Field Computation Research Articles

Activity Design for Secondary School Students’ Modeling Skills: A Design-Based Research

Models and modeling process have been used for many years in science education courses, which contain many concepts that are difficult to understand and abstract. With the help of models, students improve their knowledge level related to the subject and realize learning by hands-on activities in the production process. In the model production process, they perform some behaviours called modeling skills. The purpose of this study is to design computer-based activities to develop students' skills. In this context, design-based research method was used in the activity development process. Activities were developed within the framework of a total of two cycles. Within the scope of the first cycle, drafts of the activities were made, and the activities were transferred to Adobe Flash environment with field educators and computer experts. In the first cycle, the activities applied to 11 middle school students were made necessary arrangements before the second cycle, and after the second cycle, the activities were finalized. At the end of the development process, a total of six computer-based activities were achieved. With the help of these activities, various applications can be made for the students' related modeling skills. In this way, students can produce better models and develop their level of conceptual knowledge about science lesson subjects.

A GPU-parallelized interpolation-based fast multipole method for the relativistic space-charge field calculation

The fast multipole method (FMM) has received growing attention in the beam physics simulation. In this study, we formulate an interpolation-based FMM for the computation of the relativistic space-charge field. Different to the quasi-electrostatic model, our FMM is formulated in the lab-frame and can be applied without the assistance of the Lorentz transformation. In particular, we derive a modified admissibility condition which can effectively control the interpolation error of the proposed FMM. The algorithms and their GPU parallelization are discussed in detail. A package containing serial and GPU-parallelized solvers is implemented in the Julia programming language. The GPU-parallelized solver can reach a speedup of more than a hundred compared to the execution on a single CPU core.

Computational Description of Alkylated Iron-Sulfur Organometallic Clusters.

The radical S-adenosyl methionine (SAM) enzyme superfamily has widespread roles in hydrogen atom abstraction reactions of crucial biological importance. In these enzymes, reductive cleavage of SAM bound to a [4Fe-4S]1+ cluster generates the 5'-deoxyadenosyl radical (5'-dAdo•) which ultimately abstracts an H atom from the substrate. However, overwhelming experimental evidence has surprisingly revealed an obligatory organometallic intermediate Ω exhibiting an Fe-C5'-adenosyl bond, whose properties are the target of this theoretical investigation. We report a readily applied, two-configuration version of broken symmetry DFT, denoted 2C-DFT, designed to allow the accurate description of the hyperfine coupling constants and g-tensors of an alkyl group bound to a multimetallic iron-sulfur cluster. This approach has been validated by the excellent agreement of its results both with those of multiconfigurational complete active space self-consistent field computations for a series of model complexes and with the results from electron nuclear double-resonance/electron paramagnetic resonance spectroscopic studies for the crystallographically characterized complex, M-CH3, a [4Fe-4S] cluster with a Fe-CH3 bond. The likewise excellent agreement between spectroscopic results and 2C-DFT computations for Ω confirm its identity as an organometallic complex with a bond between an Fe of the [4Fe-4S] cluster and C5' of the deoxyadenosyl moiety, as first proposed.

Investigating Supply and Demand in European Cohesion Policy: Micro-Foundations of Macro-Behaviours

European Cohesion Policy is a complex scheme that allocates financial resources to European regions. The implementation of the policy is based on an articulated multi-level governance that involves local and national authorities and the European Commission. Local authorities often face difficulties in using structural funds due to limits in their administrative capacity (supply) and/or inefficiencies in adequately stimulating applications’ submission (demand). By modelling and simulating the implementation of the policy, we explore how operations and decisions at the local authorities’ and potential applicants’ level (micro-foundations) explain emerging patterns of funds’ absorption at a regional level (macro-behaviours). Building upon a mixed-methods approach combining field research and computer simulation, we develop a model capturing the key cause–effect relationships among agents and resources within the Cohesion Policy supply-and-demand system. The outcomes elucidate how poor local administrative capabilities, including staff skills, may entail delays and low absorption performances, while showcasing the factors affecting potential applicants’ decision to submit.

The counterbalance of endothelial glycocalyx and high wall shear stress to low-density lipoprotein concentration polarization in mouse ear skin arterioles

Background and aimsAtherosclerosis preferentially occurs at regions in arterial branching, curvature, and stenosis, which may be explained by the geometric predilection of low-density lipoprotein (LDL) concentration polarization that has been investigated in major arteries in previous studies. Whether this also happens in arterioles remains unknown. MethodsHerein, a radially non-uniform distribution of LDL particles and a heterogeneous endothelial glycocalyx layer in the mouse ear arterioles, as shown by fluorescein isothiocyanate labeled wheat germ agglutinin (WGA-FITC), were successfully observed by a non-invasive two-photon laser-scanning microscopy (TPLSM) technique. The stagnant film theory was applied as the fitting function to evaluate LDL concentration polarization in arterioles. ResultsThe concentration polarization rate (CPR, the ratio of the number of polarized cases to that of total cases) in the inner walls of curved and branched arterioles was 22% and 31% higher than the outer counterparts, respectively. Results from the binary logistic regression and multiple linear regression analysis showed that endothelial glycocalyx thickness increases CPR and the thickness of the concentration polarization layer (CPL). Flow field computation indicates no obvious disturbances or vortex in modeled arterioles with different geometries and the mean wall shear stress is about 7.7–9.0 Pa. ConclusionsThese findings suggest a geometric predilection of LDL concentration polarization in arterioles for the first time, and the existence of an endothelial glycocalyx, acting together with a relatively high wall shear stress in arterioles, may explain to some extent why atherosclerosis rarely occurs in these regions.

Numerical Investigations At High Altitudes For Nozzles Performance Monitoring

Large area ratio nozzles that are employed for space propulsion applications are not meant to be tested at the ground-level conditions because of the flow conditions that occurs in their divergent section due to their low exhaust pressures. Therefore, it is desired to perform the experimental evaluation at high-altitude to evaluate the performance of the said nozzles. Generally, a high-altitude test facility, consisting of a supersonic exhaust diffuser, is generally employed. In thispaper, a second-throat exhaust diffuser has been numerically investigated to predict its minimum starting pressure, and to understand the flow physics in the diffuser using Computational Fluid Dynamics (CFD). Numerical computation of the flow field in the diffuser system is done for the two cases: 1) when the nozzle and the diffuser system are initially evacuated to a low pressure, and 2) when the nozzle and the diffuser system are initially at ambient pressure (1 bar). Simulations have been carried out for cold flow situation (Ȗ=1.4) over a range of nozzle inlet stagnation pressures. Numerical results compare favorably with the theoretical and experimental results and provide adequate insight to the flow physics and internal shock structures formed in thediffuser in addition to minimum starting pressure, diffuser wall pressure and vacuum thrust.

Computation of Electric and Magnetic Fields Generated by Cloud-to-Cloud Lightning Channels

The paper presents analytical formulas for computation in the time domain of electromagnetic (EM) fields generated by tortuous cloud-to-cloud (CC) lightning channels over a perfectly conducting ground. For the first time, the study was not limited to a horizontal lightning path but was extended to take into account the natural, tortuous geometry of the lightning channel. After the calculation of the step response, a convolution integration was applied for the computation of the fields generated by an arbitrary current source. The produced electric and magnetic fields were then compared with the fields generated by a horizontal channel. The method can be of primary importance to evaluating the hazards for electric and electronic systems of flying aircraft, estimating the voltages induced on overhead transmission lines by CC lightning, and, in general, evaluating the induced effects on sensitive electric and electronic components. Moreover, it may represent a simple, robust, and time-saving tool for estimating important physical parameters that characterize lightning phenomena.

Controlled-source electromagnetic modeling using a versatile secondary electric-field formulation and efficient multigrid-based preconditioner

Frequency-domain controlled-source electromagnetic (CSEM) surveying is a widely used geophysical electromagnetic exploration method. To avoid the singularity near the transmitting sources and improve the accuracy of three-dimensional (3D) CSEM forward modeling, we adopt the vector finite element method and secondary electric field formulation combined with hexahedral grids to solve the frequency-domain Maxwell equations. Primary field computation applies the fast Hankel transform using digital linear filters to quickly calculate the electromagnetic field generated by different electromagnetic dipoles or loops in the layered medium. Therefore, our forward modeling algorithm is highly versatile and compatible with various electromagnetic sources and scenarios of CSEM application (e.g., airborne, offshore, or marine). To improve the convergence rate, we use an algebraic multigrid solver based on the established Hiptmair–Xu decomposition. Using direct solvers requires a vast amount of memory, while conventional iterative solvers usually fail or converge only very slowly. Our new iterative scheme does not require the divergence corrections commonly applied in finite difference or finite volume electromagnetic modeling to accelerate the convergence. We implement complete parallelism in our finite element programming to efficiently solve the CSEM forward problems on massively parallel clusters. We use different numerical methods to obtain high-precision comparison results for one-dimensional and typical 3D models to demonstrate our algorithm's effectiveness and correctness. Finally, a public model of 3 million cells is used to simulate the responses of marine CSEM surveying. The proposed new solver shows robust scalability when using nearly 1000 cores on the cluster, demonstrating that our algorithm is particularly suitable for large-scale 3D forward modeling.

3D tomographic inversion for frequency semi-airborne EM under multinary constraints

The semi-airborne electromagnetic method (SAEM) has recently gained increased interest in geophysical exploration applications. For SAEM, ground-based transmitters are deployed within the area of interest or in its vicinity, and the induced magnetic is measured airborne. Because of the large footprint of extended transmitters, three-dimensional (3D) effects can have a significant impact on the gathered data and 3D modelling and inversion approaches must be employed for data analysis. Any 3D EM simulation is a resource-consuming task and efficient tools can therefore be useful to add data interpretation. In this study, 3D tomographic inversion of frequency-domain SAEM data was accomplished based on the integral equation (IE) method. The inversion was linearised by approximating the sensitivity matrix. We further employ the quasi-linear approximation to facilitate out quick forward modelling in the inversion which is tractable on field computers. While this approach sacrifices inversion accuracy for efficiency, we guide the inversion by introducing multinary constraints. These constraints impose a priori known conductivity values into the inversion process. Our results from synthetic and field data demonstrate the efficiency of our approach in achieving a coherent geophysical model that is consistent with geological data and findings from other geophysical techniques. This method provides a practical and capable solution for unveiling conductive 3D structures in the field.

Huygens' surface excitation for the finite element method applied to Maxwell's equations – A construction based on Nitsche's method

We present a Huygens' surface for the finite element method applied to Maxwell's equations, where the equivalent electric and magnetic surface currents are incorporated in the weak form by means of Nitsche's method. The proposed method preserves the reciprocity of Maxwell's equations and it allows for the computation of the total field inside the Huygens' surface, whereas on its outside only the scattered field is computed. The equivalent magnetic surface current at the Huygens' surface requires a double representation of the discontinuous tangential component of the electric field and we demonstrate that it can be efficiently combined with a previously presented higher-order brick-tetrahedron hybridization. Also, it is demonstrated that the near-to-far-field transformation can be evaluated in an accurate manner if collocated with the Huygens' surface, which allows for a compact computational domain and a reduction in the required computational resources. The proposed Huygens' surface is tested on two scattering problems with perfect electric conductor scatterers: (i) a sphere that demonstrates second-order convergence towards the analytical result for a piecewise linear approximation of the electric field; and (ii) a double ogive with two sharp tips which gives a computed monostatic radar cross section that compares well with measurements and computations in the open literature for both polarizations.

Deep Neural Implicit Representation of Accessibility for Multi-Axis Manufacturing

One of the main concerns in design and process planning for multi-axis additive and subtractive manufacturing is collision avoidance between moving objects (e.g., tool assemblies) and stationary objects (e.g., part unified with fixtures). The collision measure for various pairs of relative rigid translations and rotations between the two pointsets can be conceptualized by a compactly supported scalar field over the 6D non-Euclidean configuration space. Explicit representation and computation of this field is costly in both time and space. If we fix O(m) sparsely sampled rotations (e.g., tool orientations), computation of the collision measure field as a convolution of indicator functions of the 3D pointsets over a uniform grid (i.e., voxelized geometry) of resolution O(n3) via fast Fourier transforms (FFTs) scales as in O(mn3logn) in time and O(mn3) in space. In this paper, we develop an implicit representation of the collision measure field via deep neural networks (DNNs). We show that our approach is able to accurately interpolate the collision measure from a sparse sampling of rotations, and can represent the collision measure field with a small memory footprint. Moreover, we show that this representation can be efficiently updated through fine-tuning to more efficiently train the network on multi-resolution data, as well as accommodate incremental changes to the geometry (such as might occur in iterative processes such as topology optimization of the part subject to CNC tool accessibility constraints).

Phase field modeling and computation of vesicle growth or shrinkage.

We present a phase field model for vesicle growth or shrinkage induced by an osmotic pressure due to a chemical potential gradient. The model consists of an Allen-Cahn equation describing the evolution of the phase field parameter that describes the shape of the vesicle and a Cahn-Hilliard-type equation describing the evolution of the ionic fluid. We establish conditions for vesicle growth or shrinkage via a common tangent construction using free energy curves. During the membrane deformation, the model ensures total mass conservation of the ionic fluid, and we weakly enforce a surface area constraint of the vesicle. We develop a stable numerical scheme and an efficient nonlinear multigrid solver to evolve the phase and concentration fields, and we use this to evolve the fields to near equilibrium for 2D vesicles. Convergence tests confirm an [Formula: see text] accuracy for our scheme and near-optimal convergence for our multigrid solver. Numerical results reveal that the diffuse interface model captures the main features of cell shape dynamics: for a growing vesicle, there exist circle-like equilibrium shapes if the concentration difference across the membrane and the initial osmotic pressure are large enough; while for a shrinking vesicle, there exists a rich collection of finger-like equilibrium morphologies.

Relativistic calculations of molecular electric dipole moments of singly charged aluminium monohalides

In this work, we have studied the permanent electric dipole moments of singly charged aluminum monohalides in their electronic ground state, , using Kramers-restricted relativistic configuration interaction method. We report our results from this method in the singles and doubles approximation with those of Dirac–Fock calculations. For our finite field computations, quadruple zeta basis sets were employed. We discuss the electron correlation trends that we find in our calculated properties and have compared our results with those from literature, wherever available.

Modeling Sediment Resuspension and Transport Processes Induced by Propeller Wash from Ship Traffic

Resuspension and redistribution of sediments induced by propeller wash may significantly influence aquatic ecosystems at contaminated sediment sites. This study describes a numerical modeling method developed to predict the sediment resuspension and subsequent transport processes resulting from ship traffic, with a fully coupled simulation of hydrodynamics, sediment transport, and propeller wash. By including propeller momentum effects in the flow field computation, the advection and dispersion of resuspended sediments are better represented than in previously available methods. To achieve this improvement, a computational algorithm was first developed to calculate the propeller wash effects from one or more ships (e.g., erosion rate and momentum flux); these results were then dynamically linked to a hydrodynamic and sediment transport computation using Environmental Fluid Dynamics Code Plus (EFDC+). This modeling framework was evaluated using a field experiment conducted by the US Navy. The model was calibrated with flow velocities and sediment erosion depths, and then validated with resuspended sediment concentrations in the water column. The model results reproduced the horizontal and vertical distributions of resuspended sediments better when the propeller-induced momentum was incorporated into the flow field computation. The sensitivity test indicated that the increased flow energy from propeller momentum resulted in significant dispersion of resuspended sediments in both longitudinal and lateral directions. The maximum scour was dependent on the propeller revolution speed, the ship engine power, and the distance between the propellers and the sediment bed.

The Ocean Surface Current in the East China Sea Computed by the Geostationary Ocean Color Imager Satellite

High-frequency observations of surface current field data over large areas and long time series are imperative for comprehending sea-air interaction and ocean dynamics. Nonetheless, neither in situ observations nor polar-orbiting satellites can fulfill the requirements necessary for such observations. In recent years, geostationary satellite data with ultra-high temporal resolution have been increasingly utilized for the computation of surface flow fields. In this paper, the surface flow field in the East China Sea is estimated using maximum cross-correlation, which is the most widely used flow field computation algorithm, based on the total suspended solids (TSS) data acquired from the Geostationary Ocean Color Imager satellite. The inversion results were compared with the modeled tidal current data and the measured tidal elevation data for verification. The results of the verification demonstrated that the mean deviation of the long semiaxis of the tidal ellipse of the inverted M2 tide is 0.0335 m/s, the mean deviation of the short semiaxis is 0.0276 m/s, and the mean deviation of the tilt angle is 6.89°. Moreover, the spatially averaged flow velocity corresponds with the observed pattern of tidal elevation changes, thus showcasing the field’s significant reliability. Afterward, we calculated the sea surface current fields in the East China Sea for the years 2013 to 2019 and created distribution maps for both climatology and seasonality. The resulting current charts provide an intuitive display of the spatial structure and seasonal variations in the East China Sea circulation. Lastly, we performed a diagnostic analysis on the surface TSS variation mechanism in the frontal zone along the Zhejiang coast, utilizing inverted flow data collected on 3 August 2013, which had a high spatial coverage and complete time series. Our analysis revealed that the intraday variation in TSS in the local surface layer was primarily influenced by tide-induced vertical mixing. The research findings of this article not only provide valuable data support for the study of local ocean dynamics but also verify the reliability of short-period surface flow inversion of high-turbidity waters near the coast using geostationary satellites.

Physics-informed machine learning and stray field computation with application to micromagnetic energy minimization

We study the full 3d static micromagnetic equations via a physics-informed neural network (PINN) ansatz for the continuous magnetization configuration. PINNs are inherently mesh-free and unsupervised learning models. In our approach we can learn to minimize the total Gibbs free energy with additional conditional parameters, such as the exchange length, by a single low-parametric neural network model. In contrast, traditional numerical methods would require the computation and storage of a large number of solutions to interpolate the continuous spectrum of quasi-optimal magnetization configurations. We also consider the important and computationally expensive stray field problem via PINNs, where we use a basically linear learning ansatz, called extreme learning machines (ELM) within a splitting method for the scalar potential. This reduces the stray field training to a linear least squares problem with precomputable solution operator. We validate the stray field method by means of numerical example comparisons from literature and illustrate the full micromagnetic approach via the NIST μMAG standard problem #3.

Gray level residual field: an effective metric for pixelwise matching quality evaluation in local digital image correlation

Gray level residual (GLR), also known as correlation residual field or image difference, reflects the intensity differences between reference and deformed images. In finite element-based global digital image correlation (DIC), GLR field can be readily computed and has been successfully used for crack or damage detection. The computation of pixelwise GLR field requires dense displacement results, which can be obtained using mesh interpolation in global DIC. To obtain the GLR field in subset-based local DIC, in which results are obtained at discrete calculation points, a simple, efficient and practical computation method for GLR field is presented, which accounts for the influence of illumination variations unavoidably occurred in real DIC tests. The proposed method can be easily implemented on both central process unit and graphics process unit to realize real-time visualization. Experiments showed that the GLR field can quantitatively and intuitively evaluate the pixelwise matching quality and provide clearer and finer locations for new components or textures (e.g. cracks) presented in deformed images. By fully leveraging the pixelwise matching quality information provided by the GLR field, the capability and robustness of local DIC is expected to be further enhanced.

Computation of group-level electric field in lower limb motor area for different tDCS montages

ObjectiveTranscranial direct current stimulation (tDCS) injects a weak electric current into the brain via electrodes attached to the scalp to modulate cortical excitability. tDCS is used to rebalance brain activity between affected and unaffected hemispheres in rehabilitation. However, a systematic quantitative evaluation of tDCS montage is not reported for the lower limbs. In this study, we computationally investigated the generated electric field intensity, polarity, and co-stimulation of cortical areas for lower limb targeting using high-resolution head models. MethodsVolume conductor models have thus been employed to estimate the electric field in the brain. A total of 18 head models of healthy subjects were used to calculate the group-level electric fields generated from four montages of tDCS for modulation of lower limbs. ResultsC1-C2 montage delivered higher electric field intensities while reaching deeper regions of the lower-limb motor area. It produced a uniform polarization on the same hemisphere target with comparable intensities between hemispheres but with higher variability. ConclusionsProper montage selection allows reaching deeper regions of the lower-limb motor area with uniform polarization. SignificanceFirst systematic computational study providing support to tDCS experimental studies using montages for the lower limb while considering polarity factor for balancing brain activity.

Closed-form solution of Timoshenko frames using the Green’s Function Stiffness Method

This paper presents the formulation of the Green’s Function Stiffness Method (GFSM) for the static analysis of Timoshenko frames subjected to arbitrary external loads and bending moments. The GFSM is a novel analytic method that provides closed-form solutions of structures by combining the strengths of the Stiffness Method (SM) (exact relation between forces and displacements at the element ends) and Green’s functions (GF) (analytical closed-form structural response to any arbitrary external load). The GFSM is based on the classical idea of decomposing the solution of differential equations into homogeneous and particular (fixed) solutions, with the latter computed through superposition integrals using Green’s functions of fixed elements as kernels. Its principal aim is the computation of the displacements fields, while the internal forces are calculated directly from their derivatives. The GFSM is directly related to the SM and the Finite Element Method (FEM), making its numerical implementation easily performed from either of them. Additionally, the basic ideas behind the GFSM can be easily extended to other physical fields. An example is presented to show the advantages of the proposed method.

Influence of flow–fiber coupling during mold-filling on the stress field in short-fiber reinforced composites

The anisotropic elastic properties of injection molded composites are fundamentally coupled to the flow of the fiber suspension during mold-filling. Regarding the modeling of mold-filling processes, both a decoupled and a flow–fiber coupled approach are possible. In the latter, the fiber-induced viscous anisotropy is considered in the computation of the flow field. This in turn influences the evolution of the fiber orientation compared to the decoupled case. This study investigates how flow–fiber coupling in mold-filling simulation affects the stress field in the solid composite under load based on the final elastic properties after fluid–solid transition. Furthermore, the effects of Newtonian and non-Newtonian polymer matrix behavior are investigated and compared. The entire process is modeled micromechanically unified based on mean-field homogenization, both for the fiber suspension and for the solid composite. Different numerical stabilization methods of the mold-filling simulation are discussed in detail. Short glass fibers with a typical aspect ratio of 20 and a volume fraction of 20% are considered, embedded in polypropylene matrix material. The results show that the flow–fiber coupling has a large effect on the fiber orientation tensor in the range of over ± 30% with respect to the decoupled simulation. As a consequence, the flow–fiber coupling affects the stress field in the solid composite under load in the range of over ± 10%. In addition, the predictions based on a non-Newtonian modeling of the matrix fluid differ significantly from the Newtonian setup and thus the necessity to consider the shear-thinning behavior is justified in a quantifiable manner.