Field Modeling Method Research Articles

Research on compressor cascade flow field modeling method based on finite volume flux-informed neural network

For compressor cascade flow field modeling, there exists strong velocity shear in the leading edge separation flow, boundary layer, and wake, which leads to increased modeling errors. To improve the accuracy of the flow field modeling method, this paper introduces the concept of numerical flux from the finite volume method into the loss function to implement Euler equation physics-informed learning, and a finite volume flux-informed neural network (FVFI-net) is constructed. Selecting a high-load, large-turning-angle compressor cascade as the study object, a comparative analysis is conducted on the advantages and disadvantages of purely data-driven, weak physical constraint, and finite volume flux-informed methods in compressor cascade flow field modeling. The study found that compared to purely data-driven and weak physical constraint methods, FVFI-net can reduce the average error of aerodynamic parameters in the flow field by approximately 45.6% and 29.5%, respectively, at a 0° angle of attack. For the flow separation problem occurring at the suction side leading edge and the blade wake area caused by a 5° angle of attack, FVFI-net can effectively reduce modeling errors near the leading edge, in the wake region, and near the periodic boundaries, thus reducing the average error of the aerodynamic parameters of the flow field by about 49.2%and 31.3%, respectively, compared to pure data-driven and weak physical constraint methods.

Research on composite pattern design and lapping performance of fixed abrasive pads controlled by multi-physical fields

The present work provides an innovative method of composite pattern design for fixed abrasive pads, addressing issues such as machining non-uniformity and passivation blockage arising from uneven lapping flow, pressure, and velocity fields in lapping. First, a multi-physical field modeling method is provided, a material removal distribution model and evaluation criteria for the performance of the abrasive pad are established, and the reliability of this model is validated. Second, based on the model, a composite pattern abrasive pad coupled with a spiral groove and concentric micro groove is designed. Comparative experiments are conducted with the grid abrasive pad. The results show that the clogging and passivation performance of the composite pattern abrasive pad is improved, and the pressure distribution is optimized. Compared with the grid abrasive pad, in the pressure range of 20 N–70 N, the surface roughness Ra of sapphire is reduced by 6.4 %–25.42 %, defects such as brittle fracture pits and scratches on the workpiece surface are reduced, and the surface quality of the workpiece is significantly improved. The material removal rate is between 0.23 μm/min to 0.34 μm/min. This confirms the effectiveness of optimizing abrasive pad pattern design based on multi-physics fields. The research results provide a novel approach for abrasive pad pattern design with engineering application value.

Investigation of the temperature field of the ice sheet in a prefabricated curling ice rink: Experiment and finite element simulation

Ice temperature is crucial for the quality of artificial ice rinks and ice sports. This study aims to investigate the temperature field of the ice sheet in the prefabricated curling rink for the Beijing Winter Olympics through a combination of experiments and simulations. Through the analysis of heat exchange in the ice sheet, three numerical models of the temperature field of the ice sheet were developed using the finite element software ABAQUS. An environmental temperature model and a comprehensive ambient temperature were proposed to consider thermal radiation and heat convection. Moreover, the simulation results at varying positions were validated through on-site observations of ice temperature, the comparison of three temperature field modeling methods was conducted, and the distribution characteristics of the temperature field were analyzed. In addition, the impact of various parameters on the ice temperature was investigated, and a parameter of the response efficiency of the ice temperature was proposed to conduct sensitivity analysis. Results show that the simplified finite element model of the ice sheet could provide a practical approach to obtain the ice temperature fields. The horizontal and vertical distribution characteristics of the ice temperature can be mathematically described using a sine function with variable amplitude and a cubic polynomial, respectively. A sensitivity analysis indicates that the response efficiency of the ice surface temperature corresponding to cooling medium, ceiling, and air is 90%, 10%, and 10%, respectively. And the ice surface is effectively regulated by the temperature of the cooling medium. The current study would help in the design, operation, and maintenance of ice sheets.

Fast fluid–structure interaction simulation method based on deep learning flow field modeling

The rapid acquisition of high-fidelity flow field information is of great significance for engineering applications such as multi-field coupling. Current research in flow field modeling predominantly focuses on low Reynolds numbers and periodic flows, exhibiting weak generalization capabilities and notable issues with temporal inferring error accumulation. Therefore, we establish a reduced order model (ROM) based on Convolutional Auto-Encoder (CAE) and Long Short-Term Memory (LSTM) neural network and propose an unsteady flow field modeling method for the airfoil with a high Reynolds number and strong nonlinear characteristics. The attention mechanism and weak physical constraints are integrated into the model architecture to improve the modeling accuracy. A broadband excitation training strategy is proposed to overcome the error accumulation problem of long-term inferring. With only a small amount of latent codes, the relative error of the flow field reconstructed by CAE can be less than 5‰. By training LSTM with broadband excitation signals, stable dynamic evolution can be achieved in the time dimension. CAE-LSTM can accurately predict the forced response and complex limit cycle behavior of the airfoil in a wide range of amplitude and frequency under subsonic/transonic conditions. The relative errors of predicted variables and integral force are less than 1%. The fluid–structure interaction framework is built by coupling the ROM and motion equations of the structure. CAE-LSTM predicts the time series response of pitch displacement and moment coefficient at different reduced frequencies, which is in good agreement with computational fluid dynamics, and the simulation time savings exceed one order of magnitude.

Causally Probing the Role of the Hippocampus in Fear Discrimination: A Precision Functional Mapping–Guided, Transcranial Magnetic Stimulation Study in Participants With Posttraumatic Stress Symptoms

BackgroundFear overgeneralization is a promising pathogenic mechanism of clinical anxiety. A dominant model posits that hippocampal pattern separation failures drive overgeneralization. Hippocampal network–targeted transcranial magnetic stimulation (HNT-TMS) has been shown to strengthen hippocampal-dependent learning/memory processes. However, no study has examined whether HNT-TMS can alter fear learning/memory. MethodsContinuous theta burst stimulation was delivered to individualized left posterior parietal stimulation sites derived via seed-based connectivity, precision functional mapping, and electric field modeling methods. A vertex control site was also stimulated in a within-participant, randomized controlled design. Continuous theta burst stimulation was delivered prior to 2 visual discrimination tasks (1 fear based, 1 neutral). Multilevel models were used to model and test data. Participants were undergraduates with posttraumatic stress symptoms (final n = 25). ResultsMain analyses did not indicate that HNT-TMS strengthened discrimination. However, multilevel interaction analyses revealed that HNT-TMS strengthened fear discrimination in participants with lower fear sensitization (indexed by responses to a control stimulus with no similarity to the conditioned fear cue) across multiple indices (anxiety ratings: β = 0.10, 95% CI, 0.04 to 0.17, p = .001; risk ratings: β = 0.07, 95% CI, 0.00 to 0.13, p = .037). ConclusionsOvergeneralization is an associative process that reflects deficient discrimination of the fear cue from similar cues. In contrast, sensitization reflects nonassociative responding unrelated to fear cue similarity. Our results suggest that HNT-TMS may selectively sharpen fear discrimination when associative response patterns, which putatively implicate the hippocampus, are more strongly engaged.

A comparative assessment of gravitational field modeling methods for binary asteroid landing

A comparative assessment of gravitational field modeling methods for binary asteroid landing

Application of Principal Component Analysis in Establishing the Dominant Pollutants in the New Calabar River.

The New Calabar River, an essential water source in Nigeria’s Niger Delta region, is facing significant water quality issues due to human activities. This research adopts a comprehensive strategy, integrating field data gathering, statistical analyses, and modeling methods to evaluate and simulate the impact of these activities on water quality. Analysis of Variance (ANOVA) outcomes revealed notable seasonal fluctuations in certain water quality parameters like Water Temperature (F=116.009, p<0.001) and pH levels (F=12.782, p<0.001), indicating clear distinctions between the specified months. Conversely, Total Dissolved Solids (TDS) and Electrical Conductivity (EC) showed insignificant variations (F=0.050, p=0.95 and F=0.036, p=0.96, respectively). Principal Component Analysis (PCA) identified crucial factors influencing water quality variations. The rotated component matrix displayed substantial loadings for parameters such as Turbidity (0.932), Dissolved Oxygen (0.919), and Biological Oxygen Demand (0.912), suggesting their significant impact on water quality dynamics. Employing GIS techniques for spatial mapping of WQI values uncovered pollution hotspots near Points 5 and 6, aligning with the PCA findings. These regions exhibited “Very Bad” water quality status, indicating severe pollution levels. Conversely, Point 3 demonstrated a “Medium” water quality status, implying better water quality conditions. Overall, the study highlights the intricate connection between human activities and water quality in the New Calabar River. The insights gained offer valuable guidance for informed decision-making in water resource management, pollution mitigation strategies, and policy development. Future research endeavors should prioritize continuous monitoring, adaptive management approaches, and community involvement to foster sustainable water quality management practices in the area.

Masked Generative Light Field Prompting for Pixel-Level Structure Segmentations

Pixel-level structure segmentations have attracted considerable attention, playing a crucial role in autonomous driving within the metaverse and enhancing comprehension in light field-based machine vision. However, current light field modeling methods fail to integrate appearance and geometric structural information into a coherent semantic space, thereby limiting the capability of light field transmission for visual knowledge. In this paper, we propose a general light field modeling method for pixel-level structure segmentation, comprising a generative light field prompting encoder (LF-GPE) and a prompt-based masked light field pretraining (LF-PMP) network. Our LF-GPE, serving as a light field backbone, can extract both appearance and geometric structural cues simultaneously. It aligns these features into a unified visual space, facilitating semantic interaction. Meanwhile, our LF-PMP, during the pretraining phase, integrates a mixed light field and a multi-view light field reconstruction. It prioritizes considering the geometric structural properties of the light field, enabling the light field backbone to accumulate a wealth of prior knowledge. We evaluate our pretrained LF-GPE on two downstream tasks: light field salient object detection and semantic segmentation. Experimental results demonstrate that LF-GPE can effectively learn high-quality light field features and achieve highly competitive performance in pixel-level segmentation tasks.

Integrated modeling method of the internal and external flow of helicopter/inlet

The internal and external integrated flow field modeling method of the helicopter/inlet system was studied. The boundary of internal flow field modeling was proposed. The internal and external integrated calculation model, including the helicopter fuselage, rotor, tail rotor, and other rotating components, as well as the internal flow field of the inlet, was established. On this basis, numerical calculation is carried out according to typical working conditions to analyze the flow field characteristics in the forward flight state and the influence of inlet back pressure on performance parameters. The results show that the integrated numerical calculation model established in this paper considers the internal and external interference of the actual rotor movement in the outflow field. The integrated flow field calculation in typical working conditions shows that the occlusion of the rotor blade and the fuselage will cause interference with the inlet flow field. The parameters of the left and right inlet ports will be different. With the decrease of inlet back pressure, the total pressure recovery decreases with the increase of flow rate and is obviously lower than that without rotor interference.

Modeling the gravitational field of the ore-bearing asteroid by using the CFD-based method

A gravitational field of an ore-bearing asteroid, which usually has an irregular shape and heterogeneous density, is a prerequisite for asteroid exploration (e.g., space mining) missions. Thus, it is a hot topic in planetary science to model the external gravitational field of the ore-bearing asteroid in an efficient and accurate way. In this study, a computational fluid dynamics (CFD)-based method proposed in our previsous studies is investigated further. Firstly, six types of density distribution in asteroid Bennu are simulated as six experimental cases; then the gravitational fields are derived by using the CFD-based method; and finally, the results are compared to the other two solutions derived from the mascons gravity model method (as a benchmark method) and polyhedron gravity model method, respectively. The CFD-based method shows a superior performance in modelling the gravitational field of an irregularly-shaped asteriod with heterogeneous density in terms of both accuracy and efficiency. For example, the CFD-based method only costs 340 s obtaining 1,650,000 gravitational vectors outside the asteroid with a relative error of 1.27 %, compared to the computation time of 14,520 s and the solution accuracy of 3.84 % for the polyhedron gravity model method on the same testing points. The comparison study demonstrates a good potential application of the CFD-based gravitational field modeling method in asteroid exploration missions.

Improving the CFD predictive accuracy of particle fate in turbulent duct flows: Four key issues and applications in in-duct UVGI system

In order to refine the CFD methodology for predicting particle fate in duct flows, this study investigated four key issues largely influencing the predictive accuracy. The flow field modeling method applicable to in-duct UVGI systems (ID-UVs) was also investigated. The particle number independence test indicated that at least 30000 particles should be released. The use of 2D duct cannot consider particle trapping at the sidewalls, thus underestimating the particle deposition behavior. The two-equation k‐ε models significantly overestimated the fluctuation velocity perpendicular to the duct walls in the near-wall region, resulting in them providing Vd+ and η were on average 1767.9 % and 451.3 % higher than those predicted by the RSM model, respectively. Corrections for fluctuation velocity had very limited benefit in improving the predictive accuracy of the two-equation k‐ε model, which unexpectedly resulted in a decrease in the predictive accuracy of the RSM model. Therefore, it was recommended to use the uncorrected RSM model to predict the 3D duct flow field to obtain a high prediction accuracy of particle fate. Similarly, the RSM model was also recommended for modeling the flow field in ID-UVs instead of the two-equation k‐ε model that was often used. This study also revealed that missing the “Wall Reflection Effects” would lead to confusing results and analyzed the reasons for the quantitative differences in the results obtained in previous studies. The findings presented may form a CFD methodological framework for further investigation of the in-duct air purification technologies.

Fluid-induced vibration analysis of centrifugal pump including rotor system based on Computational Fluid Dynamics and Computational Structural Dynamics coupling approach

The flow-induced vibration of centrifugal pump under the effect of stator-rotor interaction are studied by Computational Fluid Dynamics method and Computational Structural Dynamics method based on the principle of one-way decomposition fluid-structure interaction. Firstly, the unsteady flow characteristics in centrifugal pump are studied by adopting the Computational Fluid Dynamics method, the numerical model of the whole flow field of the centrifugal pump is established, and the pulsating pressure characteristics of volute and impeller in the centrifugal pump are analyzed. The accuracy of the flow field modeling method and calculation method in this paper is verified by external characteristic test. Secondly, the vibration characteristic test of centrifugal pump is carried out, and the structural dynamic model and boundary conditions of centrifugal pump are verified and corrected in the modal test. Finally, the flow-induced excitation calculated by the flow field is simultaneously applied to the structural dynamics model of the centrifugal pump according to different transmission ways, and the flow-induced vibration of the whole centrifugal pump including the rotor system is calculated and analyzed by the Computational Structural Dynamics method in conjunction with rotor dynamics. Compared with the vibration test results, the validity of the flow-induced vibration calculation method of centrifugal pump in this paper is verified. The results show that under the influence of stator-rotor interaction effect, the blade passing frequency and shaft frequency are the main characteristic frequencies of pressure pulsation and dynamic response in the centrifugal pump.

A framework of gravity field online modeling and trajectory optimization in asteroid soft-landing mission scenarios

Focused on asteroid soft-landing mission scenario, this paper investigates the methods of online gravity field modeling and trajectory optimization. Since the gravity field near asteroids and its surface topography are irregular, accurate asteroid soft-landing can be a challenging problem to solve, especially in the case of limited gravity data. With an actual asteroid soft-landing mission in mind, this study constructs a dataset based on the gravity field data collected in the limited area through which a soft-landing probe passed, and conducts online modeling of the asteroid inhomogeneous gravity field at the same time, using a transfer learning deep neural network (TL-DNN). To achieve fuel optimization and an accurate landing, a fast trajectory optimization method based on Bezier shape approach is implemented to achieve fast online robust re-trajectory optimization. Numerical simulation results show that the adopted TL-DNN can quickly reconstruct the gravitational field near the asteroid online, based only on the limited gravity data collected by the probe. Compared with the situation without online gravity field reconstruction and multiple online trajectory optimization, the proposed online gravity field modeling and re-trajectory optimization method can reduce the final position and velocity error between the multi-planned ideal optimal trajectory and the actual trajectory from 2396.367 m and 3.870 m/s to 14.152 m and 0.075 m/s, respectively. In other words, the soft-landing accuracy is improved by about two orders of magnitude.

Evaluating feasibility of field modeling of fire to calculate fire characteristics in buildings and premises

Introduction. The present paper describes application of a software package using a field model of fire dynamics to calculate fire characteristics in buildings and premises of nuclear power plants (NPP). The authors give necessary justifications for using the software package in performing fire calculations in multifunctional buildings and premises.Aim. To analyze different fire modeling methods, their application and use of the software package for field modeling of fire dynamics to determine the dynamics of fire hazards in complex premises, in facilities with non-uniform fire loads or complex gas exchange processes; to contribute solving the issue of safe distances ensuring that fire cannot spread between equipment elements.Materials and methods. The authors developed and verified a software package to perform calculations using the field model of fire dynamics. The paper presents the basics of the field method for fire modeling in multifunctional premises and the aspects of its application in fire simulation. The presented analytics is substantiated with examples of fire simulation results in real premises of NPPs.Results. Following the analysis of different methods of modeling the dynamics of development and spread of fire hazards, the present paper introduces the possibility of using various methods of fire modeling in the evaluation of fire hazards for buildings and premises. The authors describe the advantages of field modeling method for calculating local parameters of fire. The paper provides information on the software codes to calculate the dynamics of fire and evaluate the thermal effects of fire on building structures.Conclusion. It has been found possible to apply field model of fire dynamics for calculating fire hazards in various buildings, premises and open areas. Calculations using the presented field model enable the sufficiency of fire resistance of building structures and multifunctional premises to be substantiated due to preventing fire spread outside the fire zone during the estimated time of burnout of the total fire load.

Effectiveness of early fallow on Steppe chernozems

Topicality. Clean fallow is a reliable means of drought control, increasing productivity and sustainability of Steppe agriculture. At the same time, a fallow remains the most vulnerable field of the crop rotation, which requires perfect methods of maintenance that can counteract erosion processes, prevent humus losses, and improve the moisture availability of wheat. Purpose. To determine the soil protection and agrotechnical effectiveness of early fallow (sunflower, stubble, maize) when growing winter wheat in the conditions of the Northern Steppe of Ukraine. Materials and methods. The primary tillage of clean fallow was carried out with heavy cultivators, combined units, and plows. The erodible resistance of chernozem was assessed by field modeling and hydrological methods, to frost heaving – by soil lumpiness and the amount of post-harvest residues. The water-physical properties of the arable layer were determined in accordance with generally accepted methodical recommendations, the yield – by direct harvesting, and the grain quality – in accordance with DSTU 3768:2019. Results. It was established that maintaining arable land according to the early fallow scheme contributes the soil deflation and erosion control. At the same time, the migration of fine soil outside the field does not exceed 1.5–4.3 t/ha per year. The introduction of early fallow after cereals and row crops contributes to additionally accumulate productive soil moisture in the amount of 130–150 m3/ha compared to the control (plowing 25–27 cm) and restore moisture reserves for the spring tillering of wheat plants (207–221 mm or 86–92 % of the ultimate field water capacity, 0-150 cm layer). On sloping lands, the two-phase tillage of early fallow is preferable, which includes strip loosening to 40–45 cm depth in late autumn and shallow loosening to 14–16 cm depth in spring. In terms of productivity of winter crops, early fallows are not inferior to fall tillage. On the plains, the best variant of fallow maintenance was variant, which combines mulching with the cultivation of cover crops, on the slopes – with soil slitting. When involving all by-products of predecessors in the cycle, it is advisable to feed plants with nitrogen fertilizers in the spring with a dose of N30-60. The application of mineral nitrogen provided an average wheat yield on early fallow at the level of 5.52–6.66 t/ha and food grain with a protein content of 11.5–11.9%, gluten - 22.6–24.6%. Conclusions. Maintaining arable land according to early fallow scheme reliably protects the soil from erosion and ensures the restoration of productive moisture reserves to the level of 86–92% of the ultimate field moisture capacity in the second year. According to the wheat grain yield, spring tillage (12–16 cm) was not inferior to autumn plowing (25–27 cm). The effectiveness of early fallows is enhanced by soil slitting, cultivation of post-harvest (cover) crops, optimization of nitrogen nutrition of plants. Key words: early fallow, winter wheat, tillage, post-harvest residues, fertilizers, erosion, moisture, yield, grain quality

Modeling and implementation of vertical excursion FFA in the Zgoubi ray-tracing code

Vertical Fixed Field Accelerators (vFFAs) feature complex and highly non-linear magnetic fields, which require simulation codes allowing step-wise particle tracking. Methods to model the 3D magnetic field of scaling vFFAs have been developed in the ray-tracing code Zgoubi. The field modeling and particle tracking methods include the field non-linearities, the fringe fields, and the field superposition of neighboring magnets. The procedure implements the vFFA analytical field expressions, allowing design studies and parameter optimizations using the Zgoubi built-in fit method. The vFFA procedure has been applied to a ten-fold symmetry ring with a triplet focusing structure designed to accelerate protons from 3 MeV to 12 MeV and studied under the ISIS-II proton driver prototype project. Results from particle tracking in externally generated 3D semi-analytical field maps and the developed vFFA analytical model are shown to be in excellent agreement.

A 5-D Large-Workspace Magnetic Localization and Actuation System Based on an Eye-in-Hand Magnetic Sensor Array and Mobile Coils

Simultaneous magnetic localization and actuation in a human-scale workspace are challenging but essential for medical applications such as whole gastrointestinal (GI) tract monitoring and blood clot clearance in the leg. In this article, we propose a 5-D magnetic localization and actuation system that can track and actuate magnetic robots in a cylindrical workspace with a diameter of 500 mm. Based on the eye-in-hand configuration of the sensor array and the flexibility of the mobile electromagnetic manipulation system (mEMS), we realize a high localization accuracy in a large workspace with only 25 sensors. Moreover, we design an accurate magnetic field modeling method that can attenuate the electromagnets’ hysteresis and provide a precise actuation field estimation. Taking advantage of the mobile sensor array, we developed a signal-quality-based tracking strategy (STS) that could improve the localization performance by adjusting the movement of the sensor array. The effectiveness and advantages of the proposed methods are verified by simulations and experiments. Results show that the STS could decrease 25% position root-mean-square error (RMSE). The resulting position RMSE and orientation RMSE are 2.02 mm and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathrm {8.24}}^{\circ} $ </tex-math></inline-formula> , respectively. We experimentally prove the viability of the proposed strategy by propelling a magnetic helical robot through a 400-mm long 3-D twisted silicone phantom.

3-D Electromagnetic Force Characteristics and Modeling of Double-Sided Air-Cored Superconducting Linear Synchronous Motor for EDS Train

Double-sided air-cored superconducting linear synchronous motors (DSAC-SLSMs) play an important role in electrodynamic suspension trains. For this type of motor, the existing magnetic field modeling method is improved in this study, and a new 3-D electromagnetic force (EMF) analysis method is proposed to analyze the influence on the 3-D EMFs when the onboard superconducting coils (SCs) have multiple degrees of freedom motions such as deviation and deflection. First, based on Biot–Savart law and Poisson’s equation of magnetic vector potential, the analytical prediction of superconducting air-gap flux density is conducted. Thus, the relationship between <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> -axis armature current and 3-D EMFs is determined. Second, the equivalent circuit of DSAC-SLSM is established, and the effects of lateral and vertical displacements of the onboard SCs on armature current are analyzed. Finally, the validity of the proposed model is verified by using the finite-element model, two static experiments, and publicly available data on the Yamanashi maglev test line, while the 3-D EMF characteristics of the motor under various conditions are analyzed in detail.

Sound Field Modeling Method and Key Imaging Technology of an Ultrasonic Phased Array: A Review

An ultrasonic phased array consists of multiple ultrasonic probes arranged in a certain regular order, and the delay time of the excitation signal sent to each array element is controlled electronically. The testing system model based on ultrasonic propagation theory is established to obtain a controllable and focused sound field, which has theoretical and engineering guiding significance for the calculation and analysis of ultrasonic array sound fields. Perfecting array theory and exploring array imaging methods can obtain rich acoustic information, provide more intuitive and reliable research results, and further the development of ultrasonic phased-array systems. This paper reviews the progress of research on the application of ultrasound arrays for non-destructive testing (NDT) and brings together the most relevant published work on the application of simulation methods and popular imaging techniques for ultrasonic arrays. It mainly reviews the modeling approaches, including the angular spectrum method (ASM), multi-Gaussian beam method (MGB), ray tracing method, finite element method (FEM), finite difference method (FDM), and distributed point source method (DPSM), which have been used to assess the performance and inspection modality of a given array. In addition, the array of imaging approaches, including the total focusing method (TFM), compression sensing imaging (CSI), and acoustic nonlinearity imaging (ANI), are discussed. This paper is expected to provide strong technical support in related areas such as ultrasonic array testing theory and imaging methods.

Theoretical basis for phase field modeling of polycrystalline grain growth using a spherical-Gaussian-based 5-D computational approach

Using a previously developed phase field modeling method, where interface energies are described by spherical gaussians that allow the modeling of complex anisotropies, a new phase field model was developed to model 5-D anisotropy in polycrystalline grain growth. We present the use of quaternions, assigned to individual grains as orientations and misorientations for grain boundaries, as a means of simulating the ongoing mesoscale changes during anisotropic polycrystalline grain growth. The full 5-D landscape is scanned in MATLAB, and the grain boundary (GB) energy of each grain boundary is calculated from the continuous function developed by Bulatov et al. MATLAB is then used to find all local minima in the GB energy which are stored for use in the phase field model. The methodology of including these minima in the phase field model involves using 2-D gaussian switches, which match the misorientation between grains with misorientations for the GB energy minima. Within a threshold range of the minima misorientation, the switch activates a spherical Gaussian to set the GB energy to the desired value creating in combination a full 5D GB energy space. This creates a GB energy that morphs in real time and space as the GB plane or grain orientations change. Implementation methods of the model are outlined for the Multiphysics Object Oriented Simulation Environment (MOOSE), where reduced order parameters still retain individual grain identification useful for individually assigned quaternions.