Troubled-Cell Indicator Based on Mean Value Property for Hybrid WENO Schemes

In this paper, we introduce a new type of troubled-cell indicator to improve hybrid weighted essentially non-oscillatory (WENO) schemes for solving the hyperbolic conservation laws. The hybrid WENO schemes selectively adopt the high-order linear upwind scheme or the WENO scheme to avoid the local characteristic decompositions and calculations of the nonlinear weights in smooth regions. Therefore, they can reduce computational cost while maintaining non-oscillatory properties in non-smooth regions. Reliable troubled-cell indicators are essential for efficient hybrid WENO methods. Most of troubled-cell indicators require proper parameters to detect discontinuities precisely, but it is very difficult to determine the parameters automatically. We develop a new troubled-cell indicator derived from the mean value theorem that does not require any variable parameters. Additionally, we investigate the characteristics of indicator variable; one of the conserved properties or the entropy is considered as indicator variable. Detailed numerical tests for 1D and 2D Euler equations are conducted to demonstrate the performance of the proposed indicator. The results with the proposed troubled-cell indicator are in good agreement with pure WENO schemes. Also the new indicator has advantages in the computational cost compared with the other indicators.     

Learning to Discretize: Solving 1D Scalar Conservation Laws via Deep Reinforcement Learning

Conservation laws are considered to be fundamental laws of nature. It has broad applications in many fields, including physics, chemistry, biology, geology, and engineering. Solving the differential equations associated with conservation laws is a major branch in computational mathematics. The recent success of machine learning, especially deep learning in areas such as computer vision and natural language processing, has attracted a lot of attention from the community of computational mathematics and inspired many intriguing works in combining machine learning with traditional methods. In this paper, we are the first to view numerical PDE solvers as an MDP and to use (deep) RL to learn new solvers. As proof of concept, we focus on 1-dimensional scalar conservation laws. We deploy the machinery of deep reinforcement learning to train a policy network that can decide on how the numerical solutions should be approximated in a sequential and spatial-temporal adaptive manner. We will show that the problem of solving conservation laws can be naturally viewed as a sequential decision-making process, and the numerical schemes learned in such a way can easily enforce long-term accuracy. Furthermore, the learned policy network is carefully designed to determine a good local discrete approximation based on the current state of the solution, which essentially makes the proposed method a meta-learning approach. In other words, the proposed method is capable of learning how to discretize for a given situation mimicking human experts. Finally, we will provide details on how the policy network is trained, how well it performs compared with some state-of-the-art numerical solvers such as WENO schemes, and supervised learning based approach L3D and PINN, and how well it generalizes.     

一种医疗氧舱气路系统设计的改进

本文针对目前医疗氧舱自动化程度不高,各种治疗参数难以定量控制的特点,设计出了以微型计算机为控制核心的医疗氧舱自动供排气系统,并重点介绍了微型计算机的硬件和软件设计。     

防止银器文物变色的唑系复合缓蚀剂Ⅰ. 缓蚀剂成膜处理工艺与防变色性能的评定

:通过按正交法设计的紫外光照曝露等加速大气腐蚀实验 ,研究了用于防止银变色的唑系复合缓蚀剂成膜处理的工艺 ,并评定其对模拟文物银试片的防变色性能。采用极化曲线和交流阻抗Nyquist图 ,讨论了防变色作用的电化学机理。实验结果表明 ,缓蚀剂 PMTA、MBI和 MBO具有较好的协同作用 ,银试片在 5 0°C、p H 3.0、组分 MBO∶ PMTA∶ MBI为 1∶ 1 .7∶ 3(摩尔比 )、复合缓蚀剂浓度为 0 .0 1 89mol/L的溶液中 4h成膜处理后 ,经 48h硫华气氛和 36h紫外光曝露腐蚀实验 ,无色斑出现 ,表明缓蚀膜明显地提高了银试片的抗变色能力     

Determination of Red Blood Cell Velocity by Video Shuttering and Image Analysis

A novel modification of conventional video imaging techniques has been developed to determine the velocity of red blood cells (RBCs), which offers compatibility with existing video-based methods for determining blood oxygenation and hemoglobin concentration. Traditional frame-by-frame analysis of video recordings limits the maximum velocity that can be measured for individual cells in vivo to about 2 mm/s. We have extended this range to about 20 mm/s, by electronic shuttering of an intensified charge-coupled device camera to produce multiple images of a single RBC in the same video frame. RBCs were labeled with fluorescein isothiocyanate and the labeled cells (FRBCs) were used as probes to determine RBC velocities in microvessels of the hamster retractor muscle. Velocity was computed as the product of the distance between centroids of two consecutive image positions of a FRBC and the shuttering frequency of the camera intensifier. In vitro calibrations of the system using FRBC and Sephadex beads coated onto a rotating disk yielded an average coefficient of variation of about 6%. Flow conservation studies at bifurcations indicated that the maximum diameter of microvessels below which all the FRBCs in the lumen could be detected was 50 m. The technique was used to estimate mean-FRBC velocity distributions in vessels with diameters ranging from 8 to 50 m. The mean-FRBC velocity profiles were found to be blunter than would be expected for Poiseuille flow. Single FRBCs tracked along an unbranched arteriole exhibited significant temporal variations in velocity. © 1999 Biomedical Engineering Society. PAC99: 8719Tt, 8717Jj, 4279Pw, 8780Tq, 8719Ff, 4230Va, 0705Pj     

Integration from proteins to organs: the IUPS Physiome Project

The IUPS Physiome Project is an internationally collaborative open source project intended to provide a public domain framework for computational physiology, including the development of modeling standards, computational tools and web-accessible databases of models of structure and function at all spatial scales and across all organ systems. Here, we illustrate the application of this multi-scale modeling approach to three organ systems: the heart, the lungs and the musculo-skeletal system, and in each case we show how the organ level models incorporate tissue and cell-level physiology. Although the computational physiology framework presented here does not yet incorporate models of ageing processes, the model-based approach is certainly capable of describing ageing and disease-related processes both via parameter changes within the models of normal physiological processes and via models of additional processes added to the framework.     

金银花颗粒在旋风分离器中的流场数值模拟分析

目的 针对金银花颗粒在旋风分离器中的运动行为过程进行研究,考察不同设计参数和操作工艺条件下,颗粒在设备内部的运动过程变化规律。方法 基于仿真模拟技术,考察受不同设备长径比、入口进气雷诺数、颗粒质量流量3个因素影响的金银花颗粒在分离器内的运动规律,并以金银花颗粒得粉率为验证指标参数,对模型可靠性进行了分析。结果 通过仿真模拟得到了各个不同工艺条件下的金银花颗粒运动轨迹分布,计算出了对应设备的颗粒得粉率。提出金银花颗粒分离的最佳工艺建议为设备长径比5∶1,入口进气雷诺数3.23×10⁴,颗粒质量流量80.1 mg/s,得到的金银花颗粒得粉率为96.30%。结论 为旋风分离器内金银花颗粒的有关研究提供指导,同时改善旋风分离器在控制和设计上的不足。     

Adaptive Order WENO Reconstructions for the Semi-Lagrangian Finite Difference Scheme for Advection Problem

We present a new conservative semi-Lagrangian finite difference weighted essentially non-oscillatory scheme with adaptive order. This is an extension of the conservative semi-Lagrangian (SL) finite difference WENO scheme in [Qiu and Shu, JCP, 230 (4) (2011), pp. 863-889], in which linear weights in SL WENO framework were shown not to exist for variable coefficient problems. Hence, the order of accuracy is not optimal from reconstruction stencils. In this paper, we incorporate a recent WENO adaptive order (AO) technique [Balsara et al., JCP, 326 (2016), pp. 780-804] to the SL WENO framework. The new scheme can achieve an optimal high order of accuracy, while maintaining the properties of mass conservation and non-oscillatory capture of solutions from the original SL WENO. The positivity-preserving limiter is further applied to ensure the positivity of solutions. Finally, the scheme is applied to high dimensional problems by a fourth-order dimensional splitting. We demonstrate the effectiveness of the new scheme by extensive numerical tests on linear advection equations, the Vlasov-Poisson system, the guiding center Vlasov model as well as the incompressible Euler equations.     

Reducing unnecessary crossmatching for hip fracture patients by accounting for preoperative hemoglobin concentration

BACKGROUNDMaximum surgical blood order schedules were designed to eliminate unnecessary preoperative crossmatching prior to surgery in order to conserve blood bank resources. Most protocols recommend type and cross of 2 red blood cell (RBC) units for patients undergoing surgery for treatment of hip fracture. Preoperative hemoglobin has been identified as the strongest predictor of inpatient transfusion, but current maximum surgical blood order schedules do not consider preoperative hemoglobin values to determine the number of RBC units to prepare prior to surgery. AIMTo determine the preoperative hemoglobin level resulting in the optimal 2:1 crossmatch-to-transfusion (C:T) ratio in hip fracture surgery patients.METHODSIn 2015 a patient blood management (PBM) program was implemented at our institution mandating a single unit-per-occurrence transfusion policy and a restrictive transfusion threshold of < 7 g/dL hemoglobin in asymptomatic patients and < 8 g/dL in those with refractory symptomatic anemia or history of coronary artery disease. We identified all hip fracture patients between 2013 and 2017 and compared the preoperative hemoglobin which would predict a 2:1 C:T ratio in the pre PBM and post PBM cohorts. Prediction profiling and sensitivity analysis were performed with statistical significance set at P < 0.05. RESULTSFour hundred and ninety-eight patients who underwent hip fracture surgery between 2013 and 2017 were identified, 291 in the post PBM cohort. Transfusion requirements in the post PBM cohort were lower (51% vs 33%, P < 0.0001) than in the pre PBM cohort. The mean RBC units transfused per patient was 1.15 in the pre PBM cohort, compared to 0.66 in the post PBM cohort (P < 0.001). The 2:1 C:T ratio (inpatient transfusion probability of 50%) was predicted by a preoperative hemoglobin of 12.3 g/dL [area under the curve (AUC) 0.78 (95% confidence interval (CI), 0.72-0.83), Sensitivity 0.66] in the pre PBM cohort and 10.7 g/dL [AUC 0.78 (95%CI, 0.73-0.83), Sensitivity 0.88] in the post PBM cohort. A 50% probability of requiring > 1 RBC unit was predicted by 11.2g/dL [AUC 0.80 (95%CI, 0.74-0.85), Sensitivity 0.87] in the pre PBM cohort and 8.7g/dL [AUC 0.78 (95%CI, 0.73-0.83), Sensitivity 0.84] in the post-PBM cohort.CONCLUSIONThe hip fracture maximum surgical blood order schedule should consider preoperative hemoglobin in determining the number of units to type and cross prior to surgery.