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An iterative numerical scheme is presented for solving a system of two prescribed mean curvature equations, which are coupled together through a Lagrange multiplier ? and a mass conservation constraint. Such a system of nonlinear partial differential equations may arise from modeling the free surface deformation of a full penetration weld pool. By introducing a cost function dV (?), we construct the overall numerical strategy as a secant method that iterates on the value of ?, where the two nonlinear prescribed mean curvature equations are solved during each secant step. We analyze the dependence of the solutions on ?, together with the range of allowable ? values, for a special one-dimensional case. For more general cases, we investigate the convergence behavior by numerical experiments. We have observed in all the test cases that the objective cost function dV (?) is monotonically increasing inside the range of allowable ? values. This ensures a rapid convergence of the numerical scheme, provided that two initial guesses of ? are well chosen. We also report some experience in solving the nonlinear equations. [ABSTRACT FROM AUTHOR]

According to some theories, obstruction of CSF flow produces a pressure drop in the subarachnoid space in accordance with the Bernoulli theorem that explains the development of syringomyelia below the obstruction. However, Bernoulli's principle applies to inviscid stationary flow unlike CSF flow. Therefore, we performed a series of computational experiments to investigate the relationship between pressure drop, flow velocities, and obstructions under physiologic conditions. We created geometric models with dimensions approximating the spinal subarachnoid space with varying degrees of obstruction. Pressures and velocities for constant and oscillatory flow of a viscid fluid were calculated with the Navier-Stokes equations. Pressure and velocity along the length of the models were also calculated by the Bernoulli equation and compared with the results from the Navier-Stokes equations. In the models, fluid velocities and pressure gradients were approximately inversely proportional to the percentage of the channel that remained open. Pressure gradients increased minimally with 35% obstruction and with factors 1.4, 2.2 and 5.0 respectively with 60, 75 and 85% obstruction. Bernoulli's law underestimated pressure changes by at least a factor 2 and predicted a pressure increase downstream of the obstruction, which does not occur. For oscillatory flow the phase difference between pressure maxima and velocity maxima changed with the degree of obstruction. Inertia and viscosity which are not factored into the Bernoulli equation affect CSF flow. Obstruction of CSF flow in the cervical spinal canal increases pressure gradients and velocities and decreases the phase lag between pressure and velocity. [ABSTRACT FROM AUTHOR]

This article examines a 1D incompressible two-fluid model including artificial tensor diffusion. The aim is to obtain a formulation that provides convergent numerical solutions for all flow conditions within the stratified and the stratified wavy flow regime. With appropriate simplifications, the two-fluid model reduces to one momentum balance, one mass conservation and two algebraic equations. It has previously been established that a formulation that is well posed in possessing exclusively real characteristics can be obtained by including an axial diffusion term in the momentum balance. In this article, however, we demonstrate that this is not sufficient to obtain a system suitable for numerical simulations. Although the unbounded growth rates of the standard two-fluid model are eliminated, linear stability theory predicts that infinitesimal wavelengths still experience finite growth. This entails that grid refinement always will result in new unstable wavelengths being resolved. On the other hand, if artificial axial diffusion is added to both the mass and the momentum equations as suggested here, a cut-off wavelength is established below which all wavelengths are stable. Thus, a numerically converging model is formed, which retains the long-wavelength properties of the standard two-fluid model. The conclusions of the mathematical analysis are substantiated by numerical simulations of 1D gravity waves. [ABSTRACT FROM PUBLISHER]

With the increased directional drilling activities in the oil and gas industry, combined with the digital revolution amongst all industry aspects, the need became high to optimize all planning and operational drilling activities. One important step in planning a directional well is to select a directional tool that can deliver the well in a cost-effective manner. Rotary steerable systems (RSS) and positive displacement mud motors (PDM) are the two widely used tools, each with distinct advantages: RSS excels in hole cleaning, sticking avoidance and hole quality in general, while PDM offers versatility and lower operating costs. This paper presents a series of machine learning (ML) models to automate the selection of the optimal directional tool based on offset well data. By processing lithology, directional, drilling performance, tripping and casing running data, the model predicts section time and cost for upcoming wells. Historical data from offset wells were split into training and testing sets and different ML algorithms were tested to choose the most accurate one. The XGBoost algorithm provided the most accurate predictions during testing, outperforming other algorithms. The beauty of the model is that it successfully accounted for variations in formation thicknesses and drilling environment and adjusts tool recommendations accordingly. Results show that no universal rule favors either RSS or PDM; rather, tool selection is highly dependent on well-specific factors. This data-driven approach reduces human bias, enhances decision-making, and could significantly lower field development costs, particularly in aggressive drilling campaigns. [ABSTRACT FROM AUTHOR]

This study investigated the stress concentration phenomenon and the interlaminar stresses of laminated composite spherical, conical, and cylindrical shells using higher-order shear-normal deformation theory (HOSNT) and transverse stress recovery. The proposed theoretical model incorporates laminate deformations that account for the effects of transverse shear and normal strain/stress, thus modeling the deformation of laminated shells more accurately and eliminating the need for the shear correction factor. The governing equations are solved by applying a semi-analytical method based on the simple trigonometric series and a finite-difference method. In order to fulfill boundary conditions at both the bounding surfaces and local stress-equilibrium equations specified by elasticity theory, the transverse shear and normal stresses are reconstructed by integrating along the thickness direction three-dimensional equilibrium equations of elasticity theory with one-step stress recovery. The present mathematic model and computational procedure were validated by comparing obtained numerical results with those available in the literature. The main advantage of the proposed model is that it correctly predicts the stress components near the clamped boundary edges of laminated composite shells, where sharp changes may be observed. Using HOSNT and one-step stress recovery, this study presents the stress distribution of laminated composite shells of revolution in the clamped boundary zones and assesses the influence of main geometric and material parameters on the distribution of nondimensional deflection and stress components. The analysis results indicate that applying HOSNT in conjunction with one-step stress recovery is necessary for investigating the stress state of laminated shells of revolution. [ABSTRACT FROM AUTHOR]

An improved method for calculating smooth derivatives of multilinear finite element fields is presented. The method is also applicable to finite difference schemes. A simple one-dimensional model problem is discussed analytically, and the new method shows superior behaviour compared to existing popular smoothing techniques. Two- and three-dimensional problems involving isoparametric elements are tested, and the results show improvements over tile widely used global least-squares method, with lumped mass matrix, especially at the boundaries and for non-uniform meshes. [ABSTRACT FROM AUTHOR]

Affinity-mediated drug delivery utilizes electrostatic, hydrophobic, or other noncovalent interactions between molecules and a polymer to extend the timeframe of drug release. Cyclodextrin polymers exhibit affinity interaction, however, experimentally testing drug candidates for affinity is time-consuming, making computational predictions more effective. One option, docking programs, provide predictions of affinity, but lack reliability, as their accuracy with cyclodextrin remains unverified experimentally. Alternatively, quantitative structure-activity relationship models (QSARs), which analyze statistical relationships between molecular properties, appear more promising. Previously constructed QSARs for cyclodextrin are not publicly available, necessitating an openly accessible model. Around 600 experimental affinities between cyclodextrin and guest molecules were cleaned and imported from published research. The software PaDEL-Descriptor calculated over 1,000 chemical descriptors for each molecule, which were then analyzed with R to create several QSARs with different statistical methods. These QSARs proved highly time efficient, calculating in minutes what docking programs could accomplish in hours. Additionally, on test sets, QSARs reached R2 values of around 0.7--0.8. The speed, accuracy, and accessibility of these QSARs improve evaluation of individual drugs and facilitate screening of large datasets for potential candidates in cyclodextrin affinity-based delivery systems. An app was built to rapidly access model predictions for end users using the Shiny library. To demonstrate the usability for drug release planning, the QSAR predictions were coupled with a mechanistic model of diffusion within the app. Integrating new modules should provide an accessible approach to use other cheminformatic tools in the field of drug delivery. [ABSTRACT FROM AUTHOR]

This study examines the impact force applied from hand taps during extended column tests (ECTs), a common method of assessing snow stability. The hand-tap loading method has inherent subjectivity and inconsistencies across US, Canadian, Swiss, and Norwegian written standards. We developed a device, the "tap-o-meter", to measure the force-time curves during these taps and collected data from 286 practitioners, including avalanche forecasters and mountain guides in Scandinavia, Central Europe, and North America. The mean, median, and inner-quartile peak forces are distinctly different for each loading step (wrist, elbow, and shoulder), and the peak force approximately doubles from one loading step to the next. However, there is considerable overlap across the range of measurements and examples of participants with higher-force wrist taps than other participants' shoulder taps. This overlap challenges the reliability and reproducibility of ECT results, potentially leading to dangerous interpretations in avalanche decision-making, forecasting, and risk assessments. Our results provide an answer to the question "How hard do avalanche practitioners tap?" but not necessarily to the question "How hard should avalanche practitioners tap?" These data and insights are intended to facilitate discussion among the tests' creators, the scientific community, and the practitioner community to update thresholds, guidelines, and test interpretation. [ABSTRACT FROM AUTHOR]

Reconstructing the thermo-chemical evolution of Earth's mantle and its diverse surface manifestations is a widely recognised grand challenge for the geosciences. It requires the creation of a digital twin: a digital representation of Earth's mantle across space and time that is compatible with available observational constraints on the mantle's structure, dynamics and evolution. This has led geodynamicists to explore adjoint-based approaches that reformulate mantle convection modelling as an inverse problem, in which unknown model parameters can be optimised to fit available observational data. Whilst there has been a notable increase in the use of adjoint-based methods in geodynamics, the theoretical and practical challenges of deriving, implementing and validating adjoint systems for large-scale, non-linear, time-dependent problems, such as global mantle flow, has hindered their broader use. Here, we present the Geoscientific ADjoint Optimisation PlaTform (G-ADOPT), an advanced computational modelling framework that overcomes these challenges for coupled, non-linear, time-dependent systems by integrating three main components: (i) Firedrake, an automated system for the solution of partial differential equations using the finite-element method; (ii) Dolfin-Adjoint, which automatically generates discrete adjoint models in a form compatible with Firedrake; and (iii) the Rapid Optimisation Library, ROL, an efficient large-scale optimisation toolkit; G-ADOPT enables the application of adjoint methods across geophysical continua, showcased herein for geodynamics. Through two sets of synthetic experiments, we demonstrate the application of this framework to the initial condition problem of mantle convection, in both square and annular geometries, for both isoviscous and non-linear rheologies. We confirm the validity of the gradient computations underpinning the adjoint approach, for all cases, through second-order Taylor remainder convergence tests and subsequently demonstrate excellent recovery of the unknown initial conditions. Moreover, we show that the framework achieves theoretical computational efficiency. Taken together, this confirms the suitability of G-ADOPT for reconstructing the evolution of Earth's mantle in space and time. The framework overcomes the significant theoretical and practical challenges of generating adjoint models and will allow the community to move from idealised forward models to data-driven simulations that rigorously account for observational constraints and their uncertainties using an inverse approach. [ABSTRACT FROM AUTHOR]

We present a high-level, differentiable, and composable abstraction for the point evaluation of the solution fields of partial differential equation models. The new functionality, embedded in the Firedrake automated finite element system, enables modellers to easily assimilate point data into their models at the point locations, rather than resorting to extrapolation to a computational mesh. We demonstrate the expressiveness and ease with which more mathematically defensible data assimilation can be performed with examples in the fields of groundwater hydrology and glaciology. In various geoscience disciplines, modellers seek to estimate fields that are challenging to directly observe using measurements of other related fields. These measurements are often sparse, and it is common practice to first extrapolate these measurements to the grid or mesh used for computations. When this estimation procedure is viewed as a deterministic inverse problem, the extrapolation step is undesirable because the choice of extrapolation method introduces an arbitrary algorithmic degree of freedom that can alter the outcomes. When the estimation procedure is instead viewed through the lens of statistical inference, the extrapolation step is undesirable for the additional reason that it obscures the number of statistically independent measurements that are assimilated and thus makes it impossible to apply statistical goodness-of-fit tests or model selection criteria. The introduction of point evaluation into Firedrake, together with its integration into the automatic differentiation features of the system, greatly facilitates the direct assimilation of point data and thus improved methodology for solving both deterministic and statistical inverse problems. [ABSTRACT FROM AUTHOR]

The electron transport in current-biased superconducting nano-bridges is determined by the motion of the quantum vortex confined in the internal disorder landscape. Here we consider theoretically a simple case of a single or two neighbouring linear defects crossing a nano-bridge. The strong anharmonicity of the vortex motion along the defect leads, upon radio frequency (RF) excitation, to fractional Shapiro steps. In the case of two defects, the vortex motion becomes correlated, characterised by metastable states that can be locked to the RF-drive. The lock-unlock process causes sudden voltage jumps and drops in the voltage-current characteristics that can be observed in experiments. We analyse the parameters that promote these metastable dynamic states and discuss their possible experimental realisations. Vortex motion defines transport properties of type II superconductors. Here, authors study the effect of vortex synchronisation with an external periodic drive, that leads to the effects of integer and fractional Shapiro steps and even creates metastable states. [ABSTRACT FROM AUTHOR]

In soil sciences, parametric models known as constitutive models (e.g., the Modified Cam Clay and the NorSand) are used to represent the behavior of natural and artificial materials. In contexts where liquefaction may occur, the NorSand constitutive model has been extensively applied by both industry and academia due to its relatively simple critical state formulation and low number of input parameters. Despite its suitability as a good modeling framework to assess static liquefaction, the NorSand model still is based on premises which may not perfectly represent the behavior of all soil types. In this context, the creation of data-driven and physically informed metamodels emerges. The literature suggests that data-driven models should initially be developed using synthetic datasets to establish a general framework, which can later be applied to experimental datasets to enhance the model's robustness and aid in discovering potential mechanisms of soil behavior. Therefore, creating large and reliable synthetic datasets is a crucial step in constructing data-driven constitutive models. In this context, the NorSand model comes in handy: by using NorSand simulations as the training dataset, data-driven constitutive metamodels can then be fine-tuned using real test results. The models created that way will combine the power of NorSand with the flexibility provided by data-driven approaches, enhancing the modeling capabilities for liquefaction. Therefore, for a material following the NorSand model, the present paper presents a first-of-its-kind database that addresses the size and complexity issues of creating synthetic datasets for nonlinear constitutive modeling of soils by simulating both drained and undrained triaxial tests. Two datasets are provided: the first one considers a nested Latin hypercube sampling of input parameters encompassing 2000 soil types, each subjected to 40 initial test configurations, resulting in a total of 160 000 triaxial test results. The second one considers nested quasi-Monte Carlo sampling techniques (Sobol and Halton) of input parameters encompassing 2048 soil types, each subjected to 42 initial test configurations, resulting in a total of 172 032 triaxial test results. By using the quasi-Monte Carlo dataset and 49 of its subsamples, it is shown that the dataset of 2000 soil types and 40 initial test configurations is sufficient to represent the general behavior of the NorSand model. In this process, four machine learning algorithms (Ridge Regressor, KNeighbors Regressor and two variants of the Ridge Regressor which incorporate nonlinear Nystroem kernel mappings of the input and output values) were trained to predict the constitutive and test parameters based solely on the triaxial test results. These algorithms achieved 13.91 % and 16.18 % mean absolute percentage errors among all 14 predicted parameters for undrained and drained triaxial test inputs, respectively. As a secondary outcome, this work introduces a Python script that links the established Visual Basic implementation of NorSand to the Python environment. This enables researchers to leverage the comprehensive capabilities of Python packages in their analyses related to this constitutive model. [ABSTRACT FROM AUTHOR]

We develop randomized neural networks (RNNs) with Petrov–Galerkin (RNN-PG) methods to solve linear elasticity and Navier–Stokes equations. RNN-PGs use the Petrov–Galerkin variational framework, where the solution is approximated by randomized neural networks and the test functions are piecewise polynomials. Unlike conventional neural networks, the parameters of the hidden layers of randomized neural networks are fixed randomly while the parameters of the output layer are determined by the least-squares method, which can effectively approximate the solution. We also develop mixed RNN-PG (M-RNN-PG) methods for linear elasticity problems to ensure symmetry of the stress tensor and avoid locking effects. For the Stokes problem, we present various M-RNN-PG methods that enforce the divergence-free constraint by different techniques. For the Navier–Stokes equations, we propose a space-time M-RNN-PG that uses Picard or Newton iteration to deal with the nonlinear term. Using several examples, we compare RNN-PG methods with the finite-element method, the mixed discontinuous Galerkin method, and the physics-informed neural network. The numerical results demonstrate that RNN-PG methods achieve higher accuracy and efficiency. [ABSTRACT FROM AUTHOR]

This article presents a dataset that can be used to estimate alfalfa leaf area and predict leaf area index (LAI). The dataset includes meteorological data, soil moisture measurements, and various parameters associated with alfalfa growth. It fills a gap in publicly available alfalfa growth data in northwest China and provides essential data for optimizing water and nitrogen strategies in alfalfa field management. The document also provides information on the measurement and analysis of LAI in alfalfa plants under different water and nitrogen treatments. The research articles compiled in the document cover a range of topics related to alfalfa growth, yield, and quality, providing valuable insights for researchers and practitioners interested in improving alfalfa cultivation. [Extracted from the article]

Computer code plays a vital role in modern science, from the conception and design of experiments through to final data analyses. Open sharing of code has been widely discussed as being advantageous to the scientific process, allowing experiments to be more easily replicated, helping with error detection, and reducing wasted effort and resources. In the case of psychology, the code used to present stimuli is a fundamental component of many experiments. It is not known, however, the degree to which researchers are sharing this type of code. To estimate this, we conducted a survey of 400 psychology papers published between 2016 and 2021, identifying those working with the open-source tools Psychtoolbox and PsychoPy that openly share stimulus presentation code. For those that did, we established if it would run following download and also appraised the code's usability in terms of style and documentation. It was found that only 8.4% of papers shared stimulus code, compared to 17.9% sharing analysis code and 31.7% sharing data. Of shared code, 70% ran directly or after minor corrections. For code that did not run, the main error was missing dependencies (66.7%). The usability of the code was moderate, with low levels of code annotation and minimal documentation provided. These results suggest that stimulus presentation code sharing lags behind other forms of code and data sharing, potentially due to less emphasis on such code in open-science discussions and in journal policies. The results also highlight a need for improved documentation to maximize code utility., (© 2024. The Psychonomic Society, Inc.)

Aiming at the long-term and high-precision simulation of the magnetohydrodynamic (MHD) instabilities in the tokamak model, we developed a parallelized solver based on a fully implicit difference scheme. A 4th-order precision difference scheme and the Newton–Krylov method are employed in the proposed solver for both the flow and the electromagnetic field. To achieve high parallel efficiency, we adopt a strategy based on the spatial domain decomposition to partition the large Jacobian matrices in the iteration, and a buffer area based on the grid density is utilized to minimize the memory and time consumption. The accuracy of the methodology is verified, and the numerical results are validated by comparison with recognized results. The numerical results of the tearing mode instability in the tokamak model have demonstrated the precision and reliability of the algorithm, and the high parallel efficiency has been proven by the scalability test on the platform with up to 1280 threads, showing significant potential in the large-scale simulation of MHD problems. [ABSTRACT FROM AUTHOR]

Lateral changes in the group velocity of waves propagating in oceanic or coastal waters cause a deflection in their propagation path. Such refractive effects can be computed given knowledge of the ambient current field and/or the bathymetry. We present an open-source module for solving the wave ray equations by means of numerical integration in Python v3. The solver is implemented for waves on variable currents and arbitrary depths following the Wentzel–Kramers–Brillouin (WKB) approximation. The ray tracing module is implemented in a class structure, and the output is verified against analytical solutions and tested for numerical convergence. The solver is accompanied by a set of ancillary functions such as retrieval of ambient conditions using OPeNDAP, transformation of geographical coordinates, and structuring of data using community standards. A number of use examples are also provided. [ABSTRACT FROM AUTHOR]