Set Of Spatial Points Research Articles

Multi‐Spacecraft Magnetic Field Reconstructions: A Cross‐Scale Comparison of Methods

AbstractSpace plasma studies frequently use in situ magnetic field measurements taken from many spacecraft simultaneously. A useful data product of these measurements is the reconstructed magnetic field in a volume near the spacecraft observatory. We compare a standard Linear method of computing the magnetic field at arbitrary spatial points to two novel approaches: a Radial Basis Function interpolation and a time‐dependent 2D inverse distance weighted interpolation scheme called Timesync. These three methods, which only require in situ measurements of the magnetic fields and bulk plasma velocities at a sparse set of spatial points, are implemented on synthetic data drawn from a time‐evolving numerical simulation of plasma turbulence. We compare both the topology of the reconstructed field to the ground truth of the simulation and the statistics of the fluctuations found in the reconstructed field to those from the simulated turbulence. We conclude that the Radial Basis Function and Timesync methods outperform the Linear method in both topological and statistical comparisons.

Data Analysis of Linguistic Landscape in the Context of “Internationalization +” Urban Construction

Abstract With the rapid development of internationalization and urban construction, the urban linguistic landscape has become an area of great interest. The purpose of this paper is to explore the data analysis method of urban visual linguistic landscape based on line-of-sight orientation and to optimize the design of urban linguistic landscape based on an improved genetic algorithm. The basic visual analysis unit and the viewable area analysis unit of the linguistic landscape are proposed to quantify the visual characteristic indexes and the optimal view distance of the linguistic landscape. At the same time, the viewable spatial point set analysis unit is used to obtain the view accessibility of the language landscape. Finally, the linguistic landscape optimization model was evaluated and analyzed for application effects. The results show that through the optimized design of 10 linguistic spots in H City National Forest Park, the average score of each spot evaluation is 3.48, and the full score ratio is 63.18%. The urban language landscape optimization model proposed in this paper can effectively improve the aesthetics and visual sensitivity of the urban language landscape.

Bayesian inversion of log-normal eikonal equations

We study the Bayesian inverse problem for inferring the log-normal slowness function of the eikonal equation, given noisy observation data on its solution at a set of spatial points. We contribute rigorous proofs on the existence and well-posedness of the problem. We then study approximation of the posterior probability measure by solving the truncated eikonal equation, which contains only a finite number of terms in the Karhunen–Loeve expansion of the slowness function, by the fast marching method (FMM). The error of this approximation in the Hellinger metric is deduced in terms of the truncation level of the slowness and the grid size in the FMM resolution. It is well known that the plain Markov chain Monte Carlo (MCMC) procedure for sampling the posterior probability is highly expensive. We develop and justify the convergence of a multilevel MCMC method. Using the heap sort procedure in solving the forward eikonal equation by the FMM, our multilevel MCMC method achieves a prescribed level of accuracy for approximating the posterior expectation of quantities of interest, requiring only an essentially optimal level of complexity. Numerical examples confirm the theoretical results.

Topology optimization via implicit neural representations

Along with the rapid development of artificial intelligence (AI) technology, scientific research enters a new era of AI. Topology optimization (TO) and AI technology are recently showing a growing trend of cross development, which has received continuous attentions from relative researchers. In this paper, we introduce a concept of Implicit Neural Representations from AI into TO field and establish a novel TO framework which is named as TOINR. In TOINR, the Topology Description Function is the inherent combination factor, which is constructed by a Neural Network (NN) and determines the topology statuses of structural materials in the design domain. We adopt sine as a periodic activation function combined with MLP as the architecture of the NN. The inputs of NN are a predefined set of spatial points’ coordinates, while the outputs are the implicit representations of corresponding topological boundaries. Along with updating NN’s parameters (i.e., design variables), the structural topologies iteratively evolve according to the responses analysis results and optimization functions. A boundary-adaptive multi-resolution finite element analysis method is developed to improve the physical response accuracy. At each step of TOINR, we ensure the computational differentiability. Thus, the automatic differentiation is used in sensitivity analysis. The multi-penalty function approach is applied to handle objects with constraints. Besides, we design an adaptive adjustment scheme for learning rates to enhance the stability of the optimization process. Numerical examples illustrate that TOINR can stably obtain optimized structures for different problems with high performance and robustness.

SGPAC: generalized scalable spatial GroupBy aggregations over complex polygons

This paper studies the spatial group-by query over complex polygons. Given a set of spatial points and a set of polygons, the spatial group-by query returns the number of points that lie within the boundaries of each polygon. Groups are selected from a set of non-overlapping complex polygons, typically in the order of thousands, while the input is a large-scale dataset that contains hundreds of millions or even billions of spatial points. This problem is challenging because real polygons (like counties, cities, postal codes, voting regions, etc.) are described by very complex boundaries. We propose a highly-parallelized query processing framework to efficiently compute the spatial group-by query on highly skewed spatial data. We also propose an effective query optimizer that adaptively assigns the appropriate processing scheme based on the query polygons. Our experimental evaluation with real data and queries has shown significant superiority over all existing techniques.

Channel connection and stimulated reservoir volume estimation derived by the timing, location, and focal mechanism of microseismic events

Understanding and modeling channels of high-pressure liquids during hydraulic fracturing and stimulated reservoir volume (SRV) estimation are critical for the evaluation of the fracturing effect and the prediction of oil and gas production in unconventional (low permeability and porosity) reservoirs. In this study, we developed a “focal mechanism-to-event” channel connection criterion based on the timing, location, and focal mechanism of microseismic events, enabling the channel to be perpendicular or parallel to the fracturing plane and more in line with the mechanical properties of rock rupture. We first evaluated the two endpoints of all channels as a set of spatial points, followed by the application of the alpha-shape method to detect the concave hull shape boundary formed by the spatial points. Finally, we calculated the SRV by combining the shapes of the concave hull and Delaunay triangulation. In the experimental simulation, we found that this method could effectively calculate the hull volume, and the detected concave hull included all microseismic events and channels. Ultimately, we applied the channel connection criterion and SRV estimation method to a stage of 3.18 h real fracturing data containing 216 microseismic events. The final calculation revealed a total of 410 connection channels and 4.3154 × 105 m3 SRV, which is more consistent with the expected than the “event-to-event” or “event-to-channel” connection criteria and bin or convex hull SRV calculation methods.

State and Parameter Estimation of Non-Uniform Transmission Line Using Kronecker Product Based Modeling

The distributed parameters of a non-uniform transmission line (NTL) are assumed to depend on a finite set of unknown parameters, for example, their spatial Fourier series coefficients. The line equations are set up taking random voltage and current line loading into account with the random loading being assumed to be white Gaussian noise in the time and spatial variables. Bypassing over to the spatial Fourier series domain, these line stochastic differential equations (SDEs) are expressed as a truncated sequence of coupled stochastic differential equations for the spatial Fourier series components of the line voltage and current. The coefficients that appear in these stochastic differential equations are the spatial Fourier series coefficients of the distributed line parameters and these coefficients in turn are linear functions of the unknown parameters. By separating these complex stochastic differential equations into their real and imaginary part, the line equations become a finite set of SDEs for the extended state defined to be the real and imaginary components of the line voltage and current as well as the parameters on which the distributed parameters depend. The measurement model is assumed to be white Gaussian noise corrupted versions of the line voltage and current sampled at a discrete set of spatial points on the line and this measurement model can be expressed as a linear transformation of the state variables, i.e, of the spatial Fourier series components of the line voltage and current plus a white measurement noise vector. This work uses sparse matrix factorization using Kronecker product to implement the Fourier unitary transform. This work implements perturbation theory for non-uniform transmission line. The extended Kalman filter (EKF) equations are derived for this state and measurement model and our real timeline voltage and current and distributed parameter estimates show excellent agreement with the true values based on MATLAB simulations. The use of sparse matrix factorization using Kronecker product ease the mathematical complexity and provides compact representation.

Pressure from data-driven estimation of velocity fields using snapshot PIV and fast probes

The most explored path to obtain pressure fields from Particle Image Velocimetry (PIV) data roots its basis on accurate measurement of instantaneous velocity fields and their corresponding time derivatives. This requires time-resolved measurements, which are often difficult to achieve due to hardware limitations and expensive to implement. In alternative, snapshot PIV experiments are more affordable but require enforcing physical constraints (e.g. Taylor’s hypothesis) to extract the time derivative of the velocity field. In this work, we propose the use of data-driven techniques to retrieve time resolution from the combination of snapshot PIV and high-repetition-rate sensors measuring flow quantities in a limited set of spatial points. The instantaneous pressure fields can thus be computed by leveraging the Navier–Stokes equations as if the measurement were time-resolved. Extended Proper Orthogonal Decomposition, which can be regarded as one of the simplest algorithm for estimating velocity fields from a finite number of sensors, is used in this paper to prove the feasibility of this concept. The method is fully data-driven and, after training, it requires only probe data to obtain field information of velocity and pressure in the entire flow domain. This is certainly an advantage since model-based methods can retrieve pressure in an observed snapshot, but show increasing error as the field information is propagated over time. The performances of the proposed method are tested on datasets of increasing complexity, including synthetic test cases of the wake of a fluidic pinball and a channel flow, and experimental measurements in the wake of a wing. The results show that the data-driven pressure estimation is effective in flows with compact POD spectrum. In the cases where Taylor’s hypothesis holds well, the in-sample pressure field estimation can be more accurate for model-based methods; nonetheless, the proposed data-driven approach reaches a better accuracy for out-of-sample estimation after less than 0.20 convective times in all tested cases.

System identification of distributed parameter system with recurrent trajectory via deterministic learning and interpolation

In the paper, we propose a novel approach to identify distributed parameter system (DPS) with recurrent state trajectory. Different from existing literature, the system dynamics rather than parameters or structure of DPS is identified in the study. Due to the infinite-dimensional feature of DPS, the partial differential equation describing the DPS is first approximated by a set of ordinary differential equations. By employing finite difference method, the spatial derivatives at a set of spatial points are approximated. Then, the DPS dynamics at the set of spatial points is identified via deterministic learning. With the identification results, a mechanism based on interpolation method is proposed to approximate the DPS dynamics at any other spatial point. That is, we can accurately identify the DPS dynamics at any spatial point. Numerical results involving the identification of an important mathematical physics equation are presented to illustrate the validity of the approach.

Near-Field Experimental Verification of the EM Models for the LOFAR Radio Telescope

Modern radio astronomical facilities in the Very High-Frequency band (VHF, 30-300 MHz) consist of large antenna arrays with digital beamforming. The calibration of these instruments requires accurate models of their electromagnetic behavior. Numerical models covering the full telescope field-of-view are nowadays effectively computed by means of full-wave solvers. However, their experimental verification is still an open and challenging task. This letter proposes a verification strategy based on near-field scans. An unmanned aerial vehicle carrying a test source is used to excite the array from a limited set of spatial points, located in the radiating near-field region. The collected data are directly used to verify the telescope electromagnetic model without additional postprocessing. This exploits the capability of full-wave solvers to predict near-field patterns from the same geometrical and electrical model used to compute far-field patterns. The application of the proposed technique to the Low Frequency Array (LOFAR) radio telescope verified the predictions with residuals below 0.5 dB.

A staggered grid finite difference method for solving the elastic wave equations

We consider elasticity (elastic wave) equations for solving acoustics problems. We use the finite difference method on staggered grids to solve the elastic wave equations. On staggered grids, the pressure is computed at a set of spatial points, and the velocity is computed at another set of spatial points. An advantage of using staggered grids is that fluxes do not need to be approximated in the solving process, as the flux values are known. Numerical results confirm that our numerical method is reliable.

Linear separability in spatial databases

Given two spatial point sets R and B in the plane, with cardinalities m and n, respectively, and stored in two separate R-trees, we propose an efficient algorithm to verify whether R and B are linearly separable. The sets R and B are linearly separable if there exists a line that splits the plane into to halfplanes, one containing all R and the other one containing all B. This is the first algorithm that answers the separability question in the context of the spatial data bases. That is, it considers as input big spatial data stored in secondary storage data structures (e.g., the R-tree) which are not allowed to be completely stored in the main memory of the computer to run a classic algorithm. The algorithms designed in this context aim to minimize as much as possible the number of blocks read from the secondary storage data structures to the main memory. Studied problems in this setting are the k-nearest neighbor problem and the spatial range query problem. Our algorithm explicitly exploits the geometric and spatial properties of the R-trees to access only the nodes relevant to decide the linear separability of the given sets. Our experimental results show the efficiency of the algorithm, since it accesses between the 0.34 and 2.79% of the nodes of the R-trees. We also analyze the asymptotic running time of the algorithm, showing that it runs in $$O(m\log m + n\log n)$$ time in the worst case.

Harmonic phases of the nanoparticle magnetization: An intrinsic temperature probe

Magnetic fluid hyperthermia is a promising cancer therapy in which magnetic nanoparticles act as heat sources activated by an external AC magnetic field. The nanoparticles, located near or inside the tumor, absorb energy from the magnetic field and then heat up the cancerous tissues. During the hyperthermia treatment, it is crucial to control the temperature of different tissues: too high temperature can cause undesired damage in healthy tissues through an uncontrolled necrosis. However, the current thermometry in magnetic hyperthermia presents some important technical problems. The widely used optical fiber thermometers only provide the temperature in a discrete set of spatial points. Moreover, surgery is required to locate these probes in the correct place. In this scope, we propose here a method to measure the temperature of a magnetic sample. The approach relies on the intrinsic properties of the magnetic nanoparticles because it is based on monitoring the thermal dependence of the high order harmonic phases of the nanoparticle dynamic magnetization. The method is non-invasive and it does not need any additional probe or sensor attached to the magnetic nanoparticles. Moreover, this method has the potential to be used together with the magnetic particle imaging technique to map the spatial distribution of the temperature.

Closed balls for interpolating quasi-polynomials

The classic interpolation problem asks for polynomials to fit a set of given data. In this paper, quasi-polynomials are considered as interpolating functions passing through a set of spatial points. Existence and uniqueness is obtained by means of generalized Vandermonde determinants. By means of several estimates related to these determinants, we are also able to find closed balls for any given centers that enclose the approximating curves. By choosing proper centers based on the observed spatial points, these balls may lead us to applications such as satellite tracking and control. Mathematical subject classification: 41A05.

Asymptotic properties of nonparametric regression for long memory random fields

The kernel estimator of spatial regression function is investigated for stationary long memory (long range dependent) random fields observed over a finite set of spatial points. A general result on the strong consistency of the kernel density estimator is first obtained for the long memory random fields, and then, under some mild regularity assumptions, the asymptotic behaviors of the regression estimator are established. For the linear long memory random fields, a weak convergence theorem is also obtained for kernel density estimator. Finally, some related issues on the inference of long memory random fields are discussed through a simulation example.

Detecting feature from spatial point processes using Collective Nearest Neighbor

In a spatial point set, clustering patterns (features) are difficult to locate due to the presence of noise. Previous methods, either using grid-based method or distance-based method to separate feature from noise, suffer from the parameter choice problem, which may produce different point patterns in terms of shape and area. This paper presents the Collective Nearest Neighbor method (CLNN) to identify features. CLNN assumes that in spatial data clustered points and noise can be viewed as two homogenous point processes. The one with the higher intensity is considered as a feature and the one with the lower intensity is treated as noise. As a result, they can be separated according to the difference in intensity between them. With CLNN, points are first classified into feature and noise based on the kth nearest distance (the distance between a point and its kth nearest neighbor) at various values of k. Then, CLNN selects those classifications in which the separated classes (i.e. features and noise) are homogenous Poisson processes and cannot be further divided. Finally, CLNN identifies clustered points by averaging the selected classifications. Evaluation of CLNN using simulated data shows that CLNN reduces the number of false points significantly. The comparison between CLNN, the shared nearest neighbor, the spatial scan and the classification entropy method shows that CLNN produced the fewest false points. A case study using seismic data in southwestern China showed that CLNN is able to identify foreshocks of the Songpan earthquake ( M = 7.2), which may help to locate the epicenter of the Songpan earthquake.

DECODE: a new method for discovering clusters of different densities in spatial data

When clusters with different densities and noise lie in a spatial point set, the major obstacle to classifying these data is the determination of the thresholds for classification, which may form a series of bins for allocating each point to different clusters. Much of the previous work has adopted a model-based approach, but is either incapable of estimating the thresholds in an automatic way, or limited to only two point processes, i.e. noise and clusters with the same density. In this paper, we present a new density-based cluster method (DECODE), in which a spatial data set is presumed to consist of different point processes and clusters with different densities belong to different point processes. DECODE is based upon a reversible jump Markov Chain Monte Carlo (MCMC) strategy and divided into three steps. The first step is to map each point in the data to its mth nearest distance, which is referred to as the distance between a point and its mth nearest neighbor. In the second step, classification thresholds are determined via a reversible jump MCMC strategy. In the third step, clusters are formed by spatially connecting the points whose mth nearest distances fall into a particular bin defined by the thresholds. Four experiments, including two simulated data sets and two seismic data sets, are used to evaluate the algorithm. Results on simulated data show that our approach is capable of discovering the clusters automatically. Results on seismic data suggest that the clustered earthquakes, identified by DECODE, either imply the epicenters of forthcoming strong earthquakes or indicate the areas with the most intensive seismicity, this is consistent with the tectonic states and estimated stress distribution in the associated areas. The comparison between DECODE and other state-of-the-art methods, such as DBSCAN, OPTICS and Wavelet Cluster, illustrates the contribution of our approach: although DECODE can be computationally expensive, it is capable of identifying the number of point processes and simultaneously estimating the classification thresholds with little prior knowledge.

Distributed-parameter observer-based control implementation using finite spatial measurements

Distributed-parameter systems have infinite dimensional states and hence, in practical observer and control design applications, the problem of approximate finite-dimensional state reconstruction arises. In this paper a useful approach for implementing such an approximation is presented, which makes use of double Walsh series expansions and is based on finited output measurements at a specified set of spatial points.

Chebychev Approximations of Spatial Point Sets Using Spheres and Planes

The main problem considered is that of determining spheres which best approximate given sets of spatial points. The spheres sought are best in the sense of having the minimum-maximum radial distance from the points to be approximated. Configuration of the points with respect to the best spheres is discussed in detail. Related results are also obtained for the approximation of points by planes.

Finite-Element Analysis of Temperature and Thermal Stresses Induced by Hot Water Injection

Abstract Results of an experimental study of the temperature and pressure dependence of rock elastic moduli were used in a numerical mathematical model that describes the unsteady-state, two-dimensional flow of a single-phase, single-component, slightly compressible hot fluid and that calculates the state of stress in porous media. The numerical formulation was conducted using the finite-element method of triangular elements to discretize the space domain and backward differencing for discretizing the time domain. Sections of the model dealing with the flow of mass and heat, and stress calculations were tested separately then, the complete model was used to investigate the effect of temperature-dependent Young's moduli and Poisson's ratios on the state of stress and the propagation of thermal and pore stresses with an advancing hot water front in porous media. porous media Introduction The finite-element method forms the basis for a versatile analysis procedure applicable to problems in several different fields. Essentially, the finite-element idealization replaces the continuum with a finite number of discrete elements. Geometry of the elements is defined by a set of spatial points (called nodal points) of the system. Heat and fluid-flow problems are analyzed by using interpolation functions for the unknown temperatures and pressures. Thus, the variables within elements are pressures. Thus, the variables within elements are defined completely in terms of the values at nodal points. The isoparametric element concept, where points. The isoparametric element concept, where the geometry and displacements of the element are described in terms of the same parameters and are of the same order, is particularly useful for stress analysis in continuous bodies. The investigation of thermal stresses may be found helpful when answering questions associated with heated reservoir rocks. Creation of microfactures in formations subjected to elevated temperatures often results in increased permeabilities. A correlation between the thermal stresses induced by these high temperatures and the degree of microfracturing affecting the rock absolute permeability could be useful in understanding fluid flow permeability could be useful in understanding fluid flow in heated reservoirs. It also would be interesting to see if thermal stresses have any effect on the casing failures in steam injection or geothermal wells. The analysis under consideration involves the determination of pressures, temperatures, and stresses in a porous medium undergoing hot-water injection. The study is complicated further by the transient nature of the variables. Background The finite-element method has been used widely for studying stresses in various kinds of structures. The basic concepts of the method, first laid down by Turner et al, essentially are composed of the idealization of continuous bodies by a set of interconnected finite elements with known behavioral characteristics. Recently, this versatile method was applied to diverse kinds of engineering problems, mainly in heat and fluid-flow areas. Desai problems, mainly in heat and fluid-flow areas. Desai and Abel list the fields where the method may be applied. Visser solved the unsteady-state heat conduction equations, using a variational approach. He solved for temperature distribution, also calculating the associated stresses by determining the displacements occurring in the body due to this temperature field. Later, Zienkiewicz and Parekh used two- and three-dimensional curved isoparametric elements to solve the same equation by using the Galerkin principle. SPEJ P. 457