Phase-Field Modeling for the Three-Dimensional Space-Filling Structure of Metal Foam Materials

Phase-field modeling for three-dimensional foam structures is presented. The foam structure, which is generally applicable for porous material design, is geometrically approximated with a space-filling structure, and hence, the analysis of the space-filling structure was performed using the phase field model. An additional term was introduced to the conventional multi-phase field model to satisfy the volume constraint condition. Then, the equations were numerically solved using the finite difference method, and simulations were carried out for several nuclei settings. First, the nuclei were set on complete lattice points for a bcc or fcc arrangement, with a truncated hexagonal structure, which is known as a Kelvin cell, or a rhombic dodecahedron being obtained, respectively. Then, an irregularity was introduced in the initial nuclei arrangement. The results revealed that the truncated hexagonal structure was stable against a slight irregularity, whereas the rhombic polyhedral was destroyed by the instability. Finally, the nuclei were placed randomly, and the relaxation process of a certain cell was traced with the result that every cell leads to a convex polyhedron shape.

Efficient Flexible M-Tree Bulk Loading Using FastMap and Space-Filling Curves

Many database applications currently deal with objects in a metric space.Examples of such objects include unstructured multimedia objects and points of interest(POIs)in a road network.The M-tree is a dynamic index structure that facilitates an efficient search for objects in a metric space.Studies have been conducted on the bulk loading of large datasets in an M-tree.However,because previous algorithms involve excessive distance computations and disk accesses,they perform poorly in terms of their index construction and search capability.This study proposes two efficient M-tree bulk loading algorithms.Our algorithms minimize the number of distance computations and disk accesses using FastMap and a space-filling curve,thereby significantly improving the index construction and search performance.Our second algorithm is an extension of the first,and it incorporates a partitioning clustering technique and flexible node architecture to further improve the search performance.Through the use of various synthetic and real-world datasets,the experimental results demonstrated that our algorithms improved the index construction performance by up to three orders of magnitude and the search performance by up to 20.3 times over the previous algorithm.

Research on a toolpath generation method of NC milling based on space-filling curve

Tool path generated by space-filling curve always turns frequently causing trembling to machine,reducing toollife and affecting workpiece quality. Length and generation time of tool paths are both relatively long. In order to solve these problems,a toolpath generation method of NC milling based on space-filling curve is proposed. First,T-spline surface is regarded as the modeling surface,the grid,which is based on the limited scallop-height,can be got in the parameter space,and the influence value of grid node is determined. Second,a box is defined and planned,and the tool paths are got preliminarily,which is based on minimal spanning tree; Finally,based on an improved chamfering algorithm,the whole tool paths are got. A simulation system is developed for computer simulation,and an experiment is carried out to verify the method. The results of simulation and experiment show that the method is effective and feasible,and length and time of the tool paths are reduced.

An application of space-filling curves to improve results of turbulent aerodynamics modeling with convolutional neural networks

When carrying out calculations for turbulent flow simulation,one inevitably has to face the choice between accuracy and speed of calculations.In order to simultaneously obtain both a computationally efficient and more accurate model,a surrogate model can be built on the basis of some fast special model and knowledge of previous calculations obtained by more accurate base models from various test bases or some results of serial calculations.The objective of this work is to construct a surrogate model which allows to improve the accuracy of turbulent calculations obtained by a special model on unstructured meshes.For this purpose,we use 1D Convolutional Neural Network(CNN)of the encoder-decoder architecture and reduce the problem to a single dimension by applying space-filling curves.Such an approach would have the benefit of being applicable to solutions obtained on unstructured meshes.In this work,a non-local approach is applied where entire flow fields obtained by the special and base models are used as input and ground truth output respectively.Spalart-Allmaras(SA)model and Near-wall Domain Decomposition(NDD)method for SA are taken as the base and special models respectively.The efficiency and accuracy of the obtained surrogate model are demonstrated in a case of supersonic flow over a compression corner with different values for angleαand Reynolds number Re.We conducted an investigation into interpolation and extrapolation by Re and also into interpolation byα.

Spiralchord: a space-filling curve based location awareness, cross-layering P2P file sharing system in WMNs

The common characteristics of peer-to-peer （P2P） overlay networks and wireless multi-hop network, such as self-organization, decentralization, hop-by-hop message transmission mode and high degree of dynamicity, lead to research of operating wired P2P applications on wireless multi-hop networks. Wireless mesh network （WMN） as a relative static multi-hop wireless network which is extended from Ad-Hoc networks, has become one of the key technologies for providing increased network coverage of Internet infrastructures. This paper investigates the problem of enabling P2P file sharing in WMNs. A special chord algorithm--spiralchord is proposed to address the major problem in wireless file sharing system how to efficiently find resources currently available. Spiralchord put forward an identifier （ID） assignment technique based on spiral space-filling curve to integrate location-awareness with cross-layering. Location awareness aims at alleviating the mismatch of physical network topology and overlay network topology, and requires close-by IDs in logical ring of neighboring peers, while cross-layering aims at speeding up resource lookup operations, requires faraway IDs of neighboring peers. Spiralchord uses spiral curve to assign peers＇ IDs which meet the contradictory requirements of location-awareness and cross-layering. The simulation results show spiralchord is effective in reducing message overhead, and increasing lookup performance with respect to basic chord.

Construction of Multi-level Space-filling Designs via Code Mappings

Space-filling designs are widely used in various fields because of their nice space-filling properties.Uniform designs are one of space-filling designs,which desires the experimental points to scatter uniformly over the experimental area.For practical need,the construction and their properties of nine-level uniform designs are discussed via two code mappings in this paper.Firstly,the algorithm of constructing nine-level uniform designs is presented from an initial three-level design by the Type-I code mapping and tripling technique.Secondly,the algorithm of constructing nine-level uniform designs is presented from a three-level base design by the Type-II code mapping and generalized orthogonal arrays.Moreover,relative properties are discussed based on the two code mappings.Finally,some numerical examples are given out for supporting our theoretical results.

Novel Global Optimization Algorithm with a Space-Filling Curve and Integral Function

In this study,we consider the global optimization problem in a hypercube.We use a class of series to construct a curve in a hypercube,which can fill the hypercube,and we present an integral function on the curve.Based on the integral function,we propose an algorithm for solving the global optimization problem.Then,we perform a convergence analysis and numerical experiments to demonstrate the effectiveness of the proposed algorithm.

A Solution of a Problem of I. P. Natanson Concerning the Decomposition of an Interval into Disjoint Perfect Sets

In a previous paper published in this journal, it was demonstrated that any bounded, closed interval of the real line can, except for a set of Lebesgue measure 0, be expressed as a union of c pairwise disjoint perfect sets, where c is the cardinality of the continuum. It turns out that the methodology presented there cannot be used to show that such an interval is actually decomposable into c nonoverlapping perfect sets without the exception of a set of Lebesgue measure 0. We shall show, utilizing a Hilbert-type space-filling curve, that such a decomposition is possible. Furthermore, we prove that, in fact, any interval, bounded or not, can be so expressed.

A New Class of Strong Orthogonal Arrays of Strength Three

Strong orthogonal arrays(SOAs) were recently introduced and studied as a class of spacefilling designs for computer experiments. To surely realize better space-filling properties, SOAs of strength three or higher are desirable. In addition, orthogonality is also an important property for designs of computer experiments, because it guarantees that the estimates of the main effects are uncorrelated. This paper first provides a systematic study on the construction of(nearly) orthogonal strength-three SOAs with better space-filling properties. The newly proposed strength-three SOAs enjoy almost the same space-filling properties of strength-four SOAs, and can accommodate much more columns than the latter. Moreover, they are(nearly) orthogonal and flexible in run sizes. The construction methods are straightforward to implement, and their theoretical supports are well established. In addition to the theoretical results, many designs are tabulated for practical needs.

On the maximin distance properties of orthogonal designs via the rotation

Space-filling designs are widely used in computer experiments.They are frequently evaluated by the orthogonality and distance-related criteria.Rotating orthogonal arrays is an appealing approach to constructing orthogonal space-filling designs.An important issue that has been rarely addressed in the literature is the design selection for the initial orthogonal arrays.This paper studies the maximin L_(2)-distance properties of orthogonal designs generated by rotating two-level orthogonal arrays under three criteria.We provide theoretical justifications for the rotation method from a maximin distance perspective and further propose to select initial orthogonal arrays by the minimum G_(2)-aberration criterion.New infinite families of orthogonal or 3-orthogonal U-type designs,which also perform well under the maximin distance criterion,are obtained and tabulated.Examples are presented to show the effectiveness of the constructed designs for building statistical surrogate models.

L curve for spherical triangle region quadtrees

The sequence of facets and nodes has a direct influence on the efficiency of access to spherical triangle region quadtree. Based on the labeling schema by Lee, spatial curves both for facets and nodes are proposed and the main algorithms for coordinate translation, node Lsequence generation and visiting nodes are presented. In particular,constant time algorithms for generating node Lsequence are advanced by using bit manipulation operations,which can be easily implemented with hardware. In L curve the distance between three nodes of a facet is mostly limited in a range of small value, thus making fast access possible. Though codes of sibling facets are continuous, the difference between codes of some cousins may occasionally be very large and makes the distance of a few facets also very large, thus greatly increasing the mean node distance and the total traversing distance. Therefore an m cluster of nodes is proposed as a basic storage unit fo n cluster, which should store eery shared node in each,and the distance between three nodes of a facet is limited to a controllagle scope.

Designing Optimal Large Four-Level Experiments:A New TechniqueWithout Recourse to Optimization Softwares

Experimental design is an effective statistical tool that is extensively applied in modern industry,engineering,and science.It is proved that experimental design is a powerful and efficient means to screen the relationships between input factors and their responses,and to distinguish significant and unimportant factor effects.In many practical situations,experimenters are faced with large experiments having four-level factors.Even though there are several techniques provided to design such experiments,the challenge faced by the experimenters is still daunting.The practice has demonstrated that the existing techniques are highly time-consuming optimization procedures,satisfactory outcomes are not guaranteed,and non-mathematicians face a significant challenge in dealing with them.A new technique that can overcome these defects of the existing techniques is presented in this paper.The results demonstrated that the proposed technique outperformed the current techniques in terms of construction simplicity,computational efficiency and achieving satisfactory results capability.For non-mathematician experimenters,the new technique is much easier and simpler than the current techniques,as it allows them to design optimal large experiments without the recourse to optimization softwares.The optimality is discussed from four basic perspectives:maximizing the dissimilarity among experimental runs,maximizing the number of independent factors,minimizing the confounding among factors,and filling the experimental domain uniformly with as few gaps as possible.

SwiftArray: Accelerating Queries on Multidimensional Arrays

Scientific instruments and simulation programs are generating large amounts of multidimensional array data. Queries with value and dimension subsetting conditions are commonly used by scientists to find useful information from big array data, and data storage and indexing methods play an important role in supporting queries on multidimensional array data efficiently. In this paper, we propose SwiftArray, a new storage layout with indexing techniques to accelerate queries with value and dimension subsetting conditions. In SwiftArray, the multidimensional array is divided into blocks and each block stores sorted values. Blocks are placed in the order of a Hilbert space-filling curve to improve data locality for dimension subsetting queries. We propose a 2-D-Bin method to build an index for the blocks＇ value ranges, which is an efficient way to avoid accessing unnecessary blocks for value subsetting queries. Our evaluations show that SwiftArray surpasses the NetCDF-4 format and FastBit indexing technique for queries on multidimensional arrays.

A prediction-oriented optimal design for visualisation recommender systems

A good visualisation method can greatly enhance human-machine collaboration in target contexts.To aid the optimal selection of visualisations for users,visualisation recommender systems have been developed to provide the right visualisation method to the right person given specific contexts.A visualisation recommender system often relies on a user study to collect data and conduct analysis to provide personalised recommendations.However,a user study without employing an effective experimental design is typically expensive in terms of time and cost.In this work,we propose a prediction-oriented optimal design to determine the user-task allocation in the user study for the recommendation of visualisation methods.The proposed optimal design will not only encourage the learning of the similarity embedded in the recommendation responses(i.e.,users’preference),but also improve the modelling accuracy of the similarities captured by the covariates of contexts(i.e.,task attributes).A simulation study and a real-data case study are used to evaluate the proposed optimal design.

A discussion of objective function representation methods in global optimization

Non-convex optimization can be found in several smart manufacturing systems. This paper presents a short review on global optimization(GO) methods. We examine decomposition techniques and classify GO problems on the basis of objective function representation and decomposition techniques. We then explain Kolmogorov's superposition and its application in GO. Finally,we conclude the paper by exploring the importance of objective function representation in integrated artificial intelligence, optimization, and decision support systems in smart manufacturing and Industry 4.0.