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Abstract We study the properties of sub-Alfvénic magnetohydrodynamic (MHD) turbulence, i.e., turbulence with Alfvén mach numberM_A=V_L/V_A< 1, whereV_Lis the velocity at the injection scale andV_Ais the Alfvén velocity. We demonstrate that MHD turbulence can have different properties, depending on whether it is driven by velocity or magnetic fluctuations. If the turbulence is driven by isotropic bulk forces acting upon the fluid, i.e., is velocity driven, in an incompressible conducting fluid we predict that the kinetic energy is $M_{\mathrm{A}}^{-2}$times larger than the energy of magnetic fluctuations. This effect arises from the long parallel wavelength tail of the forcing, which excites modes withk_∥/k_⊥<M_A. We also predict that as the MHD turbulent cascade reaches the strong regime, the energy of slow modes exceeds the energy of Alfvén modes by a factor $M_{\mathrm{A}}^{-1}$. These effects are absent if the turbulence is driven through magnetic fluctuations at the injection scale. We confirm our predictions with numerical simulations. Since the assumption of magnetic and kinetic energy equipartition is at the core of the Davis–Chandrasekhar–Fermi (DCF) approach to measuring magnetic field strength in sub-Alfvénic turbulence, we conclude that the DCF technique is not universally applicable. In particular, we suggest that the dynamical excitation of long azimuthal wavelength modes in the galactic disk may compromise the use of the DCF technique. We discuss alternative expressions that can be used to obtain magnetic field strength from observations and consider ways of distinguishing the cases of velocity and magnetically driven turbulence using observational data. 

Abstract Magnetic fields and their dynamical interplay with matter in galaxy clusters contribute to the physical properties and evolution of the intracluster medium. However, the current understanding of the origin and properties of cluster magnetic fields is still limited by observational challenges. In this article, we map the magnetic fields at hundreds-kpc scales of five clusters RXC J1314.4-2515, Abell 2345, Abell 3376, MCXC J0352.4-7401, and El Gordo using the synchrotron intensity gradient technique in conjunction with high-resolution radio observations from the Jansky Very Large Array (JVLA) and the Karoo Array Telescope (MeerKAT). We demonstrate that the magnetic field orientation of radio relics derived from synchrotron intensity gradient is in agreement with that obtained with synchrotron polarization. Most importantly, the synchrotron intensity gradient is not limited by Faraday depolarization in the cluster central regions and allows us to map magnetic fields in the radio halos of RXC J1314.4-2515 and El Gordo. We find that magnetic fields in radio halos exhibit a preferential direction along the major merger axis and show turbulent structures at higher angular resolution. The results are consistent with expectations from numerical simulations, which predict turbulent magnetic fields in cluster mergers that are stirred and amplified by matter motions. 

Abstract Background Coronavirus Disease 2019 (COVID-19) led to pandemic that affected almost all countries in the world. Many countries have implemented border restriction as a public health measure to limit local outbreak. However, there is inadequate scientific data to support such a practice, especially in the presence of an established local transmission of the disease. Objective To apply a metapopulation Susceptible-Exposed-Infectious-Recovered (SEIR) model with inspected migration to investigate the effect of border restriction as a public health measure to limit outbreak of coronavirus disease 2019. Methods We apply a modified metapopulation SEIR model with inspected migration with simulating population migration, and incorporating parameters such as efficiency of custom inspection in blocking infected travelers in the model. The population sizes were retrieved from government reports, while the number of COVID-19 patients were retrieved from Hong Kong Department of Health and China Centre for Disease Control (CDC) data. The R 0 was obtained from previous clinical studies. Results Complete border closure can help to reduce the cumulative COVID-19 case number and mortality in Hong Kong by 13.99% and 13.98% respectively. To prevent full occupancy of isolation facilities in Hong Kong; effective public health measures to reduce local R 0 to below 1.6 was necessary, apart from having complete border closure. Conclusions Early complete travel restriction is effective in reducing cumulative cases and mortality. However, additional anti-COVID-19 measures to reduce local R 0 to below 1.6 are necessary to prevent COVID-19 cases from overwhelming hospital isolation facilities.