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Edge dislocations are crucial in understanding both mechanical and electrical transport in solid and are modeled as line distributions of dipole moments. The calculation of the electronic spectrum for the two dimensional dipole, represented by the potential energy V(r,θ)=pcosθ/r, has been the topic of several studies that show significant difficulties in obtaining accurate results. In this work, we demonstrate that the source of these difficulties is a logarithmic contribution to the behavior of the wave function at the origin that was neglected by previous authors. By taking into account this non-analytic deviation of the solution of Schrödinger’s equation, superior results, with the expected rate of convergence, are obtained. This goal is accomplished by “adapting” general algorithms for solving partial derivative differential equations to include the desired asymptotic behavior. We illustrate this principle for the variational principle and finite difference methods. Accurate energies and wave functions are obtained not only for the ground state but also for the first eleven excited states and are useful for designing nanoelectronic devices. This paper demonstrates that augmentary knowledge about analytic properties of the solutions leads to the improved convergence and stability of numerical methods. 

Introduction: Environmental exposure to indoor dust is known to be associated with myriad health conditions, especially among children. Established routes of exposure include inhalation and non-dietary ingestion, which result in the direct exposure of gastrointestinal epithelia to indoor dust. Despite this, little prior research is available on the impacts of indoor dust on the health of human gastrointestinal tissue. Methods: Cultured human colonic (CCD841) cells were exposed for 24 h to standard trace metal dust (TMD) and organic contaminant dust (OD) samples at the following concentrations: 0, 10, 25, 50, 75, 100, 250, and 500 µg/mL. Cell viability was assessed using an MTT assay and protease analysis (glycyl-phenylalanyl-aminofluorocoumarin (GF-AFC)); cytotoxicity was assessed with a lactate dehydrogenase release assay, and apoptosis was assessed using a Caspase-Glo 3/7 activation assay. Results: TMD and OD decreased cellular metabolic and protease activity and increased apoptosis and biomarkers of cell membrane damage (LDH) in CCD841 human colonic epithelial cells. Patterns appeared to be, in general, dose-dependent, with the highest TMD and OD exposures associated with the largest increases in apoptosis and LDH, as well as with the largest decrements in metabolic and protease activities. Conclusions: TMD and OD exposure were associated with markers of reduced viability and increased cytotoxicity and apoptosis in human colonic cells. These findings add important information to the understanding of the physiologic effects of indoor dust exposure on human health. The doses used in our study represent a range of potential exposure levels, and the effects observed at the higher doses may not necessarily occur under typical exposure conditions. The effects of long-term, low-dose exposure to indoor dust are still not fully understood and warrant further investigation. Future research should explore these physiological mechanisms to further our understanding and inform public health interventions. 

Scientific Machine Learning (SciML) is a new multidisciplinary methodology that combines the data-driven machine learning models and the principle-based computational models to improve the simulations of scientific phenomenon and uncover new scientific rules from existing measurements. This article reveals the experience of using the SciML method to discover the nonlinear dynamics that may be hard to model or be unknown in the real-world scenario. The SciML method solves the traditional principle-based differential equations by integrating a neural network to accurately model the nonlinear dynamics while respecting the scientific constraints and principles. The paper discusses the latest SciML models and apply them to the oscillator simulations and experiment. Besides better capacity to simulate, and match with the observation, the results also demonstrate a successful discovery of the hidden physics in the pendulum dynamics using SciML. 

Scientific Machine Learning (SciML) is a new multidisciplinary methodology that combines the data-driven machine learning models and the principle-based computational models to improve the simulations of scientific phenomenon and uncover new scientific rules from existing measurements. This article reveals the experience of using the SciML method to discover the nonlinear dynamics that may be hard to model or be unknown in the real-world scenario. The SciML method solves the traditional principle-based differential equations by integrating a neural network to accurately model the nonlinear dynamics while respecting the scientific constraints and principles. The paper discusses the latest SciML models and apply them to the oscillator simulations and experiment. Besides better capacity to simulate, and match with the observation, the results also demonstrate a successful discovery of the hidden physics in the pendulum dynamics using SciML. 

Indoor dust can be a major source of heavy metals, nutrients, and bacterial contamination in residential environments and may cause serious health problems. The goal of this research is to characterize chemical and bacterial contaminants of indoor, settled house dust in the Houston Metropolitan region. To achieve this, a total of 31 indoor dust samples were collected, along with household survey data, which were subsequently analyzed for elemental and bacterial concentrations. Microscopic and geospatial analysis was conducted to characterize and map potential hotspots of contamination. Interestingly Cd, Cr, Cu, Pb, and Zn concentrations of all 31 indoor dust samples were significantly enriched and exceeded soil background concentrations. Furthermore, As, Cd, Pb, and Zn concentrations in the dust samples were significantly correlated to the enteric bacterial load concentrations. Human health assessment revealed that cancer risk values via ingestion for Cd, Cr, and Ni were greater than the acceptable range. Of our 31 dust sample isolates, three Gram-negative and 16 Gram-positive pathogenic bacteria were identified, capable of causing a wide range of diseases. Our results demonstrate that both chemical and bacterial characterization of indoor dust coupled with spatial mapping is essential to assess and monitor human and ecological health risks. 

and cover changes impact the soil and water quality which are critical for environmental and human health. The goal of this study is to evaluate whether the land cover change along the Tigris River, one of the largest rivers in the Middle East, is causing any heavy metal contamination. The objectives of this study were: (1) To analyze the metal concentrations in the water and soil samples along the Tigris River and (2) identify and map the land cover changes of the Baghdad district. A total of nine water and soil samples were collected from three different Tigris River (TR) sampling locations, namely Gherai´at (TR1), Bab Al Moatham Bridge (TR2), and Karada-Masbah (TR3). Surface soil and water samples were collected, and analyzed for various metal concentrations. Landsat satellite imagery from 1984 and 2018 were analyzed and compared for land cover changes. Our water sample analysis revealed that As, Cd, Cr, Cu, Pb and Zn remained low and are within the permissible limit of WHO standards. Soil samples showed that Cu, and Pb concentrations in TR1 and TR2, respectively were higher compared to other locations. The metal concentrations in both water and soil samples at the sampled locations were at safe levels. Remote sensing analysis revealed that the water surface in the study area increased by about 5.3% while the vegetative surface decreased by 10.3% during the period of 1984 to 2018. Water and vegetative cover increased further in the south of Baghdad, along the Tigris River, compared to the north. The impact of land cover changes and increase in soil metal concentrations are higher on TR2 and TR3 locations. Environmental chemical analysis coupled with geospatial data helps to monitor the impact of land cover changes on water and soil quality by identifying areas vulnerable to change. 

The nonlinearity of activation functions used in deep learning models is crucial for the success of predictive models. Several simple nonlinear functions, including Rectified Linear Unit (ReLU) and Leaky-ReLU (L-ReLU) are commonly used in neural networks to impose the nonlinearity. In practice, these functions remarkably enhance the model accuracy. However, there is limited insight into the effects of nonlinearity in neural networks on their performance. Here, we investigate the performance of neural network models as a function of nonlinearity using ReLU and L-ReLU activation functions in the context of different model architectures and data domains. We use entropy as a measurement of the randomness, to quantify the effects of nonlinearity in different architecture shapes on the performance of neural networks. We show that the ReLU nonliearity is a better choice for activation function mostly when the network has sufficient number of parameters. However, we found that the image classification models with transfer learning seem to perform well with L-ReLU in fully connected layers. We show that the entropy of hidden layer outputs in neural networks can fairly represent the fluctuations in information loss as a function of nonlinearity. Furthermore, we investigate the entropy profile of shallow neural networks as a way of representing their hidden layer dynamics. 

Scattering phenomena between charged particles and highly excited Rydberg atoms are of critical importance in many processes in plasma physics and astrophysics. While a Maxwell–Boltzmann (MB) energy distribution for the charged particles is often assumed for calculations of collisional rate coefficients, in this contribution we relax this assumption and use two different energy distributions, a bimodal MB distribution and a $$\unicode[STIX]{x1D705}$$ -distribution. Both variants share a high-energy tails occurring with higher probability than the corresponding MB distribution. The high-energy tail may significantly affect rate coefficients for various processes. We focus the analysis to specific situations by showing the dependence of the rate coefficients on the principal quantum number of hydrogen atoms in $$n$$ -changing collisions with electrons in the excitation and ionization channels and in a temperature range relevant to the divertor region of a tokamak device. We finally discuss the implications for diagnostics of laboratory plasmas.