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  1. Abstract

    Mimetic finite difference operators$$\textbf{D}$$D,$$\textbf{G}$$Gare discrete analogs of the continuous divergence (div) and gradient (grad) operators. In the discrete sense, these discrete operators satisfy the same properties as those of their continuum counterparts. In particular, they satisfy a discrete extended Gauss’ divergence theorem. This paper investigates the higher-order quadratures associated with the fourth- and sixth- order mimetic finite difference operators, and show that they are indeed numerical quadratures and satisfy the divergence theorem. In addition, extensions to curvilinear coordinates are treated. Examples in one and two dimensions to illustrate numerical results are presented that confirm the validity of the theoretical findings.

     
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    Free, publicly-accessible full text available December 1, 2024
  2. Real-time fall detection using a wearable sensor remains a challenging problem due to high gait variability. Furthermore, finding the type of sensor to use and the optimal location of the sensors are also essential factors for real-time fall-detection systems. This work presents real-time fall-detection methods using deep learning models. Early detection of falls, followed by pneumatic protection, is one of the most effective means of ensuring the safety of the elderly. First, we developed and compared different data-segmentation techniques for sliding windows. Next, we implemented various techniques to balance the datasets because collecting fall datasets in the real-time setting has an imbalanced nature. Moreover, we designed a deep learning model that combines a convolution-based feature extractor and deep neural network blocks, the LSTM block, and the transformer encoder block, followed by a position-wise feedforward layer. We found that combining the input sequence with the convolution-learned features of different kernels tends to increase the performance of the fall-detection model. Last, we analyzed that the sensor signals collected by both accelerometer and gyroscope sensors can be leveraged to develop an effective classifier that can accurately detect falls, especially differentiating falls from near-falls. Furthermore, we also used data from sixteen different body parts and compared them to determine the better sensor position for fall-detection methods. We found that the shank is the optimal position for placing our sensors, with an F1 score of 0.97, and this could help other researchers collect high-quality fall datasets.

     
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  3. To address practical challenges in establishing and maintaining robust wireless connectivity such as multi-path effects, low latency, size reduction, and high data rate, we have deployed the digital beamformer, as a spatial filter, by using the hybrid antenna array at an operating frequency of 10 GHz. The proposed digital beamformer utilizes a combination of the two well-established beamforming techniques of minimum variance distortionless response (MVDR) and linearly constrained minimum variance (LCMV). In this case, the MVDR beamforming method updates weight vectors on the FPGA board, while the LCMV beamforming technique performs nullsteering in directions of interference signals in the real environment. The most well-established machine learning technique of support vector machine (SVM) for the Direction of Arrival (DoA) estimation is limited to problems with linearly-separable datasets. To overcome the aforementioned constraint, the quadratic surface support vector machine (QS-SVM) classifier with a small regularizer has been used in the proposed beamformer for the DoA estimation in addition to the two beamforming techniques of LCMV and MVDR. In this work, we have assumed that five hybrid array antennas and three sources are available, at which one of the sources transmits the signal of interest. The QS-SVM-based beamformer has been deployed on the FPGA board for spatially filtering two signals from undesired directions and passing only one of the signals from the desired direction. The simulation results have verified the strong performance of the QS-SVM-based beamformer in suppressing interference signals, which are accompanied by placing deep nulls with powers less than −10 dB in directions of interference signals, and transferring the desired signal. Furthermore, we have verified that the performance of the QS-SVM-based beamformer yields other advantages including average latency time in the order of milliseconds, performance efficiency of more than 90%, and throughput of nearly 100%.

     
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  4. A short-term side-effect of CO2 injection is a developing low-pH front that forms ahead of the bulk water injectant, due to differences in solute diffusivity. Observations of downhole well temperature show a reduction in aqueous-phase temperature with the arrival of a low-pH front, followed by a gradual rise in temperature upon the arrival of a high concentration of bicarbonate ion. In this work, we model aqueous-phase transient heat advection and diffusion, with the volumetric energy generation rate computed from solute-solvent interaction using the Helgeson–Kirkham–Flowers (HKF) model, which is based on the Born Solvation model, for computing specific molar heat capacity and the enthalpy of charged electrolytes. A computed injectant water temperature profile is shown to agree with the actual bottom hole sampled temperature acquired from sensors. The modeling of aqueous-phase temperature during subsurface injection simulation is important for the accurate modeling of mineral dissolution and precipitation because forward dissolution rates are governed by a temperature-dependent Arrhenius model. 
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