Finite Cloud Research Articles

Accelerating material property prediction using generically complete isometry invariants

Periodic material or crystal property prediction using machine learning has grown popular in recent years as it provides a computationally efficient replacement for classical simulation methods. A crucial first step for any of these algorithms is the representation used for a periodic crystal. While similar objects like molecules and proteins have a finite number of atoms and their representation can be built based upon a finite point cloud interpretation, periodic crystals are unbounded in size, making their representation more challenging. In the present work, we adapt the Pointwise Distance Distribution (PDD), a continuous and generically complete isometry invariant for periodic point sets, as a representation for our learning algorithm. The PDD distinguished all (more than 660 thousand) periodic crystals in the Cambridge Structural Database as purely periodic sets of points without atomic types. We develop a transformer model with a modified self-attention mechanism that combines PDD with compositional information via a spatial encoding method. This model is tested on the crystals of the Materials Project and Jarvis-DFT databases and shown to produce accuracy on par with state-of-the-art methods while being several times faster in both training and prediction time.

Assessment of clean production level in phosphate mining enterprises: Based on the fusion group decision weight and limited interval cloud model

To develop a robust cleaner production level assessment model for phosphate mining enterprises, this study investigated the key factors influencing their cleaner production levels. The model incorporates integrated group decision weights and a limited interval cloud model. Based on the comprehensive life cycle of phosphate mining production, we constructed a detailed evaluation index system to assess the cleaner production level of these enterprises. This system defined the quantitative ranges for each level and revealed the interrelationships among the indicators. To ensure comprehensive weight determination, we proposed a method that integrates the expertise of multiple stakeholders. This method leveraged group decision-making principles to effectively resolve conflicts in expert judgments during the weight determination process. In addressing the characteristics of evaluation indicators for the cleaner production level of phosphate mining enterprises, we proposed employing a finite interval cloud model to accurately characterize the distribution of the indicators. Leveraging the finite interval cloud model, we obtained numerical characteristics for various indicators and incorporated the weights of the integrated group decision-making attributes. This approach enabled us to determine the cleaner production level of phosphate mining using a finite interval cloud generator. Validation using five phosphate mining enterprises in Hubei Province, China, confirmed the model's high accuracy. This model demonstrated its applicability in evaluating cleaner production levels for phosphate mining enterprises, offering a theoretical foundation for developing targeted environmental management policies.

Biomechanical Evaluation of 2 Endoscopic Spine Surgery Methods for Treating Lumbar Disc Herniation: A Finite Element Study.

This study aimed to evaluate the effects of 2 endoscopic spine surgeries on the biomechanical properties of normal and osteoporotic spines. Based on computed tomography images of a healthy adult volunteer, 6 finite element models were created. After validating the normal intact model, a concentrated force of 400 N and a moment of 7.5 Nm were exerted on the upper surface of L3 to simulate 6 physiological activities of the spine. Five types of indices were used to assess the biomechanical properties of the 6 models, range of motion (ROM), maximum displacement value, intervertebral disc stress, maximum stress value, and articular protrusion stress, and by combining them with finite element stress cloud. In normal and osteoporotic spines, there was no meaningful change in ROM or disc stress in the 2 surgical models for the 6 motion states. Model N1 (osteoporotic percutaneous transforaminal endoscopic discectomy model) showed a decrease in maximum displacement value of 20.28% in right lateral bending. Model M2 (unilateral biportal endoscopic model) increased maximum displacement values of 16.88% and 17.82% during left and right lateral bending, respectively. The maximum stress value of L4-5 increased by 11.72% for model M2 during left rotation. In addition, using the same surgical approach, ROM, maximum displacement values, disc stress, and maximum stress values were more significant in the osteoporotic model than in the normal model. In both normal and osteoporotic spines, both surgical approaches were less disruptive to the physiologic structure of the spine. Furthermore, using the same endoscopic spine surgery, normal spine biomechanical properties are superior to osteoporotic spines.

A new method to calculate a standard set of finite cloud dose correction factors for the level 3 probabilistic safety assessment of nuclear power plants

Level 3 probabilistic safety assessment (PSA) is performed to calculate radionuclide concentrations and exposure dose resulting from nuclear power plant accidents. To calculate the external exposure dose from the released radioactive materials, the radionuclide concentrations are multiplied by two factors of dose coefficient and a finite cloud dose correction factor (FCDCF), and the obtained values are summed. This indicates that a standard set of FCDCFs is required for external exposure dose calculations.To calculate a standard set of FCDCFs, the effective distance from the release point to the receptor along the wind direction should be predetermined. The TID-24190 document published in 1968 provides equations to calculate FCDCFs and the resultant standard set of FCDCFs. However, it does not provide any explanation on the effective distance required to calculate the standard set of FCDCFs. In 2021, Sandia National Laboratories (SNLs) proposed a method to predetermine finite effective distances depending on the atmospheric stability classes A to F, which results in six standard sets of FCDCFs. Meanwhile, independently of the SNLs, the authors of this paper discovered that an infinite effective distance assumption is a very reasonable approach to calculate one standard set of FCDCFs, and they implemented it into the multi-unit radiological consequence calculator (MURCC) code, which is a post-processor of the level 3 PSA codes.This paper calculates and compares short- and long-range FCDCFs calculated using the TID-24190, SNLs method, and MURCC method, and explains the strength of the MURCC method over the SNLs method. Although six standard sets of FCDCFs are required by the SNLs method, one standard sets of FCDCFs are sufficient by the MURCC method. Additionally, the use of the MURCC method and its resultant FCDCFs for level 3 PSA was strongly recommended.

Computation of the Hausdorff Distance between Two Compact Convex Sets.

The Hausdorff distance between two closed sets has important theoretical and practical applications. Yet apart from finite point clouds, there appear to be no generic algorithms for computing this quantity. Because many infinite sets are defined by algebraic equalities and inequalities, this a huge gap. The current paper constructs Frank-Wolfe and projected gradient ascent algorithms for computing the Hausdorff distance between two compact convex sets. Although these algorithms are guaranteed to go uphill, they can become trapped by local maxima. To avoid this defect, we investigate a homotopy method that gradually deforms two balls into the two target sets. The Frank-Wolfe and projected gradient algorithms are tested on two pairs of compact convex sets, where: (1) is the box translated by and is the intersection of the unit ball and the non-negative orthant; and (2) is the probability simplex and is the unit ball translated by . For problem (2), we find the Hausdorff distance analytically. Projected gradient ascent is more reliable than the Frank-Wolfe algorithm and finds the exact solution of problem (2). Homotopy improves the performance of both algorithms when the exact solution is unknown or unattained.

An Improved Finite Cloud Method With Uniformly Distributed Clouds and Enhanced Boundary Conditions

Finite cloud method (FCM) employs the fixed kernel reproducing technique to construct the interpolation function and point collocation approach is adopted for the discretization. In this study, an improved FCM is proposed such that a node of interest is approximated with its nearest cloud. This feature enables a set of uniformly distributed clouds of various densities such that all the information in the problem domain is captured and stored in the clouds. Additionally, the instability of FCM near the boundaries is treated by having the boundary nodes also satisfy the governing differential equation. Besides, a splitting mechanism is suggested for the node refinement to improve the accuracy of solution. Parameters are introduced to control the density of clouds and the singularity of the moment matrices associated with the clouds. Thus, a more controllable numerical simulation is developed. Numerical examples are presented and the results have shown that the improved FCM produces a stable and better accuracy of solution.

Evaluation of Slope Stability within the Influence of Mining Based on Combined Weighting and Finite Cloud Model

Coal mining under slopes often leads to slope instability, resulting in substantial economic losses and human casualties. Therefore, constructing a scientific and practical slope stability evaluation model for slope disaster prevention and control is of great significance. In this study, seven evaluation indexes were selected, and their influence mechanisms were analyzed to establish a system of evaluation indexes for the stability of mining slopes in Xing County, Shanxi Province, China. A new evaluation model for the stability of mining slopes was established based on the interval analytic hierarchy process (IAHP) to determine the subjective weights of the indexes and the improved CRITIC method to determine the objective weights of the indexes, which circumvented the limitations of subjective or objective weights by combining the minimum discriminating information. The model was applied to the mining slopes in Xing County, Shanxi Province, and the results showed that slopes A, C, D and E were in an unstable state, slope B was in an understable state after mining. Finally, the accuracy of the evaluation results was verified through field surveys. The model has engineering application value in predicting the stability of mining slopes and can provide theoretical suggestions for later slope management to ensure the safe production of coal mines.

Full-Vector Mode Solver for Nonlinear Optical Waveguides Using Meshfree Finite Cloud Method

A full-vector mode solver based on the meshfree (MF) finite cloud method (FCM) is developed for analysis of nonlinear optical waveguide. Self-consistent solutions are approximated through a simple iterative scheme after the nonlinear eigenvalue matrix equation derived using the quadratic basis function as well as the MF shape function. The proposed mode solver can significantly reduce the computational requirements since major parts of formulations are tackled analytically. Results for two numerical examples are presented and compared with those from the well-known finite element method (FEM) and FEM-based imaginary-distance beam propagation method (FEM-IDBPM), respectively, showing the validity and utility of the proposed method.

Improved Full-Vectorial Meshfree Mode Solver for Step-Index Optical Waveguides With Arbitrary Dielectric Interfaces

A novel improved full-vectorial meshfree finite cloud mode solver is constructed for analysis of step-index optical waveguides with arbitrary interfaces, where the waveguide interfaces can be tilted towards the global coordinate axes or can even be curved. In order to obtain rigorous formulations capable of dealing with tilted and curved interfaces, the local coordinate transformations along with the curvilinear mapping technique are introduced to the approximation of spatial derivatives at interpolated nodes, respectively. In the improved finite cloud scheme, a simple modification to the meshfree kernel shape function is proposed to enforce the Kronecker delta property, significantly improving the computational efficiency. The computational accuracy is also greatly improved since a novel scheme is proposed to carefully treat field values in the vicinity of material interfaces. Numerical results for the fundamental and high-order modes of a rectangular rib waveguide, an equilateral triangular core waveguide, a trapezoidal rib waveguide and a circular optical fiber are presented and compared with those from the conventional mesh-based methods, which shows the validity and utility of the proposed method.

A Hybrid Multiscale Finite Cloud Method and Finite Volume Method in Solving High Gradient Problem

Meshfree methods are always the alternatives to be considered besides the finite element method in dealing with complex engineering problems. Among these complex problems, there are problems where discontinuities or high gradients may only emerge at a small region of a domain and the remaining parts of the domain are smooth and continuous. In this case, adding nodes to the critical region is essential for the better accuracy of solutions. It would be effective if a meshfree method is applied to the critical region and a mesh-based method is employed to solve the remaining part of the domain since node refinement is easier for a meshfree method whereas a mesh-based method is simple to develop and capable of producing accurate solutions for smooth regions. In this study, the finite cloud method (FCM) is coupled with the finite volume method (FVM) such that node refinement only takes place at the region where the FCM is applied. A handshaking approach is proposed to enforce the continuity near the interface where both methods are applied. Numerical examples and computation methods are presented in this paper and the numerical results are examined.

Full-Vector Analysis of Bending Waveguides by Using Meshless Finite Cloud Method in a Local Cylindrical Coordinate System

By using a meshless finite cloud method, a full-vector mode solver in terms of transverse-magnetic-field components for optical dielectric waveguide bends is developed in a local cylindrical coordinate system. To construct the interpolation function, both the point collocation and the fixed reproducing kernel technique are utilized, and then with the help of the continuity conditions of the longitudinal field components and the perfectly matched layer absorbing boundary conditions, a standard matrix eigenvalue is obtained. Compared with the conventional meshed numerical techniques, the distributions of solution points of the present meshless method can be applied to the area of complexity in a completely free manner. Consequently, excellent convergence with high accuracy can be realized. Moreover, the present method can be applied to both the uniform and non-uniform nodal distributions, thus the computational procedure is relatively flexible. To validate the proposed method, both fundamental and high-order leaky modes for a typical rib bending waveguide are analyzed and their modal field distributions and corresponding effective refractive indexes are presented. Results are in good agreement with those published earlier, showing the effectiveness of the present method.

A novel comprehensive quantitative method for various geological disaster evaluations in underground engineering: multidimensional finite interval cloud model (MFICM)

The risk prediction of geological disasters exhibits extreme uncertainty and complexity due to the random distribution of evaluation indexes within a finite interval. To improve the accuracy of disaster prediction results, a new evaluation method is in this study suggested to perform a risk evaluation of geological disasters based on multidimensional finite interval cloud model (MFICM) and combination weighting. The MFICM with a transformation between qualitative concept and quantitative data depicts uncertainties and actual distribution features of indexes in the finite interval. Analytic hierarchy process and principal component analysis are adopted to determine the subjective and objective weights of evaluation indexes, respectively, and the combination weight is calculated by a linear method to reduce the influence of subjective factors. The numerical characteristic parameters of each indexes belonging to various risk levels are first calculated based on established evaluation index system. Subsequently, a multi-dimensional finite interval cloud is generated from a forward cloud generator using MATLAB software. Finally, the comprehensive certainty degrees relative to different levels for each sample are determined combined with combination weight, which achieves a mapping of uncertainty between semantic variables and index values. The proposed method is applied to engineering cases regarding three geological disasters, i.e., water inrush, rock burst and collapse. The obtained results with accuracy and results compared with reference methods show that the MFICM is verified to be practical and universal for the risk evaluation of geological disasters, which improves and enriches the theoretical framework of geotechnical engineering disaster risk evaluation.

Risk assessment of coal and gas outburst in driving face based on finite interval cloud model

Risk assessment of coal and gas outburst in driving face based on finite interval cloud model

Geometric and probabilistic limit theorems in topological data analysis

We develop a general framework for the probabilistic analysis of random finite point clouds in the context of topological data analysis. We extend the notion of a barcode of a finite point cloud to compact metric spaces. Such a barcode lives in the completion of the space of barcodes with respect to the bottleneck distance, which is quite natural from an analytic point of view. As an application we prove that the barcodes of i.i.d. random variables sampled from a compact metric space converge to the barcode of the support of their distribution when the number of points goes to infinity. We also examine more quantitative convergence questions for uniform sampling from compact manifolds, including expectations of transforms of barcode valued random variables in Banach spaces. We believe that the methods developed here will serve as useful tools in studying more sophisticated questions in topological data analysis and related fields.

Suitability evaluation of underground space based on finite interval cloud model and genetic algorithm combination weighting

The development and utilization of urban underground space is an inevitable solution for urban sustainable development. Therefore, it is particularly important to perform suitability evaluation of underground space in various regions of a city. To improve the rationality of the evaluation results, this study proposes an evaluation method based on the finite interval cloud model and genetic algorithm combination weighting. The study considers the starting area of the Wuhan Changjiang New Town as the evaluation area. An evaluation index system is established for 12 indexes of five geological factors. The cloud characteristic parameters of each evaluation factor belonging to different classification levels are obtained through the finite interval cloud model. The forward finite interval cloud generator is used to generate cloud drop graphs of the indexes. Further, the certainty degrees of the evaluation factors belonging to different levels are obtained, which provide the mapping of uncertainty and randomness between the semantic variables and the index values. Subjective and objective weights of indexes are calculated by an improved analytic hierarchy process (AHP) and the criteria importance through intercriteria correlation (CRITIC) method improved with the entropy method. The combination weights are solved by the application of the genetic algorithm, which can comprehensively consider the attributes of discreteness, correlation, and contrast intensity of geological data. By following the above-mentioned procedures, the comprehensive certainty degree of the evaluation sample is obtained according to the combination weights and certainty degrees of the evaluation indexes. According to the principle of the maximum membership degree, the suitability grades of the underground space are determined. This evaluation method comprehensively considers the fuzziness of the suitability grade boundary of the underground space and the advantages of the subjective and objective weighting methods. Thus, the method ensures rationality of the evaluation results to the greatest extent, thereby providing a certain guiding significance for the development of underground space.

Delay-Optimal Scheduling for IRS-Aided Mobile Edge Computing

In this letter, we consider an intelligent reflecting surface (IRS)-aided mobile edge computing (MEC) system, where an IRS is deployed to assist computation offloading from two users to an access point connected with an edge cloud. For the IRS-aided data transmission, in contrast to the conventional non-orthogonal multiple-access (NOMA) and time-division multiple-access (TDMA), we propose a new flexible time-sharing NOMA scheme that allows users to flexibly divide their data into two parts transmitted via NOMA and TDMA, respectively, thus encapsulating both conventional NOMA and TDMA as special cases. We formulate an optimization problem to minimize the sum delay of the two users by designing the IRS passive reflection and users' computation-offloading scheduling under the IRS discrete-phase constraint. Although this problem is non-convex, we obtain its optimal solution for both the cases of infinite and finite cloud computing capacities. Furthermore, we show that NOMA and TDMA based transmissions are preferred in different scenarios, depending on the users' cloud-computing time as well as the rate discrepancy between NOMA and TDMA with IRS.

Energy-efficient computation offloading strategy with tasks scheduling in edge computing

In mobile edge computing systems, the energy consumption and execution delay can be reduced dramatically by mobile edge computation offloading (MECO) . However, due to the limited computing capacity of edge cloud, an energy-efficient offloading strategy plays a significant role. In this paper, the offloading decision problem for multi-device edge computing systems based on time-division multiple access is studied. The scheduling of offloading devices at the edge cloud is considered when modelling the edge computing system. Then, the offloading decision problem is formulated as an energy consumption minimization problem with the constraint of latency tolerance. It is a mixed integer programming problem of NP-hardness. To address the problem, a Dynamic Programming-based Energy Saving Offloading (DPESO) algorithm is designed to obtain the offloading strategy including the offloading option, offloading sequence and transmission power. First, the MECO with infinite edge cloud capacity is solved by device classification and transmission power decision. Then, we sort and adjust the offloading devices to meet the latency tolerance for the MECO with finite edge cloud capacity. Finally, simulation results demonstrate that the DPESO algorithm achieves better energy efficiency than the baseline strategies and has good scalability.

Accurate contrast determination for X-ray speckle visibility spectroscopy.

X-ray speckle visibility spectroscopy using X-ray free-electron lasers has long been proposed as a probe of fast dynamics in noncrystalline materials. In this paper, numerical modeling is presented to show how the data interpretation of visibility spectroscopy can be impacted by the nonidealities of real-life X-ray detectors. Using simulated detector data, this work provides a detailed analysis of the systematic errors of several contrast extraction algorithms in the context of low-count-rate X-ray speckle visibility spectroscopy and their origins are discussed. Here, it was found that the finite detector charge cloud and pixel size lead to an unavoidable `degeneracy' in photon position determination, and that the contrasts extracted using different algorithms can all be corrected by a simple linear model. The results suggest that experimental calibration of the correction coefficient at the count rate of interest is possible and essential. Thisallows computationally lightweight algorithms to be implemented for on-the-fly analysis.

Finite element model and experimental verification of Glare laminate impact

In this paper, a finite element simulation model is established for the impact of Glare laminates, and the reliability of the model is verified by experiments. Glare applies the continuum damage mechanics (CDM) model and inputs the user material subroutine VUMAT to determine the damage of the material based on the theory of CDM under plane stress state. By comparing the ultrasonic scanning experiment after impact damage with the CDM finite element simulation cloud pattern used in this paper, the constitutive relation of the fibre continuous damage model used in this paper can better simulate the damage initiation, evolution and damage of internal materials.

Effects of bone-resorptive lesion on stress distribution of the femoral head and on progression in patients with osteonecrosis of the femoral head

Objective To investigate effects of bone-resorptive lesion on stress distribution of femoral head and on progression in patients with osteonecrosis of the femoral head (ONFH). Methods From April 2014 to September 2018, a total of 155 femoral heads from 94 patients diagnosed with ARCO stage II and III ONFH were retrospectively reviewed, including 77 males and 17 females with aged 39.90±10.45 years old (ranged from 18-64 years). The hips were divided into two groups according to whether there were bone-resorptive lesions. Further, we compared whether there was statistical difference between the two groups in staging. Then, a case of ARCO II hip joint without bone-resorptive lesion was selected from the included patients. Six femoral head with different diameters of spherical bone-resorptive lesion of 5 mm, 7 mm, 10 mm, 14 mm, 18 mm, and 23 mm were simulated. The influence of bone-resorptive lesion on the stress distribution of necrotic area and a spherical shell extending 1 mm radially around the bone-resorptive lesion was investigated by finite element method in slow walking conditions. Results Of the 155 ONFH hips, 67 hips are complicated by bone-resorptive lesions, of which 17 were ARCO II, 50 were ARCO III. A total of 88 hips did not contain bone-resorptive lesions, of which 58 were ARCO II, ARCO III 30 cases. The proportion of ARCO stage II in the group with bone-resorptive lesions was significantly higher than that in the group without bone-resorptive lesions (χ2=25.03, P=0.000). The finite element stress distribution cloud diagram showed that there was a stress concentration area around the bone-resorptive lesions. The maximum von Mises stress around bone-resorptive lesions in the models that contained a synthetic bone-resorptive lesions were significantly higher than those reported in the matched, non-synthetic bone-resorptive lesions finite element models (t=3.139, P=0.026). The values for maximum von Mises stress around bone-resorptive lesions were 6.94±1.78 MPa and 5.01±0.35 MPa for the group with synthetic bone-resorptive lesions and the group non-synthetic bone-resorptive lesions, respectively. There was a positive correlation between the diameter of bone-resorptive lesions and the maximum and mean von Mises stress of necrotic areas as well as the maximum von Mises stress around bone-resorptive lesions. Conclusion Bone-resorptive lesions can increase the maximum stress and average stress in the necrotic area. The larger the bone-resorptive lesion, the more the stress increases. There is a stress concentration area around the bone-resorptive lesions, which may accelerate the collapse of the femoral head. Key words: Femur head necrosis; Bone resorption; Finite element analysis