The definitions of the third-order elastic,piezoelectric,and dielectric constants and the properties of the associated tensors are discussed.Based on the energy conservation and coordinate transformation,the relations...The definitions of the third-order elastic,piezoelectric,and dielectric constants and the properties of the associated tensors are discussed.Based on the energy conservation and coordinate transformation,the relations among the third-order constants are obtained.Furthermore,the relations among the third-order elastic,piezoelectric,and dielectric constants of the seven crystal systems and isotropic materials are listed in detail.These third-order constants relations play an important role in solving nonlinear problems of elastic and piezoelectric materials.It is further found that all third-order piezoelectric constants are 0 for 15 kinds of point groups,while all third-order dielectric constants are 0 for 16 kinds of point groups as well as isotropic material.The reason is that some of the point groups are centrally symmetric,and the other point groups are high symmetry.These results provide the foundation to measure these constants,to choose material,and to research nonlinear problems.Moreover,these results are helpful not only for the study of nonlinear elastic and piezoelectric problems,but also for the research on flexoelectric effects and size effects.展开更多
Dear Editor,This letter presents a novel latent factorization model for high dimensional and incomplete (HDI) tensor, namely the neural Tucker factorization (Neu Tuc F), which is a generic neural network-based latent-...Dear Editor,This letter presents a novel latent factorization model for high dimensional and incomplete (HDI) tensor, namely the neural Tucker factorization (Neu Tuc F), which is a generic neural network-based latent-factorization-of-tensors model under the Tucker decomposition framework.展开更多
A large-scale dynamically weighted directed network(DWDN)involving numerous entities and massive dynamic interaction is an essential data source in many big-data-related applications,like in a terminal interaction pat...A large-scale dynamically weighted directed network(DWDN)involving numerous entities and massive dynamic interaction is an essential data source in many big-data-related applications,like in a terminal interaction pattern analysis system(TIPAS).It can be represented by a high-dimensional and incomplete(HDI)tensor whose entries are mostly unknown.Yet such an HDI tensor contains a wealth knowledge regarding various desired patterns like potential links in a DWDN.A latent factorization-of-tensors(LFT)model proves to be highly efficient in extracting such knowledge from an HDI tensor,which is commonly achieved via a stochastic gradient descent(SGD)solver.However,an SGD-based LFT model suffers from slow convergence that impairs its efficiency on large-scale DWDNs.To address this issue,this work proposes a proportional-integralderivative(PID)-incorporated LFT model.It constructs an adjusted instance error based on the PID control principle,and then substitutes it into an SGD solver to improve the convergence rate.Empirical studies on two DWDNs generated by a real TIPAS show that compared with state-of-the-art models,the proposed model achieves significant efficiency gain as well as highly competitive prediction accuracy when handling the task of missing link prediction for a given DWDN.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11872186 and11272126)the Fundamental Research Funds for the Central Universities(No.HUST:2016JCTD114)
文摘The definitions of the third-order elastic,piezoelectric,and dielectric constants and the properties of the associated tensors are discussed.Based on the energy conservation and coordinate transformation,the relations among the third-order constants are obtained.Furthermore,the relations among the third-order elastic,piezoelectric,and dielectric constants of the seven crystal systems and isotropic materials are listed in detail.These third-order constants relations play an important role in solving nonlinear problems of elastic and piezoelectric materials.It is further found that all third-order piezoelectric constants are 0 for 15 kinds of point groups,while all third-order dielectric constants are 0 for 16 kinds of point groups as well as isotropic material.The reason is that some of the point groups are centrally symmetric,and the other point groups are high symmetry.These results provide the foundation to measure these constants,to choose material,and to research nonlinear problems.Moreover,these results are helpful not only for the study of nonlinear elastic and piezoelectric problems,but also for the research on flexoelectric effects and size effects.
基金supported by the National Natural Science Foundation of China(62272078)Chongqing Natural Science Foundation(CSTB2023NSCQ-LZX0069)the Science and Technology Research Program of Chongqing Municipal Education Commission(KJQN202300210)
文摘Dear Editor,This letter presents a novel latent factorization model for high dimensional and incomplete (HDI) tensor, namely the neural Tucker factorization (Neu Tuc F), which is a generic neural network-based latent-factorization-of-tensors model under the Tucker decomposition framework.
基金supported in part by the National Natural Science Foundation of China(61772493)the CAAI-Huawei MindSpore Open Fund(CAAIXSJLJJ-2020-004B)+4 种基金in part by the Natural Science Foundation of Chongqing of China(cstc2019jcyjjq X0013)in part by the Pioneer Hundred Talents Program of Chinese Academy of Sciencesin part by the Deanship of Scientific Research(DSR)at King Abdulaziz UniversityJeddahSaudi Arabia(FP-165-43)。
文摘A large-scale dynamically weighted directed network(DWDN)involving numerous entities and massive dynamic interaction is an essential data source in many big-data-related applications,like in a terminal interaction pattern analysis system(TIPAS).It can be represented by a high-dimensional and incomplete(HDI)tensor whose entries are mostly unknown.Yet such an HDI tensor contains a wealth knowledge regarding various desired patterns like potential links in a DWDN.A latent factorization-of-tensors(LFT)model proves to be highly efficient in extracting such knowledge from an HDI tensor,which is commonly achieved via a stochastic gradient descent(SGD)solver.However,an SGD-based LFT model suffers from slow convergence that impairs its efficiency on large-scale DWDNs.To address this issue,this work proposes a proportional-integralderivative(PID)-incorporated LFT model.It constructs an adjusted instance error based on the PID control principle,and then substitutes it into an SGD solver to improve the convergence rate.Empirical studies on two DWDNs generated by a real TIPAS show that compared with state-of-the-art models,the proposed model achieves significant efficiency gain as well as highly competitive prediction accuracy when handling the task of missing link prediction for a given DWDN.
