High-order accurate well-balanced energy stable finite difference schemes for multi-layer shallow water equations on fixed and adaptive moving meshes

This paper develops high-order well-balanced (WB) energy stable (ES) finite difference schemes for multi-layer (the number of layers $M\geqslant 2$) shallow water equations (SWEs) on both fixed and adaptive moving meshes, extending our previous works [20,51]. To obtain an energy inequality, the convexity of an energy function for an arbitrary $M$ is proved by finding recurrence relations of the leading principal minors or the quadratic forms of the Hessian matrix of the energy function with respect to the conservative variables, which is more involved than the single-layer case due to the coupling between the layers in the energy function. An important ingredient in developing high-order semi-discrete ES schemes is the construction of a two-point energy conservative (EC) numerical flux. In pursuit of the WB property, a sufficient condition for such EC fluxes is given with compatible discretizations of the source terms similar to the single-layer case. It can be decoupled into $M$ identities individually for each layer, making it convenient to construct a two-point EC flux for the multi-layer system. To suppress possible oscillations near discontinuities, WENO-based dissipation terms are added to the high-order WB EC fluxes, which gives semi-discrete high-order WB ES schemes. Fully-discrete schemes are obtained by employing high-order explicit SSP-RK methods and proved to preserve the lake at rest. The schemes are further extended to moving meshes based on a modified energy function for a reformulated system, relying on the techniques proposed in [51]. Numerical experiments are conducted for some two- and three-layer cases to validate the high-order accuracy, WB and ES properties, and high efficiency of the schemes, with a suitable amount of dissipation chosen by estimating the maximal wave speed due to the lack of an analytical expression for the eigenstructure of the multi-layer system.Comment: 54 pages, 19 figure

High-order accurate well-balanced energy stable adaptive moving mesh finite difference schemes for the shallow water equations with non-flat bottom topography

This paper proposes high-order accurate well-balanced (WB) energy stable (ES) adaptive moving mesh finite difference schemes for the shallow water equations (SWEs) with non-flat bottom topography. To enable the construction of the ES schemes on moving meshes, a reformulation of the SWEs is introduced, with the bottom topography as an additional conservative variable that evolves in time. The corresponding energy inequality is derived based on a modified energy function, then the reformulated SWEs and energy inequality are transformed into curvilinear coordinates. A two-point energy conservative (EC) flux is constructed, and high-order EC schemes based on such a flux are proved to be WB that they preserve the lake at rest. Then high-order ES schemes are derived by adding suitable dissipation terms to the EC schemes, which are newly designed to maintain the WB and ES properties simultaneously. The adaptive moving mesh strategy is performed by iteratively solving the Euler-Lagrangian equations of a mesh adaptation functional. The fully-discrete schemes are obtained by using the explicit strong-stability preserving third-order Runge-Kutta method. Several numerical tests are conducted to validate the accuracy, WB and ES properties, shock-capturing ability, and high efficiency of the schemes.Comment: 40 pages, 16 figure

Hepcidin as a key iron regulator mediates glucotoxicity-induced pancreatic β-cell dysfunction

It has been well established that glucotoxicity induces pancreatic β-cells dysfunction; however, the precise mechanism remains unclear. Our previous studies demonstrated that high glucose concentrations are associated with decreased hepcidin expression, which inhibits insulin synthesis. In this study, we focused on the role of low hepcidin level-induced increased iron deposition in β-cells and the relationship between abnormal iron metabolism and β-cell dysfunction. Decreased hepcidin expression increased iron absorption by upregulating transferrin receptor 1 (TfR1) and divalent metal transporter 1 (DMT1) expression, resulting in iron accumulation within cells. Prussia blue stain and calcein-AM assays revealed greater iron accumulation in the cytoplasm of pancreatic tissue isolated from db/db mice, cultured islets and Min6 cells in response to high glucose stimulation. Increased cytosolic iron deposition was associated with greater Fe2+ influx into the mitochondria, which depolarized the mitochondria membrane potential, inhibited ATP synthesis, generated excessive ROS and induced oxidative stress. The toxic effect of excessive iron on mitochondrial function eventually resulted in impaired insulin secretion. The restricted iron content in db/db mice via reduced iron intake or accelerated iron clearance improved blood glucose levels with decreased fasting blood glucose (FBG), fasting blood insulin (FIns), HbA1c level, as well as improved intraperitoneal glucose tolerance test (IPGTT) results. Thus, our study may reveal the mechanism involved in the role of hepcidin in the glucotoxcity impaired pancreatic β cell function pathway

Correction : Control of PD-L1 expression by miR-140/142/340/383 and oncogenic activation of the OCT4-miR-18a pathway in cervical cancer.

This research was supported by a grant from the Department of Women’s Health Educational System, JSPS Grant-in-Aid for Scientific Research (C) (15K10697 and 16K11123) and the Science and Technology Planning Project of Guangdong Province, China (2014A020212124). We thank Dr. Zhujie Xu for experimental assistance. The authors declare that they have no conflict of interest.Peer reviewedPublisher PD