Smooth Field Research Articles

Application of convolutional neural network for efficient turbulence modeling in urban wind field simulation

Accurate flow field estimation is crucial for the improvement of outdoor environmental quality, but computational fluid dynamics (CFD) based on the widely used Reynolds-averaged Navier–Stokes method has limitations in this regard. This study developed a turbulence modeling framework based on a convolutional neural network (CNN) to model turbulence in urban wind fields. The CNN model was trained by learning the Reynolds stress patterns and spatial correlations with the use of high-fidelity datasets. Next, the model was integrated into the CFD solver to generate accurate and continuous flow fields. The generalization capability of the proposed framework was initially demonstrated on the simplified benchmark configurations. The validated framework was then applied to case studies of urban wind environments to further assess its performance, and it was shown to be capable of delivering accurate predictions of the velocity field around an isolated building. For more complex geometries, the proposed framework performed well in regions where the flow properties were covered by the training dataset. Moreover, the present framework provided a continuous and smooth velocity field distribution in highly complicated applications, underscoring the robustness of the proposed turbulence modeling framework.

Joint [Formula: see text] and Image Reconstruction in Low-Field MRI by Physics-Informed Deep-Learning.

We present a model-based image reconstruction approach based on unrolled neural networks which corrects for image distortion and noise in low-field ( B0 ∼ 50 mT) MRI. Utilising knowledge about the underlying physics, a novel network architecture (SH-Net) is introduced which involves the estimation of spherical harmonic coefficients to guarantee a spatially smooth field map estimate. The SH-Net is integrated in an end-to-end trainable model which jointly estimates the B0-field map as well as the image. Experiments were conducted on retrospectively simulated low-field data of human knees. We compare our model to different model-based approaches at distinct noise levels and various B0-field distributions. Our results show that our physics-informed neural network approach outperforms the purely model-based methods by improving the PSNR up to 11.7% and the RMSE up to 86.3%. Our end-to-end trained model-based approach outperforms existing methods in reconstructing image and B0-field maps in the low-field regime. low-field MRI is becoming increasingly more popular as it enables access to MR in challenging situations such as intensive care units or resource poor areas. Our method allows for fast and accurate image reconstruction in such low-field imaging with B0-inhomogeneity compensation under a wide range of various environmental conditions.

Upper Bound for the Conjunction Probability of Smooth Stationary Two-dimensional Gaussian Fields

Upper Bound for the Conjunction Probability of Smooth Stationary Two-dimensional Gaussian Fields

Stress-based topology optimization using maximum entropy basis functions-based meshless method

AbstractThis paper presents volume-constrained stress minimization-based, topology optimization. The maximum entropy (maxent) basis functions-based meshless method for two-dimensional linear elastic structures is explored. This work focuses to test the effectiveness of the meshless method in handling the stress singularities during the topology optimization process. The commonly used moving least square basis functions are replaced with maximum entropy basis functions, as the latter possess weak Kronecker delta property which leads to the finite element method (FEM) like displacement boundary conditions imposition. The maxent basis functions are calculated once at the beginning of the simulation and then used in optimization at every iteration. Young’s modulus for each background cell is interpolated using the modified solid isotropic material with penalization approach. An open source pre-processor CUBIT is used. A comparison of the proposed approach with the FEM is carried out using a diverse set of problems with simple and complex geometries of structured and unstructured discretization, to establish that maxent-based meshless methods perform better in tackling the stress singularities due to its smooth stress field.

Free-Form Deformation as a non-invasive, discrete unfitted domain method: Application to the time-harmonic acoustic response of a saxophone

The Finite Element method, widely used for solving Partial Differential Equations, may result in suboptimal computational costs when computing smooth fields within complex geometries. In such situations, IsoGeometric Analysis often offers improved per degree-of-freedom accuracy but building analysis-suitable representation of complex shapes is generally not obvious. This paper introduces a non-invasive, spline-based fictitious domain method using Free-Form Deformation to efficiently solve the Helmholtz equation in complex domains, such as in musical instruments. By immersing a fine FE mesh into a simple B-spline box, the approximation subspace size is significantly reduced without compromising accuracy. Accompanied by specific conditioning treatment, the method not only proves to be efficient, but also robust and easy to implement in existing FE software. Applied to an alto saxophone, the method reduces the number of degrees of freedom by over two orders of magnitude and the computation time by more than one compared to standard FE methods with comparable accuracy when compared to experimental tests.

Mollow-like Triplets in Ultrafast Resonant Absorption.

We show that resonant absorption of smooth laser fields can yield Mollow-like triplet patterns. General conditions for such triplets are derived and illustrated with a super-Gaussian pulse sequence. Gaussian pulses cannot exhibit triplets, super-Gaussian pulses can form triplets depending on the pulse area, and flattop pulses can produce absorption triplets after one Rabi cycle. Our results are compared side by side with resonance fluorescence to emphasize similarities and differences between these unlike observables. In the high-intensity limit, we show that the central absorption peak is asymmetric, which we attribute to nonlinear photoionization, beyond two-level atomic physics.

Fast radiance field reconstruction from sparse inputs

Neural Radiance Field (NeRF) has emerged as a powerful method in data-driven 3D reconstruction because of its simplicity and state-of-the-art performance. However, NeRF requires densely captured calibrated images and lengthy training and rendering time to realize high-resolution reconstruction. Thus, we propose a fast radiance field reconstruction method from a sparse set of images with silhouettes. Our approach integrates NeRF with Shape from Silhouette, a traditional 3D reconstruction method that uses silhouette information to fit the shape of an object. To combine NeRF’s implicit representation with Shape from Silhouette’s explicit representation, we propose a novel explicit–implicit radiance field representation consisting of voxel grids with confidence and feature embedding for geometry and a multilayer perceptron network to decode view-dependent color emission for appearance. We propose to make the reconstructed geometry compact by taking advantage of silhouette images, which can avoid the majority of artifacts in sparse input scenarios and speed up training and rendering. We also apply voxel dilating and pruning to refine the geometry prediction. In addition, we impose a total variation regularization on our model to encourage a smooth radiance field. Experiments on the DTU and the NeRF-Synthetic datasets show that our algorithm surpasses the existing baselines in terms of efficiency and accuracy.

An improved 3D-UNet-based brain hippocampus segmentation model based on MR images

ObjectiveAccurate delineation of the hippocampal region via magnetic resonance imaging (MRI) is crucial for the prevention and early diagnosis of neurosystemic diseases. Determining how to accurately and quickly delineate the hippocampus from MRI results has become a serious issue. In this study, a pixel-level semantic segmentation method using 3D-UNet is proposed to realize the automatic segmentation of the brain hippocampus from MRI results. Methods: Two hundred three-dimensional T1-weighted (3D-T1) nongadolinium contrast-enhanced magnetic resonance (MR) images were acquired at Hangzhou Cancer Hospital from June 2020 to December 2022. These samples were divided into two groups, containing 175 and 25 samples. In the first group, 145 cases were used to train the hippocampus segmentation model, and the remaining 30 cases were used to fine-tune the hyperparameters of the model. Images for twenty-five patients in the second group were used as the test set to evaluate the performance of the model. The training set of images was processed via rotation, scaling, grey value augmentation and transformation with a smooth dense deformation field for both image data and ground truth labels. A filling technique was introduced into the segmentation network to establish the hippocampus segmentation model. In addition, the performance of models established with the original network, such as VNet, SegResNet, UNetR and 3D-UNet, was compared with that of models constructed by combining the filling technique with the original segmentation network. Results: The results showed that the performance of the segmentation model improved after the filling technique was introduced. Specifically, when the filling technique was introduced into VNet, SegResNet, 3D-UNet and UNetR, the segmentation performance of the models trained with an input image size of 48 × 48 × 48 improved. Among them, the 3D-UNet-based model with the filling technique achieved the best performance, with a Dice score (Dice score) of 0.7989 ± 0.0398 and a mean intersection over union (mIoU) of 0.6669 ± 0.0540, which were greater than those of the original 3D-UNet-based model. In addition, the oversegmentation ratio (OSR), average surface distance (ASD) and Hausdorff distance (HD) were 0.0666 ± 0.0351, 0.5733 ± 0.1018 and 5.1235 ± 1.4397, respectively, which were better than those of the other models. In addition, when the size of the input image was set to 48 × 48 × 48, 64 × 64 × 64 and 96 × 96 × 96, the model performance gradually improved, and the Dice scores of the proposed model reached 0.7989 ± 0.0398, 0.8371 ± 0.0254 and 0.8674 ± 0.0257, respectively. In addition, the mIoUs reached 0.6669 ± 0.0540, 0.7207 ± 0.0370 and 0.7668 ± 0.0392, respectively. Conclusion: The proposed hippocampus segmentation model constructed by introducing the filling technique into a segmentation network performed better than models built solely on the original network and can improve the efficiency of diagnostic analysis.

Lagrangian Perspectives on the Small-scale Structure of Alfvénic Turbulence and Stochastic Models for the Dispersion of Fluid Particles and Magnetic Field Lines in the Solar Wind

Lagrangian perspectives on the small-scale structure of anisotropic Alfvénic turbulence are adopted. We are interested in relating the statistical properties of the Eulerian field increments evaluated along the fluid particle trajectories, in the direction perpendicular to the guiding magnetic field and along the magnetic field lines. We establish the basis for a unified multifractal phenomenology of Eulerian and Lagrangian Alfvénic turbulence. The critical balance condition is generalized to structure functions of an order different than 2. A Lagrangian perspective is not only useful for investigating the small-scale structure of Alfvénic turbulence, it is also tailored to the modeling of large-scale turbulent transport. Therefore, we develop Lagrangian stochastic models for the dispersion of fluid particles and magnetic field lines in the solar wind. The transport models are based on the integrated Ornstein–Uhlenbeck process that is not Markov, yielding smooth stochastic fluid particle trajectories and magnetic field lines. Brownian diffusion is recovered by tending the integral scale parameter to zero while keeping the diffusivity finite.

Connes fusion of spinors on loop space

The loop space of a string manifold supports an infinite-dimensional Fock space bundle, which is an analog of the spinor bundle on a spin manifold. This spinor bundle on loop space appears in the description of two-dimensional sigma models as the bundle of states over the configuration space of the superstring. We construct a product on this bundle that covers the fusion of loops, i.e. the merging of two loops along a common segment. For this purpose, we exhibit it as a bundle of bimodules over a certain von Neumann algebra bundle, and realize our product fibrewise using the Connes fusion of von Neumann bimodules. Our main technique is to establish novel relations between string structures, loop fusion, and the Connes fusion of Fock spaces. The fusion product on the spinor bundle on loop space was proposed by Stolz and Teichner as part of a programme to explore the relation between generalized cohomology theories, functorial field theories, and index theory. It is related to the pair of pants worldsheet of the superstring, to the extension of the corresponding smooth functorial field theory down to the point, and to a higher-categorical bundle on the underlying string manifold, the stringor bundle.

Adaptively Isotropic Remeshing Based on Curvature Smoothed Field.

With the development of 3D digital geometry technology, 3D triangular meshes are becoming more useful and valuable in industrial manufacturing and digital entertainment. A high quality triangular mesh can be used to represent a real world object with geometric and physical characteristics. While anisotropic meshes have advantages of representing shapes with sharp features (such as trimmed surfaces) more efficiently and accurately, isotropic meshes allow more numerically stable computations. When there is no anisotropic mesh requirement, isotropic triangles are always a good choice. In this paper, we propose a remeshing method to convert an input mesh into an adaptively isotropic one based on a curvature smoothed field (CSF). With the help of the CSF, adaptively isotropic remeshing can retain the curvature sensitivity, which enables more geometric features to be kept, and avoid the occurrence of obtuse triangles in the remeshed model as much as possible. The remeshed triangles with locally isotropic property benefit various geometric processes such as neighbor-based feature extraction and analysis. The experimental results show that our method achieves better balance between geometric feature preservation and mesh quality improvement compared to peers. We provide the implementation codes of our resampling method at github.com/vvvwo/Adaptively-Isotropic-Remeshing.

Modified (n+1)D Laplacian for smooth pressure reconstruction based on time-resolved velocimetry (1): analysis and numerics

Abstract We analyze a smooth pressure solver based on the "modified Poisson equation": ∇2 p +ξ 2∂2 p/∂ t 2 = f(u(t)), where p is the pressure field, u (t) is the velocity field measured by time-resolved image velocimetry, and ξ 2 is a tunable parameter to control the solver's diffusive behavior in time. This modified Poisson equation aims at obtaining smooth pressure fields from potentially noisy image velocimetry measurements, and is a part of the current four-dimensional (4D) pressure solver (implemented in, for example, DaVis 10.2) by LaVision. This work focuses on investigating three aspects of the "modified Poisson equation": smoothing effect, error propagation, and drift in time. We first provide rigorous analysis and validate that this solver can sufficiently smooth the computed pressure field by setting a large enough ξ 2. However, a large value of ξ 2 may cause large errors in the reconstructed pressure fields. Then we introduce an upper bound on the error in the reconstructed pressure fields to quantify the error propagation dynamics. Finally, we discuss the potential drift due to the partitioning in time, which is an optional strategy used in LaVision's current 4D pressure solver to reduce computational costs. Our analysis and validation not only show that careful choice of the parameters (e.g., ξ 2) is needed for smooth and accurate pressure field reconstruction but provide theoretical guidelines for parameter tuning when similar pressure solvers are used for time-resolved image velocimetry data.

Harvesting deformation modes for micromorphic homogenization from experiments on mechanical metamaterials

A micromorphic computational homogenization framework has recently been developed to deal with materials showing long-range correlated interactions, i.e. displaying patterning modes. Typical examples of such materials are elastomeric mechanical metamaterials, in which patterning emerges from local buckling of the underlying microstructure. Because pattern transformations significantly influence the resulting effective behaviour, it is vital to distinguish them from the overall deformation. To this end, the following kinematic decomposition into three parts was introduced in the micromorphic scheme: (i) a smooth mean displacement field, corresponding to the slowly varying deformation at the macro-scale, (ii) a long-range correlated fluctuation field, related to the buckling pattern at the meso-scale, and (iii) the remaining uncorrelated local microfluctuation field at the micro-scale. The micromorphic framework has proven to be capable of predicting relevant mechanical behaviour, including size effects and spatial as well as temporal mixing of patterns in elastomeric metamaterials, making it a powerful tool to design metamaterials for engineering applications. The long-range correlated fluctuation fields need to be, however, provided a priori as input parameters. The main goal of this study is experimental identification of the decomposed kinematics in cellular metamaterials based on the three-part ansatz. To this end, a full-field micromorphic Integrated Digital Image Correlation (IDIC) technique has been developed. The methodology is formulated for finite-size cellular elastomeric metamaterial specimens deformed in (i) virtually generated images and (ii) experimental images attained during in-situ compression of specimens with millimetre sized microstructure using optical microscopy. The proposed IDIC method identifies the different kinematic fields, both before and after the microstructural buckling, and without any prior knowledge determines correctly the relevant patterning modes required by the homogenization scheme. It is further argued that patterning modes are independent of the unit cell size, the hole diameter to cell size ratio, as well as local material properties, allowing for modelling and design of (finite- and infinite-size) metamaterials and specimens with graded microstructures in terms of geometry and/or material properties. It is shown that the proposed methodology is also applicable to cellular metamaterials and structures with different microstructural designs.

Ultra-Wideband Vertical Transition in Coplanar Stripline for Ultra-High-Speed Digital Interfaces.

A design method for an ultra-wideband coplanar-stripline-based vertical transition that can be used for ultra-high-speed digital interfaces is proposed. A conventional via structure, based on a differential line (DL), inherently possesses performance limitations (<10 GHz) due to difficulties in maintaining constant line impedance and smooth electric field transformation, in addition to the effects of signal skews, FR4 fiber weave, and unbalanced EM interferences. DL-based digital interfaces may not meet the demands of ultra-high-speed digital data transmission required for the upcoming 6G communications. The use of a coplanar stripline (CPS), a type of planar balanced line (BL), for the vertical transition, along with the ultra-wideband DL-to-CPS transition, mostly removes the inherent and unfavorable issues of the DL and enables ultra-high-speed digital data transmission. The design process of the transition is simplified using the analytical design formulas, derived using the conformal mapping method, of the transition. The characteristic line impedances of the transition are calculated and found to be in close agreement with the results obtained from EM simulations. Utilizing these results, the CPS-based vertical transition, maintaining the characteristic line impedance of 100 Ω, is designed and fabricated. The measured results confirm its ultra-wideband characteristics, with a maximum of 1.6 dB insertion loss and more than 10 dB return loss in the frequency range of DC to 30 GHz. Therefore, the proposed CPS-based vertical transition offers a significantly wider frequency bandwidth, i.e., more than three times that of conventional DL-based via structures.

Robustness evaluation of large-scale machine learning-based reduced order models for reproducing flow fields

The robustness of an artificial neural network that performs model order reduction for flow field data is studied. The network is trained with a large-scale distributed learning approach using up to 6259 nodes of the supercomputer Fugaku. Flow around two square cylinders with a varying distance between their centers is investigated. The network is trained and tested with data from numerical simulations. First, the capability to reproduce flow fields with 2, 12, and 24 modes is investigated by comparing the reconstructed flow data to simulated data. It is shown, that reconstructions based on 2 modes cannot capture both, low- and high-frequency flow structures correctly, whereas predictions based on 12 and 24 modes yield improved flow fields, especially in the case of high-frequency waves in the vicinity of the square cylinders. Reconstructions with 24 modes provide smooth velocity fields that reproduce all relevant low- and high-frequency waves for all variations of the distance between the two square cylinders. Second, the performance of the machine learning-based reconstructions are compared to proper orthogonal decomposition, which is a commonly used reduced order model technique. The comparison only includes flow fields based on 24 modes. For all geometric variations, the mean squared errors of the reconstructions by the conventional method are higher than those of the machine learning model. This underlines the advantage of artificial neural networks over linear methods like proper orthogonal decomposition for tasks like reconstructing flow fields that are characterized by non-linear governing equations.

Radial basis point interpolation for strain field calculation in digital image correlation

In order to extract smooth and accurate strain fields from the noisy displacement fields obtained by digital image correlation (DIC), a point interpolation meshless (PIM) method with a radial basis function (RBF) is introduced for full-field strain calculation, which overcomes the problems of slow calculation speed and unstable matrix inverse calculation of the element-free Galerkin method (EFG). The radial basis point interpolation method (RPIM) with three different radial basis functions and the moving least squares (MLS) and pointwise least squares (PLS) methods are compared by analyzing and validating the strain fields with high-strain gradients in simulation experiments. The results indicate that the RPIM is nearly 80% more computationally efficient than the MLS method when a larger support domain is used, and the efficiency of the RPIM is nearly 26% higher than that of the MLS method when a smaller support domain is used; the strain calculation accuracy is slightly lower than that of the MLS method by 0.3–0.5%, but the stability of the calculation is significantly improved. In contrast with the PLS method, which is easily affected by the noise and the size of the strain calculation window, the RPIM is insensitive to the displacement noise and the size of the support domain and can obtain a similar calculation accuracy. The RPIM with multiquadric (MQ) radial basis functions performs well in balancing the computational accuracy and efficiency and is insensitive to shape parameters. The application cases show that the method can effectively compute the strain field at the crack tip, validating its applicability to the study of the plastic region at the crack tip. In conclusion, the proposed RPIM-based method provides an accurate, practical, and robust approach for full-field strain measurements.

Fully coupled discrete element method for graded particles transport in pipes

Hydraulic conveying of graded particles is much more complex than that of uniform particles but is not fully understood. A fully coupled computational fluid dynamics–discrete element method model is established for the hydraulic conveying of graded particles, which integrally considers the particle–fluid and particle–particle interactions and turbulence modulation from particles. The proposed model accounts for the stochastic motion of particles by the discrete random walk method and applies the diffusion averaging algorithm to obtain particle concentration in arbitrary cells for smooth and cell-independent data fields on unfavorable cells (fluid cell size ≤ particle size). The particle–fluid drag force is applied to slurry flows through densely packed particle beds due to the consideration of porosity modification. The proposed model well performs in simulating the hydraulic conveying of dense graded particles. Dynamics in slurry mixtures of bi-disperse particles are investigated regarding different particle size compositions. The results show obvious stratification between coarse and fine particles, e.g., fine particles settling at the pipe bottom elevate the coarse particles and form a “lubrication layer” with high velocity. The torque caused by particle–particle/wall contact is greater than the torque caused by the fluid. The pipe cross section is divided into four regions according to the particle angular velocity. The effect of particle concentration on liquid motion is small because the difference in local particle concentration is relatively small, but the maximum pressure drop corresponds to a critical particle size composition.

Smooth Matérn Gaussian random fields: Euler characteristic, expected number and height distribution of critical points

This paper studies Gaussian random fields with Matérn covariance functions with smooth parameter ν>2. Two cases of parameter spaces, the Euclidean space and N-dimensional sphere, are considered. For such smooth Gaussian fields, we have derived the explicit formulae for the expected Euler characteristic of the excursion set, the expected number and height distribution of critical points. The results are valuable for approximating the excursion probability in family-wise error control and for computing p-values in peak inference.

Elasto-visco-plastic flows in benchmark geometries: I. 4 to 1 planar contraction

We present predictions for the flow of elastoviscoplastic (EVP) fluids in the 4 to 1 planar contraction geometry. The Saramito-Herschel-Bulkley fluid model is solved via the finite-volume method with the OpenFOAM software. Both the constitutive model and the solution method require using transient simulations. In this benchmark geometry, whereas viscoelastic fluids may exhibit two vortices, referred to as lip and corner vortices, we find that EVP materials are unyielded in the concave corners. They are also unyielded along the mid-plane of both channels, but not around the contraction area where all stress components are larger. The unyielded areas using this EVP model are qualitatively similar to those using the standard viscoplastic models, when the Bingham or the Weissenberg numbers are lower than critical values, and then, a steady state is reached. When these two dimensionless numbers increase while they remain below the respective critical values, which are interdependent, (a) the unyielded regions expand and shift in the flow direction, and (b) the maximum velocity increases at the entrance of the contraction. Increasing material elasticity collaborates with increasing the yield stress, which expands the unyielded areas, because it deforms the material more prior to yielding compared to stiffer materials. Above the critical Weissenberg number, transient variations appear for longer times in all variables, including the yield surface, instead of a monotonic approach to the steady state. They may lead to oscillations which are damped or of constant amplitude or approach a flow with rather smooth path lines but complex stress field without a plane of symmetry, under creeping conditions. These patterns arise near the entrance of the narrow channel, where the curvature of the path lines is highest and its coupling with the increased elasticity triggers a purely elastic instability. Similarly, a critical value of the yield stress exists above which such phenomena are predicted.

Functional principal component analysis for incomplete space–time data

Environmental signals, acquired, e.g., by remote sensing, often present large gaps of missing observations in space and time. In this work, we present an innovative approach to identify the main variability patterns, in space–time data, when data may be affected by complex missing data structures. We formalize the problem in the framework of functional data analysis, proposing an innovative method of functional principal component analysis (fPCA) for incomplete space–time data. The functional nature of the proposed method permits to borrow information from measurements observed at nearby spatio-temporal locations. The resulting functional principal components are smooth fields over the considered spatio-temporal domain, and can lead to interesting insights in the spatio-temporal dynamic of the phenomenon under study. Moreover, they can be used to provide a reconstruction of the missing entries, also under severe missing data patterns. The proposed model combines a weighted rank-one approximation of the data matrix with a roughness penalty. We show that the estimation problem can be solved using a majorize–minimization approach, and provide a numerically efficient algorithm for its solution. Thanks to a discretization based on finite elements in space and B-splines in time, the proposed method can handle multidimensional spatial domains with complex shapes, such as water bodies with complicated shorelines, or curved spatial regions with complex orography. As shown by simulation studies, the proposed space–time fPCA is superior to alternative techniques for Principal Component Analysis with missing data. We further highlight the potentiality of the proposed method for environmental problems, by applying space–time fPCA to the study of the lake water surface temperature (LWST) of Lake Victoria, in Central Africa, starting from satellite measurements with large gaps. LWST is considered one of the fundamental indicators of how climate change is affecting the environment, and is recognized as an essential climate variable.