Jiawen Luo

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Luo

First Name

Jiawen

ORCID

0000-0003-4736-1404

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Publications1 - 6 of 6

Waves in the Earth's core. III. A perturbative approach to quasi-free-decay modes
Maitra, Matthew; Luo, Jiawen; Jackson, Andrew (2023)
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
We consider the canonical problem of magnetic field decay in an electrically conducting fluid ball. The problem is closely allied to the problem of the decay modes of a rigid ball, and the spatial form of the eigenmodes survives largely intact. The decaying but oscillatory behaviour of the new fluid eigenmodes first discovered by Schmitt a decade ago (and named quasi-free-decay (QFD) modes) is deduced by application of perturbation methods to the case of rapid rotation and a static applied background magnetic field that is uniform and axial. Some, but not all, of the rigid-case poloidal eigenmodes share decay rates with other toroidal modes, necessitating the use of both degenerate and non-degenerate perturbation theory within this paper. The perturbation theory is developed in terms of the Elsasser number Λ (measuring the competition between Coriolis and Lorentz forces), and the analytic results are in striking accord with numerical calculations even when Λ is of O(1). We find linear scaling of the QFD eigenfrequency with Λ and small changes in the decay rate that scale with Λ2. Although the modes are overdamped (quality factor Q<1), they are not strongly overdamped when the applied field is strong Λ∼1.
Understanding small Chinese cities as COVID-19 hotspots with an urban epidemic hazard index
Li, Tianyi; Luo, Jiawen; Huang, Cunrui (2021)
Scientific Reports
Multiple small- to middle-scale cities, mostly located in northern China, became epidemic hotspots during the second wave of the spread of COVID-19 in early 2021. Despite qualitative discussions of potential social-economic causes, it remains unclear how this unordinary pattern could be substantiated with quantitative explanations. Through the development of an urban epidemic hazard index (EpiRank) for Chinese prefectural districts, we came up with a mathematical explanation for this phenomenon. The index is constructed via epidemic simulations on a multi-layer transportation network interconnecting local SEIR transmission dynamics, which characterizes intra- and inter-city population flow with a granular mathematical description. Essentially, we argue that these highlighted small towns possess greater epidemic hazards due to the combined effect of large local population and small inter-city transportation. The ratio of total population to population outflow could serve as an alternative city-specific indicator of such hazards, but its effectiveness is not as good as EpiRank, where contributions from other cities in determining a specific city’s epidemic hazard are captured via the network approach. Population alone and city GDP are not valid signals for this indication. The proposed index is applicable to different epidemic settings and can be useful for the risk assessment and response planning of urban epidemic hazards in China. The model framework is modularized and the analysis can be extended to other nations.
Inviscid Convective Dynamos
Luo, Jiawen (2021)
Waves in the Earth's core. IV. The structure of inviscid torsional oscillations in a spherical shell
Yuan, Longhui; Marti, Philippe David; Luo, Jiawen; et al. (2025)
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
We study the properties of cylindrical oscillations of electrically conducting fluid in the presence of a magnetic field, a phenomenon known in geomagnetism as torsional oscillations (TOs) since their discovery by J. B. Taylor and S. I. Braginsky. The chosen geometry is a spherical shell, consistent with Earth's present-day geometry. We concentrate on the scenario where fluid viscosity is absent in our calculations, but magnetic diffusivity is retained, appropriate to the geophysical conditions in Earth's fluid outer core. Two axisymmetric background magnetic fields that provide the restoring torques to the motions are considered, one of dipole parity and the other of quadrupole parity. The anticipated class of equatorially symmetric (ES) azimuthal motions is joined by an antisymmetric class that exists in the shell geometry but is absent in the full sphere. Compared to previous studies in a full sphere, our results reveal that computing the eigenmodes of TOs in a spherical shell under the inviscid limit is considerably more computationally challenging. Only one large-scale eigenmode exists (filling the whole shell), while many modes with higher frequencies tend to be concentrated inside the tangent cylinder. We complement our inviscid calculations with calculations in which viscosity is retained, and find convergence (with decreasing viscous diffusion) towards the inviscid results.
Waves in the Earth's core. II. Magneto–Coriolis modes
Luo, Jiawen; Marti, Philippe David; Jackson, Andrew (2022)
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Waves in the Earth's core. I. Mildly diffusive torsional oscillations
Luo, Jiawen; Jackson, Andrew (2022)
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Axisymmetric oscillations of fluid in a rapidly rotating whole sphere immersed in a magnetic field can be supported by the elastic tension of the magnetic field lines. This special class of Alfven waves is largely geostrophic (invariant along the rotation axis) and describes a set of normal modes that has been extensively studied in the ideal, lossless case, a limit in which regular solutions do not exist when the background magnetic field is axisymmetric. We study the geophysically relevant limit with parameters such that magnetic diffusion plays a realistic role appropriate to the Earth's core, by choosing a Lundquist number Lu appropriately. We demonstrate for the first time the existence of normal modes in the presence of an axisymmetric background field, and obtain eigenfrequencies and decay rates that lead us to deduce quality factors Q for these modes for two simple background fields of dipole and quadrupole parity. Two scaling behaviours of Q are seen depending on the background field and normal modes' frequency, one scaling as Lu-1/2 and another as Lu, so that likely Q > 10 in the core of the Earth. A one-dimensional theory is presented that is able to capture the frequencies of oscillation quite accurately.

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Jiawen Luo

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