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A trio of simple optimized axisymmetric kinematic dynamos in a sphere.

ABSTRACT: Planetary magnetic fields are generated by the motion of conductive fluid in the planet's interior. Complex flows are not required for dynamo action; simple flows have been shown to act as efficient kinematic dynamos, whose physical characteristics are more straightforward to study. Recently, Chen et al. (2018, J. Fluid Mech. 839, 1-32. (doi:10.1017/jfm.2017.924)) found the optimal, unconstrained kinematic dynamo in a sphere, which, despite being of theoretical importance, is of limited practical use. We extend their work by restricting the optimization to three simple two-mode axisymmetric flows based on the kinematic dynamos of Dudley & James (1989, Proc. R. Soc. Lond. A 425, 407-429. (doi:10.1098/rspa.1989.0112)). Using a Lagrangian optimization, we find the smallest critical magnetic Reynolds number for each flow type, measured using an enstrophy-based norm. A Galerkin method is used, in which the spectral coefficients of the fluid flow and magnetic field are updated in order to maximize the final magnetic energy. We consider the t 0 1 s 0 1, t 0 1 s 0 2 and t 0 2 s 0 2 flows and find enstrophy-based critical magnetic Reynolds numbers of 107.7, 142.4 and 125.5 (13.7, 19.6 and 16.4, respectively, with the energy-based definition). These are up to four times smaller than the original flows. These simple and efficient flows may be used as benchmarks in future studies.

SUBMITTER: Holdenried-Chernoff D

PROVIDER: S-EPMC6784403 | biostudies-literature | 2019 Sep

REPOSITORIES: biostudies-literature

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A trio of simple optimized axisymmetric kinematic dynamos in a sphere.

Holdenried-Chernoff D D Chen L L Jackson A A

Proceedings. Mathematical, physical, and engineering sciences 20190918 2229

Planetary magnetic fields are generated by the motion of conductive fluid in the planet's interior. Complex flows are not required for dynamo action; simple flows have been shown to act as efficient kinematic dynamos, whose physical characteristics are more straightforward to study. Recently, Chen et al. (2018, J. Fluid Mech. 839, 1-32. (doi:10.1017/jfm.2017.924)) found the optimal, unconstrained kinematic dynamo in a sphere, which, despite being of theoretical importance, i ...[more]

PMID: 31611726

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Project description:BACKGROUND:Since walking is a daily activity not to require the maximal effort in healthy populations, a very few universal bio-parameters and/or methods have been defined to evaluate individual walking characteristics in those populations. A concept of "economy" is a potential candidate; however, walking economy highly depends on speed, so direct comparisons of economy values are difficult between studies. We investigated whether the vertical component of net walking "efficiency" (Effvert; %) is constant across speed. In that case, direct comparisons of Effvert will be possible between studies or individuals at any voluntary speed. METHODS:Thirty young male participants walked at eight speeds on the level or ± 5% gradients, providing vertical speeds (vvert). Differences in energy expenditure between level and uphill or downhill gradients (?EE) were calculated. The metabolic rate for vertical component (MRvert) was calculated by multiplying ?EE with body mass (BM). The mechanical power output for vertical component (Pmech) was calculated by multiplying BM, gravitational acceleration, and vvert. Effvert was obtained from the ratio of Pmech to MRvert at each vvert. Delta efficiency (Delta-E; %) was also calculated from the inverse slope of the regression line representing the relationship of Pmech to MRvert. RESULTS:Upward Effvert was nearly constant at around 35% and downward Effvert ranged widely (49-80%). No significant differences were observed between upward Delta-E (35.5 ± 8.8%) and Effvert at any speeds, but not between downward Delta-E (44.9 ± 12.8%) and Effvert. CONCLUSIONS:Upward ?EE could be proportional to vvert. Upward, but not downward, Effvert should be useful not only for healthy populations but also for clinical patients to evaluate individual gait characteristics, because it requires only two metabolic measurements on the level and uphill gradients without kinematic information at any voluntary speed. TRIAL REGISTRATION:UMIN000017690 (R000020501; registered May 26th, 2015, before the first trial) and UMIN000031456 (R000035911; registered Feb. 23rd, 2018, before the first trial).

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A trio of simple optimized axisymmetric kinematic dynamos in a sphere.

Publications

A trio of simple optimized axisymmetric kinematic dynamos in a sphere.

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