Three-dimensional Grid Research Articles

Convective-Scale Assimilation of Cloud Cover from Photographs Using a Machine Learning Forward Operator

Abstract This paper presents an innovational way of assimilating observations of clouds into the icosahedral nonhydrostatic weather forecasting model for regional scale (ICON-D2), which is operated by the German Weather Service (Deutscher Wetterdienst) (DWD). A convolutional neural network (CNN) is trained to detect clouds in camera photographs. The network’s output is a grayscale picture, in which each pixel has a value between 0 and 1, describing the probability of the pixel belonging to a cloud (1) or not (0). By averaging over a certain box of the picture a value for the cloud cover of that region is obtained. A forward operator is built to map an ICON model state into the observation space. A three-dimensional grid in the space of the camera’s perspective is constructed and the ICON model variable cloud cover (CLC) is interpolated onto that grid. The maximum CLC along the rays that fabricate the camera grid, is taken as a model equivalent for each pixel. After superobbing, monitoring experiments have been conducted to compare the observations and model equivalents over a longer time period, yielding promising results. Further we show the performance of a single assimilation step as well as a longer assimilation experiment over a time period of 6 days, which also yields good results. These findings are proof of concept and further research has to be invested before these new innovational observations can be assimilated operationally in any numerical weather prediction (NWP) model.

Weighted compact nonlinear hybrid scheme based on a family of mapping functions for aeroacoustics problem

The study of differential schemes with high accuracy and low dispersion is of great significance for the numerical simulation of aeroacoustics over complex geometries. The midpoint-and-node-to-node explicit finite difference is employed to solve the flux derivatives of the linear Euler equations for improving the robustness. To obtain the numerical flux at the center of the grid element, we adopted a hybrid interpolation method of center and upwind interpolations, combined with a symmetrical conservative metric method, to achieve high-resolution discretization of the acoustic field variables and geometric variables of the structural grid. To suppress spurious oscillations and improve the resolution of discontinuous regions, a family of mapping functions is developed to establish different smoothness indicators and applied to the sixth-order weighted compact nonlinear hybrid scheme (WCNHS), forming a new WCNHS scheme based on piecewise exponential mapping functions (WCNHS-Pe). The approximate dispersion relation shows that the dispersion error and numerical dissipation of WCNHS-Pe are smaller than those of WCNHS with a simple mapping function to the original weights in Jiang and Shu and other mapping function-weighted WCNHS schemes. We have applied various WCNHS schemes to the numerical simulation of the Shu–Osher problem, propagation of Gaussian impulses on two-dimensional wavy grids, sound transmission at discontinuous interfaces, propagation of Gaussian impulses on three-dimensional wavy grids, etc. Numerical results indicate that the WCNHS-Pe scheme has better discontinuity capture capability, higher resolution, and lower dispersion under the same differential stencil, and is suitable for computational aeroacoustics of complex geometries.

A Novel Approach to Grain Shape Factor in 3D Hexagonal Cellular Automaton

Cellular automata (CA) modeling is a powerful and efficient tool for simulating the dynamic evolution of polycrystalline microstructures in modern materials and metallurgy studies, such as solidification, plastic deformation and recrystallization. We propose a novel model to calculate the shape factor of grains in three-dimensional hexagonal grid (3D-HEX) CA, which overcomes the disadvantages of 3D-HEX CA, such as complex algorithms and a long computation time. The shape factor is a quantitative measure of grain morphology based on the ratio of the surface area of the grain to its volume-equivalent-sphere and volume-equivalent-chain. It indicates how the shape of a grain or phase affects its mechanical properties, such as stiffness, deformation and fracture. Our model can easily calculate the shape factor for any grain by counting its surface cells and volume cells. We test our model on 1000 grains with different shapes (equiaxed, irregular and chain-like) by Monte Carlo (MC) methods. MC methods evaluate the validity of a calculation model by comparing the simulated outcomes with the observed or expected outcomes. The results show that our model can accurately describe the grain morphology and has a good comparability and generality.

Promising insights in parallel grid-based algorithms for quantum chemical topology.

Some straightforward improvements designed to make grid-based quantum chemical topology more efficient and faster are presented. The strategy focuses on both the evaluation of the scalar function over three-dimensional discrete grids and the algorithms aimed to follow and integrate gradient trajectories over the basin volumes together. Beyond the density analysis, we show that the scheme is quite suitable for the electron localization function and its complex topology. With this speed-up of the parallelized process used to generate 3d-grids, this new scheme is several orders of magnitude faster than the original grid-based method implemented in our laboratory (TopMod09). The efficiency of our implementation (TopChem2) was also compared with well-known grid-based algorithms designed to assign the grid points to basins. The performances, speed versus accuracy have been discussed on the basis of results obtained from selected illustrative examples.

Energy dissipation characteristics of particle dampers with obstacle grids

When the vibration excitation intensity is high, the energy dissipation of conventional particle dampers (PDs) is low. The experiment result shows that the three-dimensional grid structure (obstacle grids) in the particle damper can improve the problem of low efficiency of energy dissipation. In order to investigate the influence of obstacle grids on the particles motion and energy dissipation, a numerical model of a particle damper with obstacle grids is established by the discrete element method (DEM). The simulation results are basically consistent with the experiment results. The influence of vibration parameters and filling ratio on the energy dissipation is studied. The spatial distribution characteristics of particle collision and energy dissipation inside the particle damper are discussed. Under frequencies of 30–160 Hz, excitation intensity Γ > 5, and filling ratios of 50–90%, results show that the obstacle grids will change the motion behavior of the particles and enhance their energy dissipation. Under this condition, the obstacle grids make the particles, which originally do not contribute significantly to energy dissipation, to agitate aggressively and participate in energy dissipation. It means that particles in the bottom space of the damper have the multiplicative collision frequencies characteristics in one vibration cycle, thus increasing energy dissipation.

Exploiting underlying crystal lattice for efficient computation of Coulomb matrix elements in multi-million atoms nanostructures

Atomistic modeling of nanostructures often leads to computationally challenging problems involving millions of atoms and tens of thousands of Coulomb matrix elements. In our previous work, we presented a practical solution to this problem, where quasi-linear efficiency, both in time and memory, was obtained by utilizing the fast Fourier transform. Here, we present an updated version of our highly-parallelized computer program, named Coulombo-Lattice, that eliminates the necessity of introducing an auxiliary basis set for the wave-function transfer to the computational grid. Here, we instead exploit the properties of the underlying crystal lattice and run calculations on a regular three-dimensional grid superimposed on the original, lower-symmetry lattice. Due to removal of spurious interactions from other supercells, the resulting Coulomb matrix elements are, up to numerical precision, identical to those obtained by the direct summation O(N2) method, yet our code maintains O(Nlog⁡N) scaling. We illustrate our approach by calculations involving up to 1.7 million integrals, and number of atoms reaching up to 2.8 million, for the problem of dopant charging energy for a single phosphorus dopant embedded in a silicon lattice. Next, to emphasize the broad applicability of our code, we show the results for mixed zinc-blend/wurtzite lattice systems, also known as crystal phase quantum dots. Program summaryProgram Title: Coulombo-LatticeCPC Library link to program files:https://doi.org/10.17632/jwkvh5ycbf.1Licensing provisions: CC BY 4.0Programming language: C++Nature of problem: Computing the Coulomb matrix elements (Coulomb and exchange integrals), while being a demanding computational task, is a necessary step in a range of quantum mechanical calculations. For example, in the field of nanostructures, such as quantum dots and nanowires or novel single dopant devices, this stage of calculation (even after a series of approximations) is at least an O(N2) operation (a summation over all pairs of N atoms or grid points in the analyzed system). Moreover, calculating the full Coulomb matrix usually requires the computation of thousands of such elements, thus presenting a formidable computational challenge.Solution method: We provide a ready-to-use implementation for calculating Coulomb matrix elements for a given set of input wavefunctions in LCAO (linear combination of atomic orbitals) form resulting from tight-binding calculation. This implementation is based on the approach introduced in [1,2], by using a fast Fourier transform. In this work, we further significantly improved the method by eliminating the need to introduce wave-function transfer via auxiliary basis set.Additional comments including Restrictions and Unusual features: The implementation is fully parallelized in a distributed-memory model, using MPI and parallel routines from FFTW [3].

A Unified Grid Approach Using Hamiltonian Paths for Computing Aerodynamic Flows

A solution algorithm using Hamiltonian paths is presented as a unified grid approach for rotorcraft applications. Hidden line structures are robustly identified on general two- and three-dimensional unstructured grids with mixed elements, providing a framework for line-based solvers. A pure quadrilateral/hexahedral mesh is a prerequisite for line identification and enables approximate factorisation along the lines. The numerical efficiency obtained using the line-implicit method on various unstructured grids is better than that of the point-implicit method. Both finite-difference and gradient reconstructions are possible regardless of grid type. A combined reconstruction method is applied, which uses different reconstructions simultaneously but for different grid directions. Finally, the solution convergence rate is further improved using a preconditioned generalized minimal residual method (GMRES), where the preconditioning step is performed using the efficient line-implicit method.

Leading-Edge separation behaviors in SA RANS and SA-based DDES: Simple modifications for improved prediction

In this study, delayed detached-eddy simulations (DDESs) based on the Spalart–Allmaras turbulence model are investigated for separation flows. Three simple modifications are considered: the Reynolds-averaged Navier–Stokes (RANS) turbulence model coefficient, Crot, is calibrated to achieve a better leading-edge separation prediction in DDES; the large-eddy simulation (LES) coefficient, CDES, is assessed to obtain better dissipation control in DDES; and dirty-cell treatments in three-dimensional unstructured grids are conducted for a smooth LES/RANS transition. Numerical results confirm the effects of the three aforementioned steps, such as the reproducibility of the measured pressure distribution over the main wing in unsteady turbulence simulations of low-speed buffet around the NASA Common Research Model. Thus, these modifications will potentially serve as good alternatives, without major programming efforts, to the conventional approaches for practitioners.

Structure and evolution of a tidally heated star

Context. The shearing motion of tidal flows that are excited in non-equilibrium binary stars transform kinetic energy into heat via a process referred to as tidal heating. Aims. We aim to explore the way tidal heating affects the stellar structure. Methods. We used the TIDES code, which solves the equations of motion of the three-dimensional (3D) grid of volume elements that conform multiple layers of a rotating binary star to obtain an instantaneous value for the angular velocity, ω″, as a function of position in the presence of gravitational, centrifugal, Coriolis, gas pressure, and viscous forces. The released energy, Ė, was computed using a prescription for turbulent viscosity that depends on the instantaneous velocity gradients. The Ė values for each radius were injected into a MESA stellar structure calculation. The method is illustrated for a 1.0 + 0.8 M⊙ binary system, with an orbital period of P = 1.44 d and departures from synchronous rotation of 5% and 10%. Results. Heated models have a larger radius and surface luminosity, a smaller surface convection zone, and lower nuclear reaction rates than the equivalent standard stellar models, and their evolutionary tracks extend to higher temperatures. The magnitude of these effects depends on the amount of injected energy, which, for a fixed set of stellar, rotation and orbital parameters, depends on the perturbed star’s density structure and turbulent viscosity. Conclusions. Tidal heating offers a possible alternative for describing phenomena such as bloated or overluminous binary components, age discrepancies, and aspherical mass ejection, as well as the extended main sequence turnoff in clusters. However, establishing its actual role requires 3D stellar structure models commensurate with the nonspherically symmetric properties of tidal perturbations.

A Controller for Delta Parallel Robot Based on Hedge Algebras Method

Based on the Hedge Algebras (HA) methodology, this paper presents a method for managing the trajectory of a delta robot. This technique is easily applied to existing devices in the process control domain. In the proposed control method, the semantically quantitative mapping may replace the verbal values of the fundamental rule in an analogous manner (SQM). Consequently, the basic rule may be represented as a three-dimensional numerical grid with linear interpolations. Compared to the Fuzzy Logic controller, it reduces the controller’s complexity. In addition, when the control strategy is applied in reality, the system’s response time is decreased. The simulation results indicate that the proposed technique is more exact than previous approaches. The experimental results reveal that the proposed technique is effective for robot trajectory tracking difficulties.

High-Wettability Poly(dimethylsiloxane) Substrate for Ultrastable Conductive Three-Dimensional Woven Ag Nanowire Grids.

Three-dimensional (3D) woven Ag nanowire (AgNW) grids have great potential for enhancing the mechanical stabilities, conductivity, and transmittance of flexible transparent electrodes (FTEs). However, it is a great challenge to control the formation of 3D woven AgNW grids on various substrates, especially the poly(dimethylsiloxane) (PDMS) substrate. This work presents a microtransfer-printing method for preparing a high-wettability poly(dimethylsiloxane) (PDMS) substrate to control the formation of 3D woven AgNW grids. The as-prepared PDMS substrate shows a high wettability performance. The surface structures of the PDMS substrate can control the sharp shrinkage of the ink membrane to give rise to a uniform liquid membrane evaporation behavior, which is the key factor for preparing a uniform 3D woven nanowire network. A thin uniform 3D woven AgNW network with a low sheet resistance of 24.3 Ω/□ and high transmittance of 92% was coated on the PDMS substrate. The networks directly coated the surface of the replicated PDMS, which simplified the peeling process and protected the networks from peeling strain and mechanical deformations. Moreover, the increment of resistance retained a small value (∼5%) when bending cycles reached 9,000. An alternating current electroluminescent (ACEL) device was prepared, and the uniform electroluminescence implies that a defect-free electrode has been fabricated. These results indicate that the as-prepared FTEs have excellent mechanical performance and great potential for flexible optoelectronic applications.

Following the Flux in diffracted fields – An efficient numerical method for tracing the Eikonal function

We report on our recently developed method for tracing lines of flux in three-dimensional diffracted wavefields using an approach we call ’non-linear ray tracing’ but which can be more accurately described as tracing the lines of flux in the context of the Eikonal function. These ’rays’ navigate through the diffracted field guided by the derivative of the phase at a sequence of successive points. Our approach is based on the Angular Spectrum method, a numerical algorithm that accurately and efficiently calculates diffracted fields for numerical apertures <0.7. This is used to generate a three-dimensional grid of complex wavefield samples in the focal region, followed by tracing the flux through this volume. The ray propagates in a straight line between two consecutive planes within the volume; the phase derivative is calculated at each plane to direct the ray on the next step of its journey. We demonstrate the effectiveness of our approach by generating results for focused laser beams with TEM00 and TEM01 laser profiles. We also simulate the effects of optical aberrations, described by Zernike polynomials, on the three-dimensional focused wavefield. Our non-linear ray tracing method provides a powerful and efficient approach for tracing lines of flux through complex three-dimensional wavefields, offering an exciting new tool for understanding these complex systems.

A vectorized spherical convolutional network for recognizing 3D mesh models with unknown rotation

目的3维目标分类是视觉领域的一个基本问题，3维目标的旋转变化给分类带来极大挑战。同时不规则3维网格模型难以运用传统2维卷积网络提取特征。针对这两个问题，提出一种基于矢量型球面卷积网络的分类方法，用于识别未知旋转的3维网格模型。方法 使用矢量型神经元作为网络的基础神经元，并提出一种新型矢量层间的卷积方式。首先，将3维模型规范化并映射到单位球上，获取球面的信号表示；然后，使用矢量型分类网络和重建网络学习等变的3维模型特征；最后，使用分类网络完成3维模型分类。结果 经过消融实验对比，使用本文提出的球面卷积模块和矢量卷积层，并在训练时加入重建模块。对原本未旋转（no rotation，NR）数据集进行任意旋转（arbitrary rotation，AR），并设定NR/AR，AR/AR，NR/NR共3种训练/测试策略的分类任务，其中NR/AR任务衡量模型识别未知旋转的能力。在刚性数据集ModelNet40上，相比基于球面卷积网络（spherical convolutional neural network，SCNN）的分类方法，在3种任务上分别提高了7.7%，1.8%，3.1%。为验证本文方法在识别非刚性3维网格目标的优越性，在非刚性数据集SHREC15（shape retrieval contest 2015）上，相比SCNN，本文方法在3种任务上分别提高了8.8%，4.5%，5.0%。结论 本文提出一种将矢量型网络运用在3维目标分类的思路，使用光线投射法获得分布在球面空间的特征，便于使用统一的球面卷积算子进行处理；设计一种球面残差模块避免梯度消失；使用矢量型神经元并设计矢量层之间的卷积方式以保证网络的等变性，使得识别任意旋转的3维模型时更加准确。;Objective The 3D meshes are concerned of spatial information-demonstrated surface triangles，which can optimize surface information than other related representations like voxel or point cloud. The 3D shape analysis is still to be resolved in relevant to mesh representation on two aspects：1）the irregular data structure of the mesh model is challenged for feature extraction using traditional 2D convolutional networks，and 2）the 3D rotation transformation is challenged for object recognition as well. The emerging convolutional neural networks（CNNs）have been developing dramatically in the context of 2D vision like classification，segmentation，detection，as well as 3D objects-oriented applications. Current CNNbased 3D mesh classification is developed from two aspects：1）the 3D object is transferred to 2D images and the following 2D-based CNN methods are used，and 2）convolution methods are designed on 3D mesh data. However，it is still challenged to recognize rotated objects due to traditional CNN-equivariant-lacked pooling operation. The lack of rotation equivariance can be improved on the basis of two networks which are vectorized and equivariant networks. The vectorized network，known as capsule network，has shown its potentials in learning spatial transformation on 2D images，but convolutionconstrained method is required to be applied on 3D mesh further. To apply the vectorized neural network to 3D mesh data and preserve rotation equivariance，we develop a vectorized spherical neural network-derived method for 3D mesh classification. Method Our method can be segmented into three categories as mentioned below：First，the 3D mesh model is preprocessed to signals on the sphere. We normalize the 3D mesh into a unit sphere and get the spherical signals on the unit sphere using the ray casting scheme. The obtained spherical signals are nearly equivalent 3D shape representations and can be further processed by spherical convolution methods. The aims of processing 3D mesh to spherical signals are 1）to utilize the spherical signals-defined equivariant spherical convolution operators，and 2）to design vectorized neurons in a coordinated manner. Second，the autoencoder-structured model is used to learn the feature of the spherical signal. The model is composed of two sub-networks：i）a vectorized spherical convolutional neural network（VSCNN）to encode the equivariant feature and classify the 3D object，and ii）a multilayer perceptron decoder to decode the extracted feature back to sphere signal. The VSCNN is based on two kinds of spherical residual convolution block and the vector convolution layer. To train deeper networks and resist overfitting，we develop two spherical convolution modules which are S2 convolution block and SO(3) convolution block，and the primary vectorized neurons are obtained after that. The vector convolution layer is used to learn high-level vectorized features derived from the lower layer. The vector convolutional layer can be used to transfer the primary vectorized neurons to get high-level ones. A deep vectorized network can be constructed through the vector convolutional layer-based stacking. To guarantee the rotation-equivariant spherical vector neurons can be learned well during convolution，we use the SO(3) convolution operator to predict the high-level neurons. The VSCNN and the network-reconstructed are trained simultaneously. Third，the VSCNN-based 3D object classification is demonstrated. For validation，we use VSCNN to clarify the category information of the 3D model only. Result The ModelNet40 and SHREC15 of two 3D datasets are verified for the effectiveness of the proposed method. Our model is trained on the non-rotated（NR） and arbitrarily rotated（AR）training set，and it is tested on the non-rotated and rotated test set as well. The robustness of the model is demonstrated to rotation. For the rigid data set ModelNet40，the accuracy of rotation-unidentified targets can be reached to 85. 2%，surpassing the baseline method by 7. 7%. The comparative analysis shows that our method proposed can surpass most of multi-view and point cloud methods compared to other related 3D data representations. The NR/NR result can show its optimization ability in comparison with the benchmarks. At the same time，to identify non-rigid threedimensional grid targets，we carry out a rotation classification experiment on the non-rigid data set SHREC15，and the accuracy rate can be reached to 90. 4%，surpassing the baseline method by 8. 8%. Conclusion We develop a 3D object classification method for rotated mesh. The robustness to 3D rotation can be optimized in terms of vectorized neurons and the equivariant vector convolution layer. The 3D models-rotated recognition is facilitated excluding rotation augmentation， and it shows the learning ability for vectorized networks-based transformation.

A Review of Research Progress in Selective Laser Melting (SLM).

SLM (Selective Laser Melting) is a unique additive manufacturing technology which plays an irreplaceable role in the modern industrial revolution. 3D printers can directly process metal powder quickly to obtain the necessary parts faster. Shortly, it will be possible to manufacture products at unparalleled speeds. Advanced manufacturing technology is used to produce durable and efficient parts with different metals that have good metal structure performance and excellent metal thermal performance, to lead the way for laser powder printing technology. Traditional creative ways are usually limited by time, and cannot respond to customers' needs fast enough; for some parts with high precision and complexity, conventional manufacturing methods are inadequate. Contrary to this, SLM technology offers some advantages, such as requiring no molds this decreases production time and helps to reduce costs. In addition, SLM technology has strong comprehensive functions, which can reduce assembly time and improve material utilization. Parts with complex structures, such as cavities and three-dimensional grids, can be made without restricting the shape of products. Products or parts can be printed quickly without the use of expensive production equipment. The product quality is better, and the mechanical load performance is comparable to traditional production technologies (such as forging). This paper introduces in detail the process parameters that affect SLM technology and how they affect SLM, commonly used metal materials and non-metallic materials, and summarizes the current research. Finally, the problems faced by SLM are prospected.

A Multilevel Spectral Framework for Scalable Vectorless Power/Thermal Integrity Verification

Vectorless integrity verification is becoming increasingly critical to the robust design of nanoscale integrated circuits. This article introduces a general vectorless integrity verification framework that allows computing the worst-case voltage drops or temperature (gradient) distributions across the entire chip under a set of local and global workload (power density) constraints. To address the computational challenges introduced by the large power grids and three-dimensional mesh-structured thermal grids, we propose a novel spectral approach for highly scalable vectorless verification of large chip designs by leveraging a hierarchy of almost linear-sized spectral sparsifiers of input grids that can well retain effective resistances between nodes. As a result, the vectorless integrity verification solution obtained on coarse-level problems can effectively help compute the solution of the original problem. Our approach is based on emerging spectral graph theory and graph signal processing techniques, which consists of a graph topology sparsification and graph coarsening phase, an edge weight scaling phase, as well as a solution refinement procedure. Extensive experimental results show that the proposed vectorless verification framework can efficiently and accurately obtain worst-case scenarios in even very large designs.

Improving the estimation of thermospheric neutral density via two-step assimilation of in situ neutral density into a numerical model

AbstractNeutral thermospheric density is an essential quantity required for precise orbit determination of satellites, collision avoidance of satellites, re-entry prediction of satellites or space debris, and satellite lifetime assessments. Empirical models of the thermosphere fail to provide sufficient estimates of neutral thermospheric density along the orbits of satellites by reason of approximations, assumptions and a limited temporal resolution. At high solar activity these estimates can be off by 70% when comparing to observations at 12-hourly averages. In recent decades, neutral density is regularly observed with satellite accelerometers on board of low Earth orbiting satellites like CHAMP, GOCE, GRACE, GRACE-FO, or Swarm. When assimilating such along-track information into global models of thermosphere–ionosphere dynamics, it has been often observed that only a very local sub-domain of the model grid around the satellite’s position is updated. To extend the impact to the entire model domain we suggest a new two-step approach: we use accelerometer-derived neutral densities from the CHAMP mission in a first step to calibrate an empirical thermosphere density model (NRLMSIS 2.0). In a second step, we assimilate—for the first time—densities predicted for a regular three-dimensional grid into the TIE-GCM (Thermosphere Ionosphere Electrodynamics General Circulation Model). Data assimilation is performed using the Local Error-Subspace Transform Kalman Filter provided by the Parallel Data Assimilation Framework (PDAF). We test the new approach using a 2-week-long period containing the 5 April 2010 Geomagnetic storm. Accelerometer-derived neutral densities from the GRACE mission are used for additional evaluation. We demonstrate that the two-step approach globally improves the simulation of thermospheric density. We could significantly improve the density prediction for CHAMP and GRACE. In fact, the offset between the accelerometer-derived densities and the model prediction is reduced by 45% for CHAMP and 20% for GRACE when applying the two-step approach. The implication is that our approach allows one to much better ’transplant’ the precise CHAMP thermospheric density measurements to satellites flying at a similar altitude. Graphical Abstract

Scaling of the quantum approximate optimization algorithm on superconducting qubit based hardware

Quantum computers may provide good solutions to combinatorial optimization problems by leveraging the Quantum Approximate Optimization Algorithm (QAOA). The QAOA is often presented as an algorithm for noisy hardware. However, hardware constraints limit its applicability to problem instances that closely match the connectivity of the qubits. Furthermore, the QAOA must outpace classical solvers. Here, we investigate swap strategies to map dense problems into linear, grid and heavy-hex coupling maps. A line-based swap strategy works best for linear and two-dimensional grid coupling maps. Heavy-hex coupling maps require an adaptation of the line swap strategy. By contrast, three-dimensional grid coupling maps benefit from a different swap strategy. Using known entropic arguments we find that the required gate fidelity for dense problems lies deep below the fault-tolerant threshold. We also provide a methodology to reason about the execution-time of QAOA. Finally, we present a QAOA Qiskit Runtime program and execute the closed-loop optimization on cloud-based quantum computers with transpiler settings optimized for QAOA. This work highlights some obstacles to improve to make QAOA competitive, such as gate fidelity, gate speed, and the large number of shots needed. The Qiskit Runtime program gives us a tool to investigate such issues at scale on noisy superconducting qubit hardware.

A Non-Rigid Hierarchical Discrete Grid Structure and Its Application to UAVs Conflict Detection and Path Planning

<p xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Following the development of the unmanned aerial vehicle (UAV) industry, the number of UAVs has increased significantly, and higher expectations regarding the effect of spatial path planning have been expressed. Traditional coordinate-based conflict detection and path planning methods of UAVs are highly complex and have low computational efficiency. While the conflict detection method based on the grid system can improve efficiency, the rigid grid structure of the existing local grid system or discrete global grid system is insufficient. Since the rigid structure only encodes grid cells, multiple or different size grids are required to identify UAVs in motion, further complicating path planning. The main contributions of this article are as follows. First, we proposed a nonrigid hierarchical discrete grid structure and coding method for spatial three-dimensional grids and grid data model. This method can accomplish the aggregation of any adjacent eight grids to form multiple nonrigid structures, making the original fixed relationship between parent and child grids more flexible. Second, the nonrigid grid structure optimizes the identification ability of grid vertices, grid edges, and grid faces. It has eight times the identification ability of the rigid grid structure. We exploited this structure for UAV identification with the same size grid at any position of the grid structure. Third, based on the nonrigid grid structure, an improved UAV conflict detection method and path planning method are designed. Experimental results indicate that, on an average, the efficiency of the improved conflict detection is an order of magnitude higher than that of the traditional computational detection method. The improved path planning method reduces the path length by an average of 11% compared to the single-grid planning method, and is 3.85 times more efficient than the multi-grid buffer planning method.

Unified fast reconstruction algorithm for conventional, phase-contrast, and diffraction tomography.

A unified method for three-dimensional reconstruction of objects from transmission images collected at multiple illumination directions is described. The method may be applicable to experimental conditions relevant to absorption-based, phase-contrast, or diffraction imaging using x rays, electrons, and other forms of penetrating radiation or matter waves. Both the phase retrieval (also known as contrast transfer function correction) and the effect of Ewald sphere curvature (in the cases with a shallow depth of field and significant in-object diffraction) are incorporated in the proposed algorithm and can be taken into account. Multiple scattering is not treated explicitly but can be mitigated as a result of angular averaging that constitutes an essential feature of the method. The corresponding numerical algorithm is based on three-dimensional gridding which allows for fast computational implementation, including a straightforward parallelization. The algorithm can be used with any scanning geometry involving plane-wave illumination. A software code implementing the proposed algorithm has been developed, tested on simulated and experimental image data, and made publicly available.

How does turbulence mix a stratified fluid?

A principal topic of interest and importance in stably stratified flows is how turbulence irreversibly mixes the ambient density field. Because the density field is coupled dynamically to the velocity field through the stable stratification, this mixing affects the overall flow dynamics, and its accurate parameterisation has become a ‘grand challenge’ in environmental fluid mechanics (Dauxois et al., Phys. Rev. Fluids, vol. 6, issue 2, 2021, 020501). In order to better understand the detailed kinematics of mixing in a stably stratified fluid, Jiang et al. (2022) perform experiments using a unique laboratory facility, capable of generating controllable stratified shear flows, and providing almost instantaneous density and three-component velocity measurements on a high-resolution, three-dimensional grid. Using three-dimensional data sets from the experiments, they employ the rortex–shear decomposition to identify the morphology of instantaneous rortices in the flow fields, leading to the interpretation of the motion of the rortices and ultimately to how the rortices cause irreversible mixing of the density field. This marks one of the first studies where, in a laboratory setting, full use has been made of somewhat high-resolution, three-dimensional near-instantaneous measurements; it demonstrates what can be accomplished in the laboratory, setting a new standard for future experiments.