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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]

In the field of computational hemodynamics, sensitivity quantification of pressure and flow wave dynamics has received little attention. This work presents a novel study of the sensitivity of pressure-wave timing and amplitude in the arterial system with respect to arterial stiffness. Arterial pressure and flow waves were simulated with a one-dimensional distributed wave propagation model for compliant arterial networks. Sensitivity analysis of this model was based on a generalized polynomial chaos expansion evaluated by a stochastic collocation method. First-order statistical sensitivity indices were formulated to assess the effect of arterial stiffening on timing and amplitude of the pressure wave and backward-propagating pressure wave in the ascending aorta, at the maximum pressure and inflection point in the systolic phase. Only the stiffness of aortic arteries was found to significantly influence timing and amplitude of the backward-propagating pressure wave, whereas other large arteries in the systemic tree showed marginal impact. Furthermore, the ascending aorta, aortic arch, thoracic aorta, and infrarenal abdominal aorta had the largest influence on amplitude, whereas only the thoracic aorta influenced timing. Our results showed that the non-intrusive polynomial chaos expansion is an efficient method to compute statistical sensitivity measures for wave propagation models. These sensitivities provide new knowledge in the relative importance of arterial stiffness at various locations in the arterial network. Moreover, they will significantly influence clinical data collection and effective composition of the arterial tree for in-silico clinical studies. Copyright © 2015 John Wiley & Sons, Ltd. [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]

SUMMARY - Phase contrast MR in patients with the Chiari I malformation demonstrates abnormal CSF flow in the foramen magnum and upper cervical spinal canal, related to abnormal pressure gradients. The purpose of this study was to analyze the role of CSF pressure in the pathogenesis of syringomyelia, with computational models. The spinal cord was modeled as a cylindrical poro-elastic structure with homogenous and isotropic permeability. The permeability was then made heterogeneous and anisotropic to represent the different properties of the central canal, gray and white matter. Fluid with a defined pressure, varying both in time and space, was prescribed in the SAS. Simulations were performed to quantify deformations and fluid movement within the cord. In the simulations with uniform permeability fluid moved into the cord in regions of higher pressure and out of the cord in regions of lower pressure. With permeability differences simulating gray and white matter the pattern was more complex, but similar. Adding the central spinal canal, fluid moved into the cord as in the previous case. However, preferential flow along the central canal hindered fluid from flowing back into the SAS. Pressure gradients in the SAS produce movement of fluid in the spinal cord. Assuming different relative permeability in gray matter, white matter and the central spinal canal, abnormal CSF gradients lead to accumulation of fluid within and adjacent to the spinal cord central canal. [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]

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]

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]

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 recent years have seen 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 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 aim to better understand the overriding plate deformation during the megathrust earthquake cycle. We estimate the spatial patterns of interseismic GNSS velocities in South America, Southeast Asia and northern Japan and the associated uncertainties due to variations in network density and observation uncertainties. Interseismic velocities with respect to the overriding plate generally decrease with distance from the trench with a steep gradient up to a 'hurdle', beyond which the gradient is distinctly lower and velocities are small. The hurdle is located 500–1000 km away from the trench for the trench-perpendicular velocity component, and either at the same distance or closer for the trench-parallel component. Significant coseismic displacements were observed beyond these hurdles during the 2010 Maule, 2004 Sumatra–Andaman, and 2011 Tohoku earthquakes. We hypothesize that both the interseismic hurdle and the coseismic response result from a mechanical contrast in the overriding plate. We test our hypothesis using physically consistent, generic, 3-D finite element models of the earthquake cycle. Our models show a response similar to the interseismic and coseismic observations for a compliant near-trench overriding plate and an at least five times stiffer overriding plate beyond the contrast. The model results suggest that hurdles are more prominently expressed in observations near strongly locked megathrusts. Previous studies inferred major tectonic or geological boundaries and seismological contrasts located close to the observed hurdles in the studied overriding plates. The compliance contrast probably results from thermal, compositional and thickness contrasts and might cause the observed focusing of smaller-scale deformation like backthrusting. [ABSTRACT FROM AUTHOR]

To learn, humans observe and experience the world, collect data, and establish patterns through repetition. In scientific discovery, these patterns and relationships are expressed as laws and equations, data as properties and variables, and observations as events. Data-driven techniques aim to provide an impartial approach to learning using raw data from actual or simulated observations. In soil science, parametric models known as constitutive models are used to represent the behavior of natural and artificial materials. Creating data-driven constitutive models using deep learning techniques requires large and consistent datasets, which are challenging to acquire through experiments. Synthetic data can be generated using a theoretical function, but there is a lack of literature on high-volume and robust datasets of this kind. Digital soil models can be utilized to conduct numerical simulations that produce synthetic results of triaxial tests, which are regarded as the preferred tests for assessing soil's constitutive behavior. Due to its limitations for modeling real sands, the Modified Cam Clay model has been replaced by the NorSand model in some situations where sand-like materials need to be modelled. 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 of 2000 soil types, each subjected to 40 initial test configurations, resulting in a total of 160000 triaxial test results. Each simulation dataset comprises a 4000 × 10 matrix that can be used for general multivariate forecasting benchmarks, in addition to direct geotechnical and soil science applications. [ABSTRACT FROM AUTHOR]

Tensors are a popular programming interface for developing artificial intelligence (AI) algorithms. Layout refers to the order of placing tensor data in the memory and will affect performance by affecting data locality; therefore the deep neural network library has a convention on the layout. Since AI applications can use arbitrary layouts, and existing AI systems do not provide programming abstractions to shield the layout conventions of libraries, operator developers need to write a lot of layout-related code, which reduces the efficiency of integrating new libraries or developing new operators. Furthermore, the developer assigns the layout conversion operation to the internal operator to deal with the uncertainty of the input layout, thus losing the opportunity for layout optimization. Based on the idea of polymorphism, we propose a layout-agnostic virtual tensor programming interface, namely the VTensor framework, which enables developers to write new operators without caring about the underlying physical layout of tensors. In addition, the VTensor framework performs global layout inference at runtime to transparently resolve the required layout of virtual tensors, and runtime layout-oriented optimizations to globally minimize the number of layout transformation operations. Experimental results demonstrate that with VTensor, developers can avoid writing layout-dependent code. Compared with TensorFlow, for the 16 operations used in 12 popular networks, VTensor can reduce the lines of code (LOC) of writing a new operation by 47.82% on average, and improve the overall performance by 18.65% on average. [ABSTRACT FROM AUTHOR]

We present an efficient numerical scheme based on Monte Carlo integration to approximate statistical solutions of the incompressible Euler equations. The scheme is based on finite volume methods, which provide a more flexible framework than previously existing spectral methods for the computation of statistical solutions for incompressible flows. This finite volume scheme is rigorously proven, under experimentally verifiable assumptions, to converge in an appropriate topology and with increasing resolution to a statistical solution. The convergence obtained is stronger than that of measure-valued solutions, as it implies convergence of multi-point correlation marginals. We present results of numerical experiments that support the claim that the aforementioned assumptions are very natural and appear to hold in practice. [ABSTRACT FROM AUTHOR]

SUMMARY: With the increasing advances in the oil and gas industry, seismic imaging near or under salt structures has become an important point in deep-water exploration. Detailed velocity models of these areas are particularly interesting not only to characterize hydrocarbon reservoirs but also to identify potential sites for hydrogen and carbon dioxide storage in offshore salt caverns. Thus, we study the full-waveform inversion for the salt reconstruction in acoustic media with constant density considering the time-harmonic wave propagation in a finite element formulation using the topology optimization (TO) method. This problem is challenging due to the strong velocity contrast between salt bodies and the sedimentary background, in addition to the lack of low-frequency data and the inherent ill-posedness of the inverse problem. In this context, we incorporate techniques from the TO field, usually used in design applications, to overcome or reduce these known problems. We initially defined the squared slowness as a combination of two fields, one related to the salt shape and the other to the background. An interpolation rule based on the solid isotropic material with penalization method, combined with filtering and projection schemes, is used to find the shape of the salt bodies with increased sharpness interfaces. A Helmholtz-type filter is applied to modify the gradient aimed to regularize the problem and provide a more stable way for the salt shape to evolve during the inversion process. In particular, we demonstrate that the proposed approach may be relevant for reconstructing media with salt bodies when a suitable starting model is unavailable, and sharp interfaces are required. In addition, we present inversion results from synthetic data generated by a variable density model to demonstrate the approach capability when subjected to a reconstruction application. [ABSTRACT FROM AUTHOR]

This work analyzes the implementation of a continuous method of structural topology optimization (STO) using open-source software for all stages of the topology optimization problem: modeling, sensitivity analysis and optimization. Its implementation involves three main components: numerical analysis using the Finite Element Method (FEM), sensitivity analysis using an Adjoint method and an optimization solver. In order to allow the automated numerical solution of Partial Differential Equations (PDEs) and perform a sensitivity analysis, FEniCS and Dolfin Adjoint software are used as tools, which are open-source code. For the optimization process, Ipopt (Interior Point OPTimizer) is used, which is a software package for nonlinear optimization scale designed to find (local) solutions of mathematical optimization problems. The topological optimization method used is based on the SIMP-Solid Isotropic Material with Penalization interpolation. The considered problem is the minimization of compliance/maximization of stiffness, considering the examples of recurrent structures in the literature in 2D and 3D. A density filtering algorithm based on Helmholtz formulation is used. The complete code involves 51 lines of programming and is presented and commented in detail in this article. [ABSTRACT FROM AUTHOR]

In this paper, we analyze discontinuous Galerkin methods based in the interior penalty method in order to approximate the eigenvalues and eigenfunctions of the Stokes eigenvalue problem. The considered methods in this work are based in discontinuous polynomials approximations for the velocity field and the pressure fluctuation in two and three dimensions. The methods under consideration are symmetric and nonsymmetric, leading to variations on the associated matrices and, hence, on the computation of the eigenvalues and eigenfunctions where real and complex results may appear, depending on the choice of the method. We derive a convergence result and error estimates for the proposed methods, together with a rigorous computational analysis of the effects of the stabilization parameter in the appearance of spurious modes when the spectrum is computed, when symmetric and nonsymmetric methods are performed. [ABSTRACT FROM AUTHOR]

How the behavior of cells emerges from their constituent subcellular biochemical and physical parts is an outstanding challenge at the intersection of biology and physics. A remarkable example of single-cell behavior occurs in the ciliate Lacrymaria olor, which hunts for its prey via rapid movements and protrusions of a slender neck, many times the size of the original cell body. The dynamics of this cell neck is powered by a coat of cilia across its length and tip. How a cell can program this active filamentous structure to produce desirable behaviors like search and homing to a target remains unknown. Here, we present an active filament model that allows us to uncover how a “program” (time sequence of active forcing) leads to “behavior” (filament shape dynamics). Our model captures two key features of this system—time- varying activity patterns (extension and compression cycles) and active stresses that are uniquely aligned with the filament geometry—a “follower force” constraint. We show that active filaments under deterministic, time-varying follower forces display rich behaviors including periodic and aperiodic dynamics over long times. We further show that aperiodicity occurs due to a transition to chaos in regions of a biologically accessible parameter space. We also identify a simple nonlinear iterated map of filament shape that approximately predicts long-term behavior suggesting simple, artificial “programs” for filament functions such as homing and searching space. Last, we directly measure the statistical properties of biological programs in L. olor, enabling comparisons between model predictions and experiments. [ABSTRACT FROM AUTHOR]

A lower and upper solution method is introduced for control problems related to abstract operator equations. The method is illustrated on a control problem for the Lotka--Volterra model with seasonal harvesting and applied to a control problem of cell evolution after bone marrow transplantation. [ABSTRACT FROM AUTHOR]

Intrathecal administration is an important mode for delivering biological agents targeting central nervous system (CNS) diseases. However, current clinical practices lack a sound theorical basis for a quantitative understanding of the variables and conditions that govern the delivery efficiency and specific tissue targeting especially in the brain. This work presents a distributed mechanistic pharmacokinetic model (DMPK) for predictive analysis of intrathecal drug delivery to CNS. The proposed DMPK model captures the spatiotemporal dispersion of antisense oligonucleotides (ASO) along the neuraxis over clinically relevant time scales of days and weeks as a function of infusion, physiological and molecular properties. We demonstrate its prediction capability using biodistribution data of antisense oligonucleotide (ASO) administration in non-human primates. The results are in close agreement with the observed ASO pharmacokinetics in all key compartments of the central nervous system. The model enables determination of optimal injection parameters such as intrathecal infusion volume and duration for maximum ASO delivery to the brain. Our quantitative model-guided analysis is suitable for identifying optimal parameter settings to target specific brain regions with therapeutic drugs such as ASOs. [ABSTRACT FROM AUTHOR]

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As thermoset polymers find frequent implementation in engineering design, their application in structural engineering is rather limited. One key reason relies on the ongoing curing process in typical applications such as post-installed adhesive anchors, joints by structural elements or surface-mounted laminates glued by adhesive polymers. Mechanochemistry including curing and aging under thermal as well as mechanical loading causes a multiphysics problem to be discussed. For restricting the variety of material models based on empirical observations, we aim at a thermodynamically sound strategy for modeling thermosets. By providing a careful analysis and clearly identifying the assumptions and simplifications, we present the general framework for modeling and computational implementation of thermo-mechano-chemical processes by using open-source codes. [ABSTRACT FROM AUTHOR]

The learning assistant (LA) model is a widely used and researched model for institutional and course transformation towards research-based instructional strategies (RBIS). The LA model leverages learning assistants, pedagogically trained students, to facilitate student learning in active learning environments. However, although the LA model has shown significant results when implemented in university contexts in the United States, there has as yet been little documentation of similar implementation or results in European higher education. In this study, we present the results of a three-semester design-based research project to implement the LA Model in a Scandinavian physics department. The three core elements of the LA model (pedagogical training, course content meetings, and teaching in active learning environments) were implemented and iteratively refined, with necessary adjustments due to the specific institutional and cultural contexts documented. Throughout all three semesters, data was collected on how participation in the LA model affected LAs' buy-in to RBIS using focus groups, pre/post surveys, and teaching observations. A thematic analysis of these data showed that participation in the LA model helped ensure LA buy-in to both the interactive engagement methods and goal of cultivating conceptual understanding that underlie most RBIS, and that the combination of teaching practice and pedagogical training seminars were key to this buy-in. We argue that these results demonstrate the potential usefulness of the LA model for creating institutional and cultural change in European higher education. [ABSTRACT FROM AUTHOR]

The Mjølnir impact crater in the Norwegian Barents Sea features among the 20 largest impact craters listed in the Earth Impact Database. The impact is dated to 142 ± 2.6 Ma, corresponding closely to the Jurassic/Cretaceous boundary in the Boreal stratigraphy. Multidisciplinary studies carried out over the last three decades have suggested that the up to 40 km wide crater was created by a 1–3 km diameter impactor colliding with a shallow epicontinental sea, causing regional havoc and a regional ecological crisis that followed in its wake. Only minor evidence for the consequences of the impact for the surrounding depositional basins has been documented so far. This study describes a large submarine slump penetrated by hydrocarbon exploration well 7121/9‐1, located in the southern Hammerfest Basin and approximately 350 km away from the impact site. The slump is dated by a black shale drape, which contains characteristic impact‐related biotic assemblages and potential ejecta material. This precise dating enables us to associate the slump with large‐scale fault movements and footwall collapse along the basin‐bounding Troms‐Finnmark Fault Complex, which we conclude were caused by shock waves from the Mjølnir impact and the passage of associated tsunami trains. The draping black shale is interpreted to represent significant reworking of material from the contemporary seabed by tsunamis and currents set up by the impact. [ABSTRACT FROM AUTHOR]

A finite difference algorithm that evaluates the health conditions of a bonded joint is presented and discussed. The mathematical formulation of the problem is developed, paying particular attention to the singularity around the corners of the joint and implementing an original discretisation method of the partial differential equations governing the propagation of the elastic waves. The equations are solved under the only hypothesis of a bidimensional field. The algorithm is sensible to defects in the bonded joint and can be used as an effective structural health monitoring tool, as proven by the experiments that show close agreement with the numerical simulations. [ABSTRACT FROM AUTHOR]

As sediment accumulation indicates basin subsidence, erosion often is understood as tectonic uplift, but the amplitude and timing may be difficult to determine because the sedimentary record is missing. Quantification of erosion therefore requires indirect evidence, for example thermal indicators such as temperature, vitrinite reflectance and fission tracks in apatite. However, as always, the types and quality of data and the choice of models are important to the results. For example, considering only the thermal evolution of the sedimentary section discards the thermal time constant of the lithosphere and essentially ignores the temporal continuity of the thermal structure. Furthermore, the types and density of thermal indicators determine the solution space of deposition and erosion, the quantification of which calls for the use of inverse methods, which can only be successful when all models are mutually consistent. Here, we use integrated basin modelling and Markov Chain Monte Carlo inversion of four deep boreholes to show that the erosional pattern along the Sorgenfrei–Tornquist Zone (STZ) in the eastern North Sea is consistent with a tectonic model of tectonic inversion based on compression and relaxation of an elastic plate. Three wells in close proximity SW of the STZ have different data and exhibit characteristic differences in erosion estimates but are consistent with the formation of a thick chalk sequence, followed by minor Cenozoic erosion during relaxation inversion. The well on the inversion ridge requires ca. 1.7 km Jurassic‐Early Cretaceous sedimentation followed by Late Cretaceous–Palaeocene erosion during inversion. No well demands thick Cenozoic sedimentation followed by equivalent significant Neogene exhumation. When data are of high quality and models are consistent, the thermal indicator method yields significant results with important tectonic and geodynamic implications. [ABSTRACT FROM AUTHOR]

Traits have become a crucial part of ecological and evolutionary sciences, helping researchers understand the function of an organism's morphology, physiology, growth and life history, with effects on fitness, behaviour, interactions with the environment and ecosystem processes. However, measuring, compiling and analysing trait data comes with data‐scientific challenges.We offer 10 (mostly) simple rules, with some detailed extensions, as a guide in making critical decisions that consider the entire life cycle of trait data.This article is particularly motivated by its last rule, that is, to propagate good practice. It has the intention of bringing awareness of how data on the traits of organisms can be collected and managed for reuse by the research community.Trait observations are relevant to a broad interdisciplinary community of field biologists, synthesis ecologists, evolutionary biologists, computer scientists and database managers. We hope these basic guidelines can be useful as a starter for active communication in disseminating such integrative knowledge and in how to make trait data future‐proof. We invite the scientific community to participate in this effort at http://opentraits.org/best‐practices.html. [ABSTRACT FROM AUTHOR]

We develop an efficient and robust iterative framework suitable for solving the linear system of equations resulting from the spectral element discretisation of the curl-curl equation of the total electric field encountered in geophysical controlled-source electromagnetic applications. We use the real-valued equivalent form of the original complex-valued system and solve this arising real-valued two-by-two block system (outer system) using the generalised conjugate residual method preconditioned with a highly efficient block-based PREconditioner for Square Blocks (PRESB). Applying this preconditioner equates to solving two smaller inner symmetric systems which are either solved using a direct solver or iterative methods, namely the generalised conjugate residual or the flexible generalised minimal residual methods preconditioned with the multigrid-based auxiliary-space preconditioner AMS. Our numerical experiments demonstrate the robustness of the outer solver with respect to spatially variable material parameters, for a wide frequency range of five orders of magnitude (0.1-10'000 Hz), with respect to the number of degrees of freedom, and for stretched structured and unstructured as well as locally refined meshes. For all the models considered, the outer solver reaches convergence in a small (typically < 20) number of iterations. Further, our numerical tests clearly show that solving the two inner systems iteratively using the indicated preconditioned iterative methods is computationally beneficial in terms of memory requirement and time spent as compared to a direct solver. On top of that, our iterative framework works for large-scale problems where direct solvers applied to the original complex-valued systems succumb due to their excessive memory consumption, thus making the iterative framework better suited for large-scale 3D problems. Comparison to a similar iterative framework based on a block-diagonal and the auxiliary-space preconditioners reveals that the PRESB preconditioner requires slightly fewer iterations to converge yielding a certain gain in time spent to obtain the solution of the two-by-two block system. [ABSTRACT FROM AUTHOR]

The fourth-order differential equation describing elastic flexure of the lithosphere is one of the cornerstones of geodynamics that is key to understanding topography, gravity, glacial isostatic rebound, foreland basin evolution, and a host of other phenomena. Despite being fully formulated in the 1940s, a number of significant issues concerning the basic equation have remained overlooked to this day. We first explain the different fundamental forms the equation can take and their difference in meaning and solution procedures. We then show how numerical solutions to flexure problems as they are currently formulated are in general potentially unreliable in an unpredictable manner for cases in which the coefficient of rigidity varies in space due to variations of the elastic thickness parameter. This is due to fundamental issues related to the numerical discretisation scheme employed. We demonstrate an alternative discretisation that is stable and accurate across the broadest conceivable range of conditions and variations of elastic thickness, and we show how such a scheme can simulate conditions up to and including a completely broken lithosphere more usually modelled as an end-loaded, single, continuous plate. Importantly, our scheme will allow breaks in plate interiors, allowing, for instance, the creation of separate blocks of lithosphere which can also share the support of loads. The scheme we use has been known for many years but remains rarely applied or discussed. We show that it is generally the most suitable finite-difference discretisation of fourth-order, elliptic equations of the kind describing many phenomena in elasticity, including the problem of bending of elastic beams. We compare the earlier discretisation scheme to the new one in one-dimensional form and also give the two-dimensional discretisation based on the new scheme. We also describe a general issue concerning the numerical stability of any second-order finite-difference discretisation of a fourth-order differential equation like that describing flexure wherein contrasting magnitudes of coefficients of different summed terms lead to round-off problems, which in turn destroy matrix positivity. We explain the use of 128 bit floating-point storage for variables to mitigate this issue. [ABSTRACT FROM AUTHOR]

Introduction: Direct quantification of hemodynamic factors applied to a cerebral aneurysm (CA) remains inaccessible due to the lack of technologies to measure the flow field within an aneurysm precisely. This study aimed to develop an in vitro validated 3D in silico patient-specific internal carotid artery sidewall aneurysm (ICASA) model which can be used to investigate hemodynamic factors on the CA pathophysiology. Methods: The validated ICASA model was developed by quantifying and comparing the flow field using particle image velocimetry (PIV) measurements and computational fluid dynamics (CFD) simulations. Specifically, the flow field characteristics, i.e., blood flowrates, normalized velocity profiles, flow streamlines, and vortex locations, have been compared at representative time instants in a cardiac pulsatile period in two designated regions of the ICASA model, respectively. One region is in the internal carotid artery (ICA) inlet close to the aneurysm sac, the other is across the middle of the aneurysmal sac. Results and Discussion: The results indicated that the developed computational fluid dynamics model presents good agreements with the results from the parallel particle image velocimetry and flowrate measurements, with relative differences smaller than 0.33% in volumetric flow rate in the ICA and relative errors smaller than 9.52% in averaged velocities in the complex aneurysmal sac. However, small differences between CFD and PIV in the near wall regions were observed due to the factors of slight differences in the 3D printed model, light reflection and refraction near arterial walls, and flow waveform uncertainties. The validated model not only can be further employed to investigate hemodynamic factors on the cerebral aneurysm pathophysiology statistically, but also provides a typical model and guidance for other professionals to evaluate the hemodynamic effects on cerebral aneurysms. [ABSTRACT FROM AUTHOR]

This paper presents the message passing interface (MPI)-based parallelization of the three-dimensional hydrodynamic model SHYFEM (System of HydrodYnamic Finite Element Modules). The original sequential version of the code was parallelized in order to reduce the execution time of high-resolution configurations using state-of-the-art high-performance computing (HPC) systems. A distributed memory approach was used, based on the MPI. Optimized numerical libraries were used to partition the unstructured grid (with a focus on load balancing) and to solve the sparse linear system of equations in parallel in the case of semi-to-fully implicit time stepping. The parallel implementation of the model was validated by comparing the outputs with those obtained from the sequential version. The performance assessment demonstrates a good level of scalability with a realistic configuration used as benchmark. [ABSTRACT FROM AUTHOR]

We study a commonly-used second-kind boundary-integral equation for solving the Helmholtz exterior Neumann problem at high frequency, where, writing Γ for the boundary of the obstacle, the relevant integral operators map L 2 (Γ) to itself. We prove new frequency-explicit bounds on the norms of both the integral operator and its inverse. The bounds on the norm are valid for piecewise-smooth Γ and are sharp up to factors of log k (where k is the wavenumber), and the bounds on the norm of the inverse are valid for smooth Γ and are observed to be sharp at least when Γ is smooth with strictly-positive curvature. Together, these results give bounds on the condition number of the operator on L 2 (Γ) ; this is the first time L 2 (Γ) condition-number bounds have been proved for this operator for obstacles other than balls. [ABSTRACT FROM AUTHOR]

Granular avalanches are dangerous phenomena characterized by the rapid gravity-driven motion of granular solids. The complex dynamics of these flows can be effectively modeled by a multilayer approach, which, however, requires particular attention to the derivation of the model equations in order to allow stable solutions. In this work, we use a well-posed multilayer model, in which the μ(I)-rheology is employed and a dilatancy law, depending on the inertial number I, is also taken into account, and systematically compare it with various laboratory experiments. The model, whose well-posedness is guaranteed by a physically based viscous regularization, describes the evolution of a preset number of superimposed granular layers. As the sidewall friction is relevant under most experimental conditions, the model is fitted here with suitable resistance terms. Moreover, non-trivial closures for the mass exchanges are introduced to avoid any unrealistic partitioning of the flow domain during the avalanche evolution, and, hence, guarantee a regular spatial discretization along the normal to flow direction. The velocity fields are compared with different experiments in unsteady state, and comparisons of both velocity and volume fraction profiles are provided with steady uniform flow experiments. The results confirm the good capabilities of the multilayer model and the underlying μ(I)-rheology in capturing the granular flow dynamics. The experimental volume fraction profiles are qualitatively well reproduced by the proposed dilatancy law, while an overestimation is observed only in the upper, more dilute flow region with a thickness of a few grain diameters. [ABSTRACT FROM AUTHOR]

Embryonic epithelial cells exhibit strong coupling of mechanical responses to chemical signals and most notably to calcium. Recent experiments have shown that the disruption of calcium signals during neurulation strongly correlates with the appearance of neural tube defects. We, thus, develop a multi-dimensional mechanochemical model and use it to reproduce important experimental findings that describe anterior neural plate morphogenetic behaviour during neural tube closure. The governing equations consist of an advectiondiffusion-reaction system for calcium concentration which is coupled to a force balance equation for the tissue. The tissue is modelled as a linear viscoelastic material that includes a calcium-dependent contraction stress. We implement a random distribution of calcium sparks that is compatible with experimental findings. A finite element method is employed to generate numerical solutions of the model for an appropriately chosen range of parameter values. We analyse the behaviour of the model as three parameters vary: the level of IP3 concentration, the strength of the stretchsensitive activation and the maximum magnitude of the calcium-dependent contraction stress. Importantly, the simulations reproduce important experimental features, such as the spatio-temporal correlation between calcium transients and tissue deformation, the monotonic reduction of the apical surface area and the constant constriction rate, as time progresses. The model could also be employed to gain insights into other biological processes where the coupling of calcium signalling and mechanics is important, such as carcinogenesis and wound healing. [ABSTRACT FROM AUTHOR]

Numerous liver cancer oncologists suggest bridging therapies to limit cancer growth until donors are available. Interventional radiology including radiofrequency ablation (RFA) is one such bridging therapy. This locoregional therapy aims to produce an optimal amount of heat to kill cancer cells, where the heat is produced by a radiofrequency (RF) needle. Less experienced Interventional Radiologists (IRs) require a software-assisted smart solution to predict the optimal heat distribution as both overkilling and untreated cancer cells are problematic treatments. Therefore, two of the big three partial differential equations, 1) heat equation (Pennes, Journal of Applied Physiology, 1948, 1, 93-122) to predict the heat distribution and 2) Laplace equation (Prakash, Open Biomed. Eng. J., 2010, 4, 27-38) for electric potential along with different cell death models (O'Neill et al., Ann. Biomed. Eng., 2011, 39, 570-579) are widely used in the last three decades. However, solving two differential equations and a cell death model is computationally expensive when the number of finite compact coverings of a liver topological structure increases in millions. Since the heat source from the Joule losses Qr = σ|∇V|2 is obtained from Laplace equation σΔV = 0, it is called the Joule heat model. The traditional Joule heat model can be replaced by a point source model to obtain the heat source term. The idea behind this model is to solve σΔV = δ0 where δ0 is a Diracdelta function. Therefore, using the fundamental solution of the Laplace equation (Evans, Partial Differential Equations, 2010) we represent the solution of the Joule heat model using an alternative model called the point source model which is given by the Gaussian distribution. ... where K and ci are obtained by using needle parameters. This model is employed in one of our software solutions called RFA Guardian (Voglreiter et al., Sci. Rep., 2018, 8, 787) which predicted the treatment outcome very well for more than 100 patients. [ABSTRACT FROM AUTHOR]

In this paper we analyze a posteriori error estimates for a mixed formulation of the linear elasticity eigenvalue problem. A posteriori estimators for the nearly and perfectly compressible elasticity spectral problems are proposed. With a post-process argument, we are able to prove reliability and efficiency for the proposed estimators. The numerical method is based in Raviart-Thomas elements to approximate the pseudostress and piecewise polynomials for the displacement. We illustrate our results with numerical tests in two and three dimensions. [ABSTRACT FROM AUTHOR]