Using Python to Solve the Navier-Stokes Equations - Applications in the Preconditioned Iterative Methods

This article describes a new numerical solver for the Navier-Stokes equations. The proposed solver is written in Python which is a newly developed language. The Python packages are built to solve the Navier-Stokes equations with existing libraries. We have created discretized coefficient matrices from systems of the Navier-Stokes equations by the finite difference method. In addition we focus on the preconditioned Krylov subspace iterative methods in the linearized systems. Numerical results of performances for the Preconditioned iterative methods are demonstrated. The comparison between Python and Matlab is discussed at the end of the paper

Crossmodal emotional modulation of time perception

The thesis that consists of three studies investigated how visual affective stimuli or action as contexts influence crossmodal time processing, particularly on the role of the crossmodal/sensorimotor linkage in time perception. By using different types of emotional stimuli (e.g., threat, disgust, and neutral pictures) and manipulating the possibility of near-body interactions, three studies disassociated the impacts of embodied action from emotional dimensions (arousal and valence) on crossmodal emotional modulation in time perception. The whole thesis thus offered the first behavioral evidence that embodied action is an important factor that expands subjective tactile duration and facilitates tactile selection (modality-specific temporal processing) in emotion and action contexts. Moreover, subjective expansion of duration by threat and action contexts may reflect the evolutionary coupling of our perceptual and motor systems to adapt to the specific environments for survival and success

Phrase Depicting Immoral Behavior Dilates Its Subjective Time Judgment

Intuitive moral emotions play a major role in forming our opinions and moral decisions. However, it is not yet known how we perceive the subjective time of moral-related information. In this study, we compared subjective durations of phrases depicting immoral, disgust, or neutral behaviors in a duration bisection task and found that phrases depicting immoral behavior were perceived as lasting longer than the neutral and disgusting phrases. By contrast, the subjective duration of the disgusting phrase, unlike the immoral phrase, was comparable to the neutral phrase. Moreover, the lengthening effect of the immoral phrase relative to the neutral phrase was significantly correlated to the anonymously prosocial tendency of the observer. Our findings suggest that immoral phrases induce embodied moral reaction, which alters emotional state and subsequently lengthens subjective time

Discovering Geometric and Topological Properties of Ellipsoids by Curvatures

Aims/ Objectives: We are interested in discovering the geometric, topological and physical properties of ellipsoids by analyzing curvature properties on ellipsoids. We begin with studying ellipsoids as a starting point. Our aim is to find a way to study geometric, topological and physical properties from the analytic curvature properties for convex hyper-surfaces in the general setting. Study Design: Multiple-discipline study between Differential Geometry, Topology and Mathematical Physics. Place and Duration of Study: Department of Mathematics (Borough of Manhattan Community College-The City University of New York), Department of Mathematics (University of Oklahoma), Department of Mathematics and Statistics (University of West Florida), and Department of Mathematics (Central Michigan University), between January 2014 and February 2015. Methodology: Calculating curvatures of a surface is now at the threshold of a better understanding regarding geometric, topological and physical properties on a surface. In order to calculate various curvatures, we demonstrate the way to compute the second fundamental form associated with curvatures by extending the calculation method from spheres to ellipsoids. Results: Just as curvatures of a sphere are determined by its radius, curvatures of an ellipsoid are determined by its longest axis and its shortest axis. On an ellipsoid, the value of the ratio of its longest axis to its shortest axis is also a critical index to characterize its geometric, topological and physical behaviors. Conclusion: Our results on ellipsoids are extensions or generalizations of results of Lawson-Simons, Wei, and Simons on spheres, and Kobayashi-Ohnita-Takeuchi on an ellipsoid with “one variable”. Methods and research findings in this paper can lead to future research on convex hyper-surfaces

Microstructure, tensile behavior and oxidation resistance of the two step heat treated Nb- Ti-Si based alloy

Although the temperatures of the hottest section of advanced turbine engines are approaching the limit of nickel-based superalloys, the desire for continued performance improvements for gas turbine engines continues [1]. Nb-Ti-Si based alloys have attracted much attention for their high temperature melting points, relatively low densities and excellent high temperature mechanical properties [2]. In this alloy system, the constitute phases are niobium solid solution (NbSS), silicides (Nb5Si3 and / or Nb3Si) and with / without Cr2Nb. Among these phases, NbSS ensures room temperature fracture toughness and tensile strength, silicides offers high temperature strength, and Cr2Nb provides the oxidation resistance [3].In this study, the Nb-Ti-Si based alloy was firstly prepared by arc-melting and then directional solidification at a rapid speed. Two-step heat treatments were carried out on the directionally solidified Nb-Ti-Si based alloy. The first-step heat treatment was performed at 1375, 1400, 1425 and 1450 °C for 10hours, respectively. According to the microstructure characteristic and their resulting tensile strength, the best condition for the first-step heat treatment is 1425 °C/10 h. Then the second step heat treatment was conducted at 1000, 1100, 1200 and 1300 °C for 50 hours, respectively. The precipitation of nano-scale Cr2Nb particles in the NbSS matrix substantially improved the tensile strength from 850 MPa to 950 MPa, and reduced the weight gain of the alloy from 218.27 to 144.41mg/cm2 by the second step heat treatment at 1000 °C. References [1] B. P. Bewlay, M. R. Jackson, P. R. Subramanian, J. C. Zhao, Metall. Mater. Trans., 34A (2003) 2043-2052 [2] L.N. Jia, J.F. Weng, Z. Li, Z. Hong, L.F. Su, H. Zhang. Mater. Sci. Eng., 623A (2015) 32-37 [3] L. F. Su, L. N. Jia, Y. B. Feng, H. R. Zhang, S. N. Yuan, H. Zhang, Mater. Sci. Eng., 560A(2013) 672-67

Performance evaluation of on-chip wavelength conversion based on InP/In1−x_{1-x}Gax_xAsy_yP1−y_{1-y} semiconductor waveguide platforms

We propose and design the high confinement InP/In1-xGaxAsyP1-y semiconductor waveguides and report the results of effective wavelength conversion based on this platform. Efficient confinement and mode field area fluctuation at different wavelength is analyzed to achieve the high nonlinear coefficient. The numerical results show that nearly zero phase-mismatch condition can be satisfied through dispersion tailoring of InP/In1-xGaxAsyP1-y waveguides, and the wavelength conversion ranging over 40 nm with the maximum conversion efficiency -26.3 dB is achieved for fixing pump power 100 mW. Meanwhile, the influences of the doping parameter y and pumping wavelength on the bandwidth and conversion efficiency are also discussed and optimized. It is indicated the excellent optical properties of the InP/In1-xGaxAsyP1-y waveguides and pave the way towards direct integration telecom band devices on stand semiconductor platforms.Comment: 21 page

Coseismic response characteristics of groundwater temperature and level of Yunnan well network to several earthquakes

Based on the coseismic response data of water temperature and water level of 26 observation wells in Yunnan well network from 2008 to 2023, the coseismic response characteristics of water temperature and water level of each observation well were compared and analyzed with 8 earthquakes that have a significant impact on Yunnan region. The coseismic response mechanism was discussed from the perspectives of seismic wave energy density, lithology, control of fault zone and dynamic coordination. The results indicate that the response of water temperature and water level in the well pattern of Yunnan to the far-field earthquakes is more significant than near earthquakes, with the response primarily concentrated in the middle of Yunnan. The water level exhibits a more pronounced response than the water temperature. The coseismic variation of water level is mainly characterized by oscillation and rise, while the water temperature is mainly characterized by pulses. Dehong Fapa Dian No.22 well and Lijiang Xiangshan well have better seismic reflection performance in Yunnan well pattern. On the other hand, No.06 well in Jianchuan, No.01 well in Huize Gangou Dian, Xiaoshao well in Kunming Guandu District, Dayao geothermal well, and Nanhua Zhen 2 well exhibit weaker coseismic responses compared to the other 21 wells. Further analysis shows that the linear fitting correlation coefficient between seismic wave energy density and epicenter distance is greater than −0.9, which is significantly negative correlation and positive correlation with magnitude, and shows the corresponding relationship between energy density and permeability coefficient. Finally, we analyzed the mechanism of coseismic response of water temperature and water level

Association of Maternal Body Mass Index With Risk of Infant Mortality: A Dose-Response Meta-Analysis

Objective: This study presumed that a high or low bodymass index (BMI)might increase the risk of infant mortality. Therefore, a meta-analysis was performed to systematically assess the association between maternal BMI and the risk of infant mortality. Methods: The electronic databases, including Pubmed, Embase database, and Cochrane Library, were systemically searched by two investigators from inception to November 26th, 2020, with no language restriction. In parallel, a dose-response was assessed. Results: Finally, 22 cohort studies involving 13,532,293 participants were included into this paper, which showed that compared with normal BMI, maternal overweight significantly increased the risks of infant mortality [risk ratio (RR), 1.16; 95% confidence interval (CI), 1.13–1.19], neonatal mortality (RR, 1.23; 95% CI, 1.08–1.39), early neonatal mortality (RR, 1.55; 95% CI, 1.26–1.92) and post-neonatal mortality (RR, 1.18; 95% CI, 1.07–1.29). Similarly, maternal obesity significantly increased the risk of infant mortality (RR, 1.55; 95% CI, 1.41–1.70), neonatal mortality (RR, 1.55; 95% CI, 1.28–1.67), early neonatal mortality (RR, 1.37; 95% CI, 1.13–1.67), and post-neonatal mortality (RR, 1.30; 95% CI, 1.03–1.65), whereas maternal underweight potentially decreased the risk of infant mortality (RR, 0.93; 95% CI, 0.88–0.98). In the dose-response analysis, the risk of infant mortality significantly increased when the maternal BMI was >25 kg/m2. Conclusions: Maternal overweight or obesity significantly increases the risks of infant mortality, neonatal mortality, early neonatal mortality, and post-neonatal mortality compared with normal BMI in a dose-dependentmanner. Besides,maternal underweight will not increase the risk of infant mortality, neonatal mortality, early neonatal mortality, or postneonatal mortality; instead, it tends to decrease the risk of infant mortality. Early weight management may provide potential benefits to infants, and more large-scale prospective studies are needed to verify this finding in the future

Study of a prediction model for acute penetrating artery territory infarction based on machine learning

Objective To evaluate the performance of prediction models for acute penetrating artery territory occlusive cerebral infarction based on machine learning algorithms and select the optimal model， aiming to provide evidence for clinical management of acute penetrating artery territory infarction. Methods A total of 441 patients diagnosed with acute perforator artery territory infarction were enrolled in this study. Patients with incomplete clinical information （n = 10） and multiple cerebral infarctions （n = 28） were excluded， resulting in a final sample size of 403 patients. The outcome variables were divided into two groups： good prognosis （mRS scores of 0-2） and poor prognosis （mRS scores>2）. Univariate and multi-variate Logistic regression （LR） using the stepwise regression method were employed to identify prediction variables. LR， random forest （RF） and support vector machine （SVM） models were utilized to develop a prognostic prediction model. The dataset was further divided randomly into a training set and a test set in a 7：3 ratio. In the test set， the predictive performance of the model for 90-day functional prognosis in patients with BAD （with poor prognosis defined as mRS scores > 2） was evaluated using metric such as the area under the receiver operating characteristic （ROC） curve （AUC）， accuracy， sensitivity and specificity， etc. Results Among 403 patients with BAD， 68.73% of them were male， with an average age of （60.4±11.4） years. Using the stepwise regression method， 7 prediction variables were selected from a pool of 44 variables： white blood cell count， platelet count， blood glucose， cholesterol， history of diabetes mellitus， history of taking hypoglycemic drugs， and history of smoking （all P < 0.05）. The AUC of LR， RF and SVN for predicting clinical prognosis was 0.610， 0.690， and 0.780， respectively. Conclusions Machine learning algorithms have demonstrated certain predictive ability for acute penetrating artery territory infarction. The performance of RF and SVM models （nonlinear models） is superior to traditional logistic regression model （linear model）