Semi-Analytical Numerical Methods for Convection-Dominated Problems with Turning Points

Mechanical EngineeringIn this thesis, we aim to study finite volume approximations which approximate the solutions of convection-dominated problems possessing the so-called interior transition layers. The stiffness of such problems is due to a small parameter multiplied to the highest order derivative which introduces various transition layers at the boundaries and at the interior points where certain compatibility conditions do not meet. Here, we are interested in resolving interior transition layers at turning points. Depending on the characteristics, the latters are identified as turning point layers or characteristic interior layers. The proposed semi-analytic method features interior layer correctors which are obtained from singular perturbation analysis near the turning points. We demonstrate this method is efficient, stable and is of 2nd-order convergence in the approximations.ope

Numerical Methods for Hyperbolic Partial Differential Equations

Department of Mathematical SciencesIn this dissertation, new numerical methods are proposed for different types of hyperbolic partial differential equations (PDEs). The objectives of these developments aim for the improvements in accuracy, robustness, efficiency, and reduction of the computational cost. The dissertation consists of two parts. The first half discusses shock-capturing methods for nonlinear hyperbolic conservation laws, and proposes a new adaptive weighted essentially non-oscillatory WENO-?? scheme in the context of finite difference. Depending on the smoothness of the large stencils used in the reconstruction of the numerical flux, a parameter ?? is set adaptively to switch the scheme between a 5th-order upwind or 6th-order central discretization. A new indicator depending on parameter ?? measures the smoothness of the large stencils in order to choose a smoother one for the reconstruction procedure. ?? is devised based on the possible highest-order variations of the reconstructing polynomials in an L2 sense. In addition, a new set of smoothness indicators ??_k???s of the sub-stencils is introduced. These are constructed in a central sense with respect to the Taylor expansions around point x_j . Numerical results show that the new scheme combines good properties of both 5th-order upwind and 6th-order central schemes. In particular, the new scheme captures discontinuities and resolves small-scaled structures much better than other 5th-order schemes; overcomes the loss of resolution near some critical regions; and is able to maintain symmetry which are drawbacks detected in other 6th-order central WENO schemes. The second part extends the scope to hyperbolic PDEs with uncertainty, and semi-analytical methods using singular perturbation analysis for dispersive PDEs. For the former, a hybrid operator splitting method is developed for computation of the two-dimensional transverse magnetic Maxwell equations in media with multiple random interfaces. By projecting the solutions into random space using the Polynomial Chaos (PC) expansions, the deterministic and random parts of the solution are solved separately. The deterministic parts are then numerically approximated by the FDTD method with domain decomposition implemented on a staggered grid. Statistic quantities are obtained by the Monte Carlo sampling in the post-processing stage. Parallel computing is proposed for which the computational cost grows linearly with the number of random interfaces. The last section deals with spectral methods for dispersive PDEs. The Kortewegde Vries (KdV) equation is chosen as a prototype. By Fourier series, the PDE is transformed into a system of ODEs which is stiff, that is, there are rapid oscillatory modes for large wavenumbers. A new semi-analytical method is proposed to tackle the difficulty. The new method is based on the classical integrating factor (IF) and exponential time differencing (ETD) schemes. The idea is to approximate analytically the stiff parts by the so-called correctors and numerically the non-stiff parts by the IF and ETD methods. It turns out that rapid oscillations are well absorbed by our corrector method, yielding better accuracy in the numerical results. Due to the nonlinearity, all Fourier modes interact with each other, causing the computation of the correctors to be very costly. In order to overcome this, the correctors are recursively constructed to accurately capture the stiffness of the mode interactions.ope

A Rare Colonic Metastasis Case from Hepatocellular Carcinoma

BACKGROUND: Hepatocellularcarcinoma (HCC) metastasis include intrahepatic and extrahepatic metastasis. Similar to intrahepatic metastasis, extrahepatic metastases are not unusual in cases with HCC. However, colonic metastasis is infrequent. CASE REPORT: We describe a clinical case, he was diagnosed with HCC a year ago, treated with TACE (transarterialchemoembolisation), re-examined with abdominal pain and defecation disorder. The tests such as CT scan, colorectal endoscopy, fine needle aspiration (FNA) revealed secondary metastatic lesion of HCC in sigmoid colon. This is the first gastrointestinal (GI) tract metastatic we have encountered. CONCLUSION: HCC metastases of the colon are rare, especially cases of hematogenous spread. The prognosis of these patients is often very critical. Indications for surgical removal of the lesion may be used if the general situation of patient is acceptable

Application of AHP algorithm on power distribution of load shedding in island microgrid

This paper proposes a method of load shedding in a microgrid system operated in an Island Mode, which is disconnected with the main power grid and balanced loss of the electrical power. This proposed method calculates the minimum value of the shed power with reference to renewable energy sources such as wind power generator, solar energy and the ability to control the frequency of the generator to restore the frequency to the allowable range and reduce the amount of load that needs to be shed. Computing the load importance factor (LIF) using AHP algorithm supports to determine the order of which load to be shed. The damaged outcome of load shedding, thus, will be noticeably reduced. The experimental results of this proposed method is demonstrated by simulating on IEEE 16-Bus microgrid system with six power sources

STRESS AND COPING STRATEGIES OF SECONDARY SCHOOL TEACHERS IN TRA CU DISTRICT, TRA VINH PROVINCE, VIETNAM

By using a cross-sectional study, this study aimed to determine the ratio of occupational stress, stress levels and the relationship between stress status and social characteristics of the sample, factors at work, as well as how secondary school teachers respond to stress in Tra Cu District, Tra Vinh Province. The study conducted a survey to investigate 466 teachers currently teaching at 14 secondary schools in Tra Cu District, Tra Vinh Province, from May 2020 to June 2020. Research results showed that the percentage of teachers who suffered mild stress and severe stress was 18.9% and 8.1%, respectively. The signs of stress in teachers correlated with several factors such as job demand, work control and ways of coping at work. When the average score of the assessment “job demand” or “work control” increased by one point, the rate of stress on teachers was reduced by 23% (95% CI: 0.73 – 0.81) and 12% (95% CI: 0.84 – 0.93) respectively. By contrast, the average score of “confrontation” increased by one point  leading to 3.21 times higher (95% CI: 2.61 – 3.96) possibility of causing stress. As well as the average score of "avoidance" increased by one point, the possibility of causing stress in teachers increased 3.03 times (95% CI: 2.45 – 3.74). The findings showed that mental health problems in teachers at secondary schools, in general and in Tra Cu District, Tra Vinh Province in particular, had not received sufficient attention. Therefore, the problems should be taken seriously not only by teachers school administration

Physical therapy for sleep apnea: a smartphone application for home-based physical therapy for patients with obstructive sleep apnea

PurposeIn this study, we described “PT for Sleep Apnea”, a smartphone application for home-based physical therapy of patients with Obstructive Sleep Apnea (OSA).MethodsThe application was created in a joint program between the University of Medicine and Pharmacy at Ho Chi Minh City (UMP), Vietnam, and National Cheng Kung University (NCKU), Taiwan. Exercises maneuvers were derived from the exercise program previously published by the partner group at National Cheng Kung University. They included exercises for upper airway and respiratory muscle training and general endurance training.ResultsThe application provides video and in-text tutorials for users to follow at home and a schedule function to assist the user in organizing the training program, which may improve the efficacy of home-based physical therapy in patients with Obstructive Sleep Apnea.ConclusionIn the future, our group plans to conduct a user study and randomized-controlled trials to investigate whether our application can benefit patients with OSA

TextANIMAR: Text-based 3D Animal Fine-Grained Retrieval

3D object retrieval is an important yet challenging task, which has drawn more and more attention in recent years. While existing approaches have made strides in addressing this issue, they are often limited to restricted settings such as image and sketch queries, which are often unfriendly interactions for common users. In order to overcome these limitations, this paper presents a novel SHREC challenge track focusing on text-based fine-grained retrieval of 3D animal models. Unlike previous SHREC challenge tracks, the proposed task is considerably more challenging, requiring participants to develop innovative approaches to tackle the problem of text-based retrieval. Despite the increased difficulty, we believe that this task has the potential to drive useful applications in practice and facilitate more intuitive interactions with 3D objects. Five groups participated in our competition, submitting a total of 114 runs. While the results obtained in our competition are satisfactory, we note that the challenges presented by this task are far from being fully solved. As such, we provide insights into potential areas for future research and improvements. We believe that we can help push the boundaries of 3D object retrieval and facilitate more user-friendly interactions via vision-language technologies.Comment: arXiv admin note: text overlap with arXiv:2304.0573

Effects of water scarcity awareness and climate change belief on recycled water usage willingness: Evidence from New Mexico, United States

The global water crisis is being exacerbated by climate change, even in the United States. Recycled water is a feasible alternative to alleviate the water shortage, but it is constrained by humans’ perceptions. The current study examines how residents’ water scarcity awareness and climate change belief influence their willingness to use recycled water directly and indirectly. Bayesian Mindsponge Framework (BMF) analytics was employed on a dataset of 1831 residents in Albuquerque, New Mexico, an arid inland region in the US. We discovered that residents’ willingness to use direct recycled potable water is positively affected by their awareness of water scarcity, but the effect is conditional on their belief in the impacts of climate change on the water cycle. Meanwhile, the willingness to use indirect recycled potable water is influenced by water scarcity awareness, and the belief in climate change further enhances this effect. These findings implicate that fighting climate change denialism and informing the public of the water scarcity situation in the region can contribute to the effectiveness and sustainability of long-term water conservation and climate change alleviation efforts