The nonlinear evolution of the m/n = 2/1 double tearing mode (DTM) is investigated by the toroidal resistive magnetohydrodynamic code CLT. It is found that the m/n = 2/1 DTM can lead to either a core pressure crash or an off-axis pressure crash. Unlike the core pressure crash, the plasma pressure at the magnetic axis remains almost unchanged during the off-axis pressure crash. The pressure crash only occurs in the annular region during the off-axis crash, and the on-axis plasma pressure slowly reduces after the crash, which is consistent with TFTR observations. A series of simulations are carried out to investigate the influence of the radial position of the inner resonant surface r1, the magnetic shear at the inner resonance surface, and the spatial separation between the two resonant surfaces on nonlinear behaviors of DTMs. We find that r1 plays a dominant role in the nonlinear DTM behaviors. It is more likely for the DTM to lead to the core pressure crash with a smaller r1. It is also found that the magnetic shear at the inner resonant surface and the spatial separation between the two resonant surfaces can also largely influence the nonlinear evolution of the DTM. A simple theoretical formula of the transition criterion between the two pressure crashes is proposed, which agrees well with the simulation results.

In this paper, we study the almost global existence and uniqueness of the small solution for the two‐dimensional (2D) magnetohydrodynamics (MHD) boundary layer system with small initial data, which are analytic in the x variable. If the initial data lie within ϵ of a stable shear flow, then we can extend the life span at least up to time Tϵ≥expfalse(ϵ−1false/lnfalse(ϵ−1false)false). The analytical estimates and the nonlinear terms of this system with the special structure play essential roles in proving this result.

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Persistent cloaca (PC) is the most intricate anorectal malformation. Contrast-enhanced ultrasound (CEUS) is safe for hepatic, renal, splenic, vascular, and intracavitary assessment in children, but it is little applied for cloacal malformation. Our results demonstrate that CEUS can not only display the uterine, vagina, bladder, urethra, rectum, and rectovaginal fistula, but also measure the length of the common channel, bladder neck to the common channel, and distal urethra to the perineum. To our knowledge this may be the first report of preoperative evaluation by CEUS in an infant with PC.

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