High-Order Positivity-Preserving Well-Balanced Discontinuous Galerkin Methods for Euler Equations with Gravitation on Unstructured Meshes

In this paper, we propose a high-order accurate discontinuous Galerkin (DG) method for the compressible Euler equations under gravitational fields on unstructured meshes. The scheme preserves a general hydrostatic equilibrium state and provably guarantees the positivity of density and pressure at the same time. Comparing with the work on the well-balanced scheme for Euler equations with gravitation on rectangular meshes, the extension to triangular meshes is conceptually plausible but highly nontrivial. We first introduce a special way to recover the equilibrium state and then design a group of novel variables at the interface of two adjacent cells, which plays an important role in the well-balanced and positivity-preserving properties. One main challenge is that the well-balanced schemes may not have the weak positivity property. In order to achieve the well-balanced and positivity-preserving properties simultaneously while maintaining high-order accuracy, we carefully design DG spatial discretization with well-balanced numerical fluxes and suitable source term approximation. For the ideal gas, we prove that the resulting well-balanced scheme, coupled with strong stability preserving time discretizations, satisfies a weak positivity property. A simple existing limiter can be applied to enforce the positivity-preserving property, without losing high-order accuracy and conservation. Extensive one- and two-dimensional numerical examples demonstrate the desired properties of the proposed scheme, as well as its high resolution and robustness.     

保乳术后放疗中钛夹动度与乳腺大小及钛夹位置的相关性

【摘要】目的:分析保乳术后放疗患者钛夹动度，并探讨其与乳腺大小、钛夹位置的相关性。方法:随机选取保乳术后放疗患者15例，每周两次锥形束CT。测量乳腺基底面直径（D）和乳高轴（H），以瘤床质心为原点将临床靶区分4个象限。记录各象限内钛夹在左右、腹背、头脚方向动度（MLR、MAP、MSI）以及其与临床靶区最内、最前、最上的距离（DSLR、DSAP、DSSI）。结果:MLR、MAP、MSI分别为（2.2±3.0）、（-1.1±3.6）、（0.8±4.7） mm；系统误差Σ在左、右、腹、背、头、脚分别为1.7、2.2、2.0、2.4、2.9、3.0 mm，随机误差σ分别为2.4、4.0、3.2、4.0、4.7、4.7 mm；靶区对应外放5.9、8.3、7.2、8.8、10.5、10.9 mm。一象限内，当D×H<99.89 cm2，MAP和D×H强相关（r=0.805），MLR、MAP均和DSLR、DSAP、DSSI强正相关（r=0.94, 0.94, 0.91；0.87, 0.91, 0.92），MSI和DSLR、DSAP强正相关（r=0.91, 0.94）；四象限内，当D×H<90.71 cm2，MAP和DSLR，MSI和DSAP均强负相关（r=-0.96；-0.95），MLR和DSLR强正相关（r=0.91）。结论:钛夹动度有各向异性，以SI方向外扩最大，并易受乳腺大小、钛夹位置影响。     

A Well-Balanced Positivity-Preserving Quasi-Lagrange Moving Mesh DG Method for the Shallow Water Equations

A high-order, well-balanced, positivity-preserving quasi-Lagrange moving mesh DG method is presented for the shallow water equations with non-flat bottom topography. The well-balance property is crucial to the ability of a scheme to simulate perturbation waves over the lake-at-rest steady state such as waves on a lake or tsunami waves in the deep ocean. The method combines a quasi-Lagrange moving mesh DG method, a hydrostatic reconstruction technique, and a change of unknown variables. The strategies in the use of slope limiting, positivity-preservation limiting, and change of variables to ensure the well-balance and positivity-preserving properties are discussed. Compared to rezoning-type methods, the current method treats mesh movement continuously in time and has the advantages that it does not need to interpolate flow variables from the old mesh to the new one and places no constraint for the choice of a update scheme for the bottom topography on the new mesh. A selection of one- and two-dimensional examples are presented to demonstrate the well-balance property, positivity preservation, and high-order accuracy of the method and its ability to adapt the mesh according to features in the flow and bottom topography.     

Hernias de la incisión de asistencia tras resección colorrectal laparoscópica. Influencia de la localización de la incisión y del uso de una malla profiláctica

Objectives

To determine the incidence of incisional hernia (IH) in the extraction incision (EI) in colorectal resection for cancer. To analyze whether the location of the incision has any relationship with the incidence of hernias and whether mesh could be useful for prevention in high-risk patients.

Treatment of skeletal open bite using a navigation system: CAD/CAM osteotomy and drilling guides combined with pre-bent titanium plates

Severe skeletal open bite associated with posterior vertical maxillary excess and mandibular deformity is considered a difficult problem in orthodontic and surgical treatment. This study used a navigation system for the correction of severe skeletal open bite in order to accurately transfer the virtual plan to the actual operation and achieve precise rigid internal fixation in bimaxillary osteotomies of the jaws. Twelve patients with a severe skeletal open bite associated with vertical maxillary excess and mandibular deformity were recruited. All patients underwent Le Fort I osteotomy and bilateral sagittal split ramus osteotomy with the guidance of this navigation system. Computed tomography and cephalometric examinations were performed to evaluate the correction of the deformity. Deviations between the simulated plan and actual postoperative outcome were measured to determine the precision of the surgery. Satisfactory and stable results were achieved in all patients postoperatively, without complications or relapse during follow-up. Photographs and cephalometric evaluations showed that the facial profile and occlusion were improved. Assessment of the deviations between the simulated plan and actual postoperative outcome showed that the navigation system can precisely transfer the virtual plan to the actual operation. The results suggest that the navigation system can accurately transfer the virtual plan to the actual operation during bimaxillary jaw osteotomies, without relapse, in patients with a severe skeletal open bite.     

青年腹股沟疝治疗中补片修补存在的问题及组织修补的价值

世界卫生组织定义青年为14~25岁，而这一年龄段的腹股沟疝病人还处于身体发育期具有特殊的生理特点以及对生育功能保护的特殊需求，所以对其应谨慎选择修补方法。合成补片存在无法随生长发育一同延展、瘢痕过度增生压迫输精管以及远期侵袭等问题，生物补片也存在远期复发或局部膨隆的风险。对于青年人群，规范的组织修补手术可以良好地修补缺损，配合合理的围手术期管理，也可以最大限度地减轻术后早期张力过大所引起的不适感。同时，组织修补可以适应身体的生长，对生殖功能的影响相对较小，必要情况下也可以配合生物材料修补较大的缺损。术者熟练掌握技术后，组织修补的复发率是可以接受的。所以组织修补对于青年腹股沟疝病人的治疗，具有不可替代的价值。