Data-driven optimization study of the multi-relaxation-time lattice Boltzmann method for solid-liquid phase change

Sharp phase interfaces and accurate temperature distributions are important criteria in the simulation of solid-liquid phase changes.The multi-relaxation-time lattice Boltzmann method(MRT-LBM)shows great numerical performance during simulation;however,the value method of the relaxation parameters needs to be specified.Therefore,in this study,a random forest(RF)model is used to discriminate the importance of different relaxation parameters to the convergence,and a support vector machine(SVM)is used to explore the decision boundary of the convergent samples in each dimensional model.The results show that the convergence of the samples is consistent with the sign of the decision number,and two types of the numerical deviations appear,i.e.,the phase mushy zone and the non-physical heat transfer.The relaxation parameters chosen on the decision boundary can further suppress the numerical bias and improve numerical accuracy.

Surface lattice resonance of circular nano-array integrated on optical fiber tips

As metallic nanoparticles are arranged to form a 2D periodic nano-array,the coupling of the localized surface plasmonic resonance(LSPR)results in the well-known phenomenon of surface lattice resonances(SLRs).We theoretically investigate the SLR effect of the circular nano-array fabricated on the fiber tips.The difference between the 2D periodic and circular periodic arrays results in different resonant characteristics.For both structures,the resonant peaks due to the SLRs shift continuously as the array structures are adjusted.For some specific arrangements,the circular nano-array may generate a single sharp resonant peak with extremely high enhancement,which originates from the collective coupling of the whole array.More interestingly,the spatial pattern of the vector near-field corresponding to the sharp peak is independent of the polarization state of the incidence,facilitating its excitation and regulation.This finding may be helpful for designing multifunctional all-fiber devices.

On the completeness of eigen and root vector systems for fourth-order operator matrices and their applications

In this paper, we consider the eigenvalue problem of a class of fourth-order operator matrices appearing in mechan- ics, including the geometric multiplicity, algebraic index, and algebraic multiplicity of the eigenvalue, the symplectic orthogonality, and completeness of eigen and root vector systems. The obtained results are applied to the plate bending problem.

Completeness of system of root vectors of upper triangular infinitedimensional Hamiltonian operators appearing in elasticity theory

This paper deals with a class of upper triangular infinite-dimensional Hamilto- nian operators appearing in the elasticity theory. The geometric multiplicity and algebraic index of the eigenvalue are investigated. Furthermore, the algebraic multiplicity of the eigenvalue is obtained. Based on these properties, the concrete completeness formulation of the system of eigenvectors or root vectors of the Hamiltonian operator is proposed. It is shown that the completeness is determined by the system of eigenvectors of the operator entries. Finally, the applications of the results to some problems in the elasticity theory are presented.

Lattice Vector Quantization Applied to Speech and Audio Coding

Lattice vector quantization （LVQ） has been used for real-time speech and audio coding systems. Compared with conventional vector quantization, LVQ has two main advantages： It has a simple and fast encoding process, and it significantly reduces the amount of memory required. Therefore, LVQ is suitable for use in low-complexity speech and audio coding. In this paper, we describe the basic concepts of LVQ and its advantages over conventional vector quantization. We also describe some LVQ techniques that have been used in speech and audio coding standards of international standards developing organizations （SDOs）.

ROTATED BARNES-WALL LATTICE BASED VECTOR QUANTIZER AND ITS APPLICATION IN IMAGE-SEQUENCE CODING

A new scheme is presented to design a rotated Barnes-Wall lattice based vector quantizer(LVQ). The construction method of the LVQ and its fast quantizing algorithm are described at first. Then gain-shape lattice vector quantizer(GSLVQ) with LVQ as shape quantizer is discussed. Finally the GSLVQ is used in image-sequence coding and good experimental results are obtained.

Lattices Associated with a Finite Vector Space

Let be a n-dimensional row vector space over a finite field For , let be a d-?dimensional subspace of . denotes the set of all the spaces which are the subspaces of and not the subspaces of except . We define the partial order on by ordinary inclusion (resp. reverse inclusion), and then is a poset, denoted by (resp. ). In this paper we show that both and are finite atomic lattices. Further, we discuss the geometricity of and , and obtain their characteristic polynomials.

Secure Network Coding Based on Lattice Signature

To provide a high-security guaran- tee to network coding and lower the comput- ing complexity induced by signature scheme, we take full advantage of homomorphic prop- erty to build lattice signature schemes and sec- ure network coding algorithms. Firstly, by means of the distance between the message and its sig- nature in a lattice, we propose a Distance-bas- ed Secure Network Coding （DSNC） algorithm and stipulate its security to a new hard problem Fixed Length Vector Problem （FLVP）, which is harder than Shortest Vector Problem （SVP） on lattices. Secondly, considering the bound- ary on the distance between the message and its signature, we further propose an efficient Bo- undary-based Secure Network Coding （BSNC） algorithm to reduce the computing complexity induced by square calculation in DSNC. Sim- ulation results and security analysis show that the proposed signature schemes have stronger unforgeability due to the natural property of lattices than traditional Rivest-Shamir-Adleman （RSA）-based signature scheme. DSNC algo- rithm is more secure and BSNC algorithm greatly reduces the time cost on computation.

THE LARGEST SOLUTION OF LINEAR EQUATION OVER THE COMPLETE HEYTING ALGEBRA

Let （L, 〈, V, A） be a complete Heyting algebra. In this article, the linear system Ax = b over a complete Heyting algebra, where classical addition and multiplication operations are replaced by V and A respectively, is studied. We obtain： （i） the necessary and sufficient conditions for S（A,b）≠Ф; （ii） the necessary conditions for IS（A,b）｜ = 1. We also obtain the vector x ∈ Ln and prove that it is the largest element of S（A, b） if S（A, b）≠Ф.

CONTACT PROCESS ON HEXAGONAL LATTICE

In this article, we discuss several properties of the basic contact process on hexagonal lattice H, showing that it behaves quite similar to the process on d-dimensional lattice Zd in many aspects. Firstly, we construct a coupling between the contact process on hexagonal lattice and the oriented percolation, and prove an equivalent finite space-time condition for the survival of the process. Secondly, we show the complete convergence theorem and the polynomial growth hold for the contact process on hexagonal lattice. Finally, we prove exponential bounds in the supercritical case and exponential decay rates in the subcritical case of the process.

Notes on Preregular Operators in Banach Lattices

Some characterizations of preregular operators between two Banach lattices are presented. Then several sufficient conditions for preregular operators being regular are given, and some related results are also obtained.

The Lattice of Fully Invariant Subgroups of the Cotorsion Hull

The paper considers the lattice of fully invariant subgroups of the cotorsion hull ?when a separable primary group T?is an arbitrary direct sum of torsion-complete groups.The investigation of this problem in the case of a cotorsion hull is important because endomorphisms in this class of groups are completely defined by their action on the torsion part and for mixed groups the ring of endomorphisms is isomorphic to the ring of endomorphisms of the torsion part if and only if the group is a fully invariant subgroup of the cotorsion hull of its torsion part. In the considered case, the cotorsion hull is not fully transitive and hence it is necessary to introduce a new function which differs from an indicator and assigns an infinite matrix to each element of the cotorsion hull. The relation ?difined on the set ?of these matrices is different from the relation proposed by the autor in the countable case and better discribes the lower semilattice. The use of the relation ?essentially simplifies the verification of the required properties. It is proved that the lattice of fully invariant subgroups of the group is isomorphic to the lattice of filters of the lower semilattice.

Lattice Stability and Reflection Symmetry

Reflection symmetry properties play important roles for the stability of crystal lattices in which electrons and phonons move. Based on the reflection symmetry properties, cubic, tetragonal, orthorhombic, rhombohedral (trigonal) and hexagonal crystal systems are shown to have three-dimensional (3D) k-spaces for the conduction electrons (“electrons”, “holes”). The basic stability condition for a general crystal is the availability of parallel material planes. The monoclinic crystal has a 1D k-space. The triclinic has no k-vectors for electrons, whence it is a true insulator. The monoclinic (triclinic) crystal has one (three) disjoint sets of 1D phonons, which stabilizes the lattice. Phonons’ motion is highly directional;no spherical phonon distributions are generated for monoclinic and triclinic crystal systems.

再议量子理论的表述形式与诠释

量子力学建立至今已达百年,关于量子力学仍存留许多困惑与争议。我们注意到可能的原因是状态矢量表示理念的不一致,以及混淆了不同的波函数概率诠释。我们认识到,坚持把状态矢量表示为无量纲的对象,认清波函数的薛定谔、玻恩和狄拉克各自诠释的不同以及薛定谔、玻恩的概率诠释可以经由狄拉克完备性关系联系起来,认识到概率行为出现在无量纲的态矢/波函数与决定性的状态方程之外,则可以消除不少关于量子力学的误解。

基于特征判定系数的电力变压器振动信号故障诊断

变压器带电故障诊断对于保证电力变压器安全平稳运行具有重要的意义。针对变压器工作环境复杂且单一参数表征变压器故障类型不全面的问题,文中提出一种基于自适应噪声完备集合经验模态分解(complete ensemble empirical mode decomposition with adaptive noise,CEEMDAN)和特征熵权法(entropy weight method,EWM)进行故障诊断的方法。通过相关系数与峭度加权(correlation coefficient and weighted kurtosis,CCWK)原则筛选CEEMDAN分量并重构信号,在实现剔除冗余分量的同时,提升变压器振动信号特征的表征能力;利用EWM构建特征判定系数实现单一数据诊断变压器故障类型;通过主成分分析法减小混合域特征尺度,采用鸡群优化算法优化支持向量机(support vector machine,SVM)模型进行故障诊断。对某变电站110 kV三相油浸式变压器进行分析,结果表明与概率神经网络和SVM等变压器故障诊断方法相比,文中方法能在提前定性故障类型的同时,进一步提高变压器故障诊断的准确率与效率。

基于一般二元关系粗糙近似算子的格结构研究

刻画了基于一般二元关系及悲观多粒度粗糙近似算子的完备格结构,证明了在选取蕴涵算子之后,基于一般二元关系的粗糙近似算子构成MV、R0与布尔代数。

基于AVX512的格密码高速并行实现

量子计算的迅速发展可能对当前广泛使用的公钥密码算法造成严重威胁。格密码因优秀的抗量子安全性和高效的计算效率在后量子密码中占据重要地位。美国国家标准技术研究院于2022年5月公布4个后量子密码标准,其中3个是格密码算法,Kyber算法便是其中之一。随着后量子密码标准的确定,Kyber算法高效实现的需求日益增加。基于512位高级向量扩展(AVX512),对Kyber算法进行优化与高速并行实现。使用惰性模约减、优化的蒙哥马利模约减及优化的快速数论变化等技术,充分利用计算机的存储空间,减少大量不必要的模约减操作,提高多项式计算的效率与并行性。采用冗余比特技术,增强多项式抽样过程中比特的并行处理能力。通过AVX512的512 bit位宽和8路并行实现哈希运算,并对其产生的伪随机比特串进行合理调度,充分发挥并行性能。基于AVX512指令集高速并行实现Kyber上的多项式计算和抽样,并进一步实现整个Kyber公钥加密方案。性能测试结果表明,与C语言实现相比,基于AVX512实现的密钥生成和加密算法获得了10~16倍的加速,解密算法获得了约56倍的加速。

基于ICEEMDAN与POA-SVM的感应电机故障诊断

针对感应电机定子电流故障特征提取困难,支持向量机(SVM)惩罚系数c和核函数参数g的选择对诊断结果影响较大等问题,提出一种改进自适应噪声平均总体经验模态分解(ICEEMDAN)与鹈鹕优化算法(POA)优化支持向量机(POA-SVM)相结合的感应电机故障诊断方法。首先,利用ICEEMDAN经陷波器滤除工频的定子电流获得一系列固有模态函数(IMF);然后,选取各状态信号的前7阶IMF分量并计算能量熵作为故障特征向量;最后,将故障特征向量输入POA-SVM模型得到诊断结果。通过仿真软件Ansoft/Maxwell建立电机模型来获得电流数据,诊断准确率达到了100%,实现了感应电机的故障诊断。为进一步验证诊断方法的优越性,搭建电机故障模拟试验台来采集电流信号,结果表明,该方法在空载、半载和满载3种负载情况下诊断准确率均可达到97.5%以上,与其他故障诊断方法相比,所提方法对感应电机电气故障具有更好的识别能力。

基于CEEMDAN-GSA-LSTM和SVR的光伏功率短期区间预测

针对光伏输出功率存在间歇性和波动性的问题,提出一种光伏功率短期区间预测模型.首先,该模型采用自适应噪声完备集合经验模态分解将历史光伏出力数据分解为不同的分量并按照其与赤纬角、时角等时序特征量的相关性定义为时序分量和随机分量.其次,分别使用经过引力搜索算法优化的长短期记忆神经网络和支持向量回归模型对时序分量和随机分量进行预测.再次,叠加时序分量和随机分量的预测结果得到点预测结果.然后,对误差进行Johnson变换及正态分布建模后得到光伏功率区间预测结果.最后,利用算例验证该模型的有效性.结果表明:在不同天气情况下,上述模型比现有预测模型精度更高,具有较好的鲁棒性,能够基于预测值提供较为精准的置信区间.

基于混合孪生支持向量机的径流区间预测

径流具有非线性和随机性特征,单一点预测模型难以精确刻画和描述径流演化过程。为此,提出了一种可有效量化径流波动范围的智能区间预测方法。首先采用自适应噪声完备集合经验模态分解将非线性径流序列划分为若干子序列,并采用样本熵方法重构得到修正序列;其次以孪生支持向量机为基础,分别对复杂度较高的子序列构建区间预测模型、复杂度较低的子序列建立点预测模型,同时采用鲸鱼优化方法寻求满意的模型参数组合;最后将各子模型的预测结果叠加得到最终的预测区间。结果表明:所提方法具有良好的稳健性和可靠性,在点预测、区间预测等不同场景、不同预见期的性能指标均优于对比模型;如预见期为3 d时,对于黄河流域唐乃亥水文站,所得预测区间具有较高的可靠度与清晰度,其预测区间覆盖率PICP值为98.30%,预测区间平均宽度PINAW值为0.0792,可靠度、清晰度分别平均提高了9.47%和32.66%。研究成果可为智能化径流预测提供行之有效的方法。