorotational instability in Taylor-Couette flows between cylinders with finite electrical conductivity
Published in Geophysical & Astrophysical Fluid Dynamics, 2018
G. Rüdiger, M. Schultz, F. Stefani, R. Hollerbach
For flatter rotation profiles–for example, the flow with , i.e. uniform linear velocity –the scaling for small changes dramatically. The neutral-stability curves now converge in the () plane formed by the Lundquist number and the magnetic Reynolds number as the cordinates. Note that this is – except for the Rayleigh limit – also true for the standard magnetorotational instability (MRI) with axial magnetic fields. The immediate consequence is that for small – the relevant limit for liquid metals – laboratory experiments to probe the existence of MRI or AMRI are very difficult. Such experiments, however, are needed to get data for the instability-induced angular momentum transport in astrophysically relevant parameter regimes that are hardly accessible to numerics (see Rüdiger et al.2018a).
An Open Boundary Condition for High-order Solutions of Magnetohydrodynamics on Unstructured Grids
Published in International Journal of Computational Fluid Dynamics, 2020
Xiaoliang Zhang, Chunlei Liang
As shown in the above magnetic reconnection simulations, the Sweet-Parker current is indeed unstable once the Lundquist number exceeds a critical value. However, as discussed above, the theoretical scaling relation for the reconnection rate with S, i.e. , has an intrinsic problem due to the contradictory fact that an infinitely large Lundquist number would lead to infinitely fast instabilities. In an ideal MHD model, such a magnetic reconnection rate is impossible. The recent ideal tearing instability theory provides a new perspective that can resolve this paradoxical issue very nicely. For the purpose of demonstration, the ideal tearing mode instability is reproduced using the same test cases investigated by Del Zanna et al. (2016). The results obtained from simulations in this paper agree very well with those provided in Del Zanna et al (2016) at both linear and nonlinear stages. The initial conditions with a small perturbation on velocity fields are shown below, where the pressure ratio is set to , the width of current sheet is the Lundquist number is set to the perturbation magnitude is specified as while the wave number is computed from with . The periodic and open boundary conditions are chosen along x and y directions, respectively. The rectangular domain size is . The number of grid cells is . The fifth-order FR scheme is employed. The evolution of magnetic reconnection is shown in Figures 19 and 20. In the first snapshot, the process is still in the linear stage with mode dominating the current sheet. When the tearing instability growth is over, the nonlinear phase sets in leading to further reconnection events and island coalescence as shown at the second and third snapshot. At this stage one can clearly observe the process leading to the creation of a single, large magnetic island as arising from coalescence. The whole process is very dynamic with the explosive creation of smaller and smaller islands. The small-scale islands then move towards the largest one, which is continually fed and agglomerating and thus continuously enlarges its size. Such a cascading explosive magnetic reconnection process is reminiscent of the flaring activity.