We propose an eigen microstate approach(EMA)for analyzing quantum phase transitions in quantum many-body systems,introducing a novel framework that does not require prior knowledge of an order parameter.Using the tran...We propose an eigen microstate approach(EMA)for analyzing quantum phase transitions in quantum many-body systems,introducing a novel framework that does not require prior knowledge of an order parameter.Using the transversefield Ising model(TFIM)as a case study,we demonstrate the effectiveness of EMA by identifying key features of the phase transition through the scaling behavior of eigenvalues and the structure of associated eigen microstates.Our results reveal substantial changes in the ground state of the TFIM as it undergoes a phase transition,as reflected in the behavior of specific componentsξ_(i)^((k))within the eigen microstates.This method is expected to be applicable to other quantum systems where predefining an order parameter is challenging.展开更多
This paper presents a comprehensive framework for analyzing phase transitions in collective models such as theVicsek model under various noise types. The Vicsek model, focusing on understanding the collective behavior...This paper presents a comprehensive framework for analyzing phase transitions in collective models such as theVicsek model under various noise types. The Vicsek model, focusing on understanding the collective behaviors of socialanimals, is known due to its discontinuous phase transitions under vector noise. However, its behavior under scalar noiseremains less conclusive. Renowned for its efficacy in the analysis of complex systems under both equilibrium and nonequilibriumstates, the eigen microstate method is employed here for a quantitative examination of the phase transitions inthe Vicsek model under both vector and scalar noises. The study finds that the Vicsek model exhibits discontinuous phasetransitions regardless of noise type. Furthermore, the dichotomy method is utilized to identify the critical points for thesephase transitions. A significant finding is the observed increase in the critical point for discontinuous phase transitions withescalation of population density.展开更多
The analysis of microstates in EEG signals is a crucial technique for understanding the spatiotemporal dynamics of brain electrical activity.Traditional methods such as Atomic Agglomerative Hierarchical Clustering(AAH...The analysis of microstates in EEG signals is a crucial technique for understanding the spatiotemporal dynamics of brain electrical activity.Traditional methods such as Atomic Agglomerative Hierarchical Clustering(AAHC),K-means clustering,Principal Component Analysis(PCA),and Independent Component Analysis(ICA)are limited by a fixed number of microstate maps and insufficient capability in cross-task feature extraction.Tackling these limitations,this study introduces a Global Map Dissimilarity(GMD)-driven density canopy K-means clustering algorithm.This innovative approach autonomously determines the optimal number of EEG microstate topographies and employs Gaussian kernel density estimation alongside the GMD index for dynamic modeling of EEG data.Utilizing this advanced algorithm,the study analyzes the Motor Imagery(MI)dataset from the GigaScience database,GigaDB.The findings reveal six distinct microstates during actual right-hand movement and five microstates across other task conditions,with microstate C showing superior performance in all task states.During imagined movement,microstate A was significantly enhanced.Comparison with existing algorithms indicates a significant improvement in clustering performance by the refined method,with an average Calinski-Harabasz Index(CHI)of 35517.29 and a Davis-Bouldin Index(DBI)average of 2.57.Furthermore,an information-theoretical analysis of the microstate sequences suggests that imagined movement exhibits higher complexity and disorder than actual movement.By utilizing the extracted microstate sequence parameters as features,the improved algorithm achieved a classification accuracy of 98.41%in EEG signal categorization for motor imagery.A performance of 78.183%accuracy was achieved in a four-class motor imagery task on the BCI-IV-2a dataset.These results demonstrate the potential of the advanced algorithm in microstate analysis,offering a more effective tool for a deeper understanding of the spatiotemporal features of EEG signals.展开更多
BACKGROUND A growing number of recent studies have explored underlying activity in the brain by measuring electroencephalography(EEG)in people with depression.However,the consistency of findings on EEG microstates in ...BACKGROUND A growing number of recent studies have explored underlying activity in the brain by measuring electroencephalography(EEG)in people with depression.However,the consistency of findings on EEG microstates in patients with depression is poor,and few studies have reported the relationship between EEG microstates,cognitive scales,and depression severity scales.AIM To investigate the EEG microstate characteristics of patients with depression and their association with cognitive functions.METHODS A total of 24 patients diagnosed with depression and 32 healthy controls were included in this study using the Structured Clinical Interview for Disease for The Diagnostic and Statistical Manual of Mental Disorders,Fifth Edition.We collected information relating to demographic and clinical characteristics,as well as data from the Repeatable Battery for the Assessment of Neuropsychological Status(RBANS;Chinese version)and EEG.RESULTS Compared with the controls,the duration,occurrence,and contribution of microstate C were significantly higher[depression(DEP):Duration 84.58±24.35,occurrence 3.72±0.56,contribution 30.39±8.59;CON:Duration 72.77±10.23,occurrence 3.41±0.36,contribution 24.46±4.66;Duration F=6.02,P=0.049;Occurrence F=6.19,P=0.049;Contribution F=10.82,P=0.011]while the duration,occurrence,and contribution of microstate D were significantly lower(DEP:Duration 70.00±15.92,occurrence 3.18±0.71,contribution 22.48±8.12;CON:Duration 85.46±10.23,occurrence 3.54±0.41,contribution 28.25±5.85;Duration F=19.18,P<0.001;Occurrence F=5.79,P=0.050;Contribution F=9.41,P=0.013)in patients with depression.A positive correlation was observed between the visuospatial/constructional scores of the RBANS scale and the transition probability of microstate class C to B(r=0.405,P=0.049).CONCLUSION EEG microstate,especially C and D,is a possible biomarker in depression.Patients with depression had a more frequent transition from microstate C to B,which may relate to more negative rumination and visual processing.展开更多
Emergence refers to the existence or formation of collective behaviors in complex systems.Here,we develop a theoretical framework based on the eigen microstate theory to analyze the emerging phenomena and dynamic evol...Emergence refers to the existence or formation of collective behaviors in complex systems.Here,we develop a theoretical framework based on the eigen microstate theory to analyze the emerging phenomena and dynamic evolution of complex system.In this framework,the statistical ensemble composed of M microstates of a complex system with N agents is defined by the normalized N×M matrix A,whose columns represent microstates and order of row is consist with the time.The ensemble matrix A can be decomposed as■,where r=min(N,M),eigenvalueσIbehaves as the probability amplitude of the eigen microstate U_I so that■and U_I evolves following V_I.In a disorder complex system,there is no dominant eigenvalue and eigen microstate.When a probability amplitudeσIbecomes finite in the thermodynamic limit,there is a condensation of the eigen microstate UIin analogy to the Bose–Einstein condensation of Bose gases.This indicates the emergence of U_I and a phase transition in complex system.Our framework has been applied successfully to equilibrium threedimensional Ising model,climate system and stock markets.We anticipate that our eigen microstate method can be used to study non-equilibrium complex systems with unknown orderparameters,such as phase transitions of collective motion and tipping points in climate systems and ecosystems.展开更多
Macrostate and microstate characteristics of interregional nonlinear interdependence of brain dynamics are investigated for Zen-meditation and normal resting EEG. Evaluation of nonlinear interdependence based on nonli...Macrostate and microstate characteristics of interregional nonlinear interdependence of brain dynamics are investigated for Zen-meditation and normal resting EEG. Evaluation of nonlinear interdependence based on nonlinear dynamic theory and phase space reconstruction is employed in the 30-channel electroencephalographic (EEG) signals to characterize the functioning interactions among different local neuronal networks. This paper presents a new scheme for exploring the microstate and macrostate of interregional brain neural network interactivity. Nonlinear interdependence quantified by similarity index is applied to the phase trajectory reconstructed from multi-channel EEG. The microstate similarity-index matrix (miSIM) is evaluated every 5 millisecond. The miSIMs are classified by K-means clustering. The cluster center corresponds to the macrostate SIM (maSIM) evaluated by conventional scheme. Zen-meditation EEG exhibits rather stationary and stronger interconnectivity among frontal midline regional neural oscillators, whereas resting EEG appears to drift away more often from the midline and extend to the inferior brain regions.展开更多
Entropy-stabilized multi-component alloys have been considered to be prospective structural materials attributing to their impressive mechanical and functional properties.The local chemical complexions,microstates and...Entropy-stabilized multi-component alloys have been considered to be prospective structural materials attributing to their impressive mechanical and functional properties.The local chemical complexions,microstates and configurational transformations are essential to reveal the structure–property relationship,thus,to promote the development of advanced multicomponent alloys.In the present work,effects of local lattice distortion(LLD)and microstates of various configurations on the equilibrium volume(V0),total energy,Fermi energy,magnetic moment(μMag)and electron work function(Φ)and bonding structures of the Fe–Mn–Al medium entropy alloy(MEA)have been investigated comprehensively by first-principles calculations.It is found that theΦandμMag of those MEA are proportional to the V 0,which is dominated by lattice distortion.In terms of bonding charge density,both the strengthened clusters or the so-called short-range order structures and the weakly bonded spots or weak spots are characterized.While the presence of weakly bonded Al atoms implies a large LLD/mismatch,the Fe–Mn bonding pairs result in the formation of strengthened clusters,which dominate the local microstates and the configurational transitions.The variations ofμMag are associated with the enhancement of the nearest neighbor magnetic Fe and Mn atoms,attributing to the LLD caused by Al atoms,the local changes in the electronic structures.This work provides an atomic and electronic insight into the microstate-dominated solid-solution strengthening mechanism of Fe–Mn–Al MEA.展开更多
Unlike other groups of elements, Group 3 constituency remains unsettled. This article argues that ground level microstates and atomic number parity suggest Sc-Y-Lu-Lr Group 3 membership.
The Kuramoto model is one of the most profound and classical models of coupled phase oscillators.Because of the global couplings between oscillators,its precise critical exponents can be obtained using the mean-field ...The Kuramoto model is one of the most profound and classical models of coupled phase oscillators.Because of the global couplings between oscillators,its precise critical exponents can be obtained using the mean-field approximation(MFA),where the time average of the modulus of the mean-field is defined as the order parameter.Here,we further study the phase fluctuations of oscillators from the mean-field using the eigen microstate theory(EMT),which was recently developed.The synchronization of phase fluctuations is identified by the condensation and criticality of eigen microstates with finite eigenvalues,which follow the finite-size scaling with the same critical exponents as those of the MFA in the critical regime.Then,we obtain the complete critical behaviors of phase oscillators in the Kuramoto model.We anticipate that the critical behaviors of general phase oscillators can be investigated by using the EMT and different critical exponents from those of the MFA will be obtained.展开更多
In a statistical ensemble with M microstates, we introduce an M × M correlation matrix with correlations among microstates as its elements. Eigen microstates of ensemble can be defined using eigenvectors of the c...In a statistical ensemble with M microstates, we introduce an M × M correlation matrix with correlations among microstates as its elements. Eigen microstates of ensemble can be defined using eigenvectors of the correlation matrix. The eigenvalue normalized by M represents weight factor in the ensemble of the corresponding eigen microstate. In the limit M →∞, weight factors drop to zero in the ensemble without localization of the microstate. The finite limit of the weight factor when M →∞ indicates a condensation of the corresponding eigen microstate. This finding indicates a transition into a new phase characterized by the condensed eigen microstate. We propose a finite-size scaling relation of weight factors near critical point, which can be used to identify the phase transition and its universality class of general complex systems. The condensation of eigen microstate and the finite-size scaling relation of weight factors are confirmed using Monte Carlo data of one-dimensional and two-dimensional Ising models.展开更多
随着智慧水利建设的推进,水利水电高边坡工程面临着信息反馈滞后、现场监控不足、施工质量控制不到位等状况。基于这些问题,提出了一种结合建筑信息模型(building information modeling,BIM)、有限元分析与混合现实(mixed reality,MR)...随着智慧水利建设的推进,水利水电高边坡工程面临着信息反馈滞后、现场监控不足、施工质量控制不到位等状况。基于这些问题,提出了一种结合建筑信息模型(building information modeling,BIM)、有限元分析与混合现实(mixed reality,MR)的数字化解决方案。基于MicroStation软件,通过钻孔数据创建BIM模型,导入ABAQUS进行三维地应力平衡以及二维边坡降雨入渗分析,通过部署现场监测系统,结合进行二次开发,将分析结果和监测数据反馈至MicroStation中,实现了数值计算结果与BIM环境的互通;同时将BIM模型导入Unity3D平台中,并借助HoloLens2头戴式MR设备,将虚拟的三维模型、分析结果和监测数据与现实环境叠加,实现了工程现场的可视化和交互式分析。通过迈湾水利枢纽工程的案例,展示了该技术的实际应用效果,有效提升了水利水电高边坡工程的数字化管理水平和安全保障能力。这些技术的融合不仅促进了信息模型在实际工程中的优化和协同,还为工程安全性、可靠性和效率性提供了新的支持和解决方案。展开更多
针对Bentley平台的三维建模基础软件Microstation无法进行桥梁结构参数化建模配筋及钢筋工程量统计问题,利用MICROSTATION SDK软件开发工具、WPF界面、选用主流开发语言C#,辅以C++/CLI,以Vi⁃sual Studio 2019为开发平台,进行二次开发。...针对Bentley平台的三维建模基础软件Microstation无法进行桥梁结构参数化建模配筋及钢筋工程量统计问题,利用MICROSTATION SDK软件开发工具、WPF界面、选用主流开发语言C#,辅以C++/CLI,以Vi⁃sual Studio 2019为开发平台,进行二次开发。开发出了适用于该类桥梁的快速配筋插件以及钢筋工程量统计插件。以某桥梁工程中的30 m长等截面预制箱梁为例,应用箱梁建模配筋及工程量统计插件程序,高效准确地完成了30 m长等截面预制箱梁的三维建模配筋及钢筋工程量统计,验证了该二次开发建模及配筋插件程序的可用性和高效性,大大提高了设计人员的配筋及工作效率。展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12475033,12135003,12174194,and 12405032)the National Key Research and Development Program of China(Grant No.2023YFE0109000)+1 种基金supported by the Fundamental Research Funds for the Central Universitiessupport from the China Postdoctoral Science Foundation(Grant No.2023M730299).
文摘We propose an eigen microstate approach(EMA)for analyzing quantum phase transitions in quantum many-body systems,introducing a novel framework that does not require prior knowledge of an order parameter.Using the transversefield Ising model(TFIM)as a case study,we demonstrate the effectiveness of EMA by identifying key features of the phase transition through the scaling behavior of eigenvalues and the structure of associated eigen microstates.Our results reveal substantial changes in the ground state of the TFIM as it undergoes a phase transition,as reflected in the behavior of specific componentsξ_(i)^((k))within the eigen microstates.This method is expected to be applicable to other quantum systems where predefining an order parameter is challenging.
基金the National Natural Science Foundation of China(Grant No.62273033).
文摘This paper presents a comprehensive framework for analyzing phase transitions in collective models such as theVicsek model under various noise types. The Vicsek model, focusing on understanding the collective behaviors of socialanimals, is known due to its discontinuous phase transitions under vector noise. However, its behavior under scalar noiseremains less conclusive. Renowned for its efficacy in the analysis of complex systems under both equilibrium and nonequilibriumstates, the eigen microstate method is employed here for a quantitative examination of the phase transitions inthe Vicsek model under both vector and scalar noises. The study finds that the Vicsek model exhibits discontinuous phasetransitions regardless of noise type. Furthermore, the dichotomy method is utilized to identify the critical points for thesephase transitions. A significant finding is the observed increase in the critical point for discontinuous phase transitions withescalation of population density.
基金funded by National Nature Science Foundation of China,Yunnan Funda-Mental Research Projects,Special Project of Guangdong Province in Key Fields of Ordinary Colleges and Universities and Chaozhou Science and Technology Plan Project of Funder Grant Numbers 82060329,202201AT070108,2023ZDZX2038 and 202201GY01.
文摘The analysis of microstates in EEG signals is a crucial technique for understanding the spatiotemporal dynamics of brain electrical activity.Traditional methods such as Atomic Agglomerative Hierarchical Clustering(AAHC),K-means clustering,Principal Component Analysis(PCA),and Independent Component Analysis(ICA)are limited by a fixed number of microstate maps and insufficient capability in cross-task feature extraction.Tackling these limitations,this study introduces a Global Map Dissimilarity(GMD)-driven density canopy K-means clustering algorithm.This innovative approach autonomously determines the optimal number of EEG microstate topographies and employs Gaussian kernel density estimation alongside the GMD index for dynamic modeling of EEG data.Utilizing this advanced algorithm,the study analyzes the Motor Imagery(MI)dataset from the GigaScience database,GigaDB.The findings reveal six distinct microstates during actual right-hand movement and five microstates across other task conditions,with microstate C showing superior performance in all task states.During imagined movement,microstate A was significantly enhanced.Comparison with existing algorithms indicates a significant improvement in clustering performance by the refined method,with an average Calinski-Harabasz Index(CHI)of 35517.29 and a Davis-Bouldin Index(DBI)average of 2.57.Furthermore,an information-theoretical analysis of the microstate sequences suggests that imagined movement exhibits higher complexity and disorder than actual movement.By utilizing the extracted microstate sequence parameters as features,the improved algorithm achieved a classification accuracy of 98.41%in EEG signal categorization for motor imagery.A performance of 78.183%accuracy was achieved in a four-class motor imagery task on the BCI-IV-2a dataset.These results demonstrate the potential of the advanced algorithm in microstate analysis,offering a more effective tool for a deeper understanding of the spatiotemporal features of EEG signals.
基金Supported by Suzhou Key Technologies Program,No.SKY2021063Suzhou Clinical Medical Center for Mood Disorders,No.Szlcyxzx202109+4 种基金Suzhou Clinical Key Disciplines for Geriatric Psychiatry,No.SZXK202116Jiangsu Province Social Development Project,No.BE2020764the Gusu Health Talents Project,No.GSWS2022091the Science and Technology Program of Suzhou,No.SKYD2022039 and No.SKY2023075the Doctoral Scientific Research Foundation of Suzhou Guangji Hospital,No.2023B01.
文摘BACKGROUND A growing number of recent studies have explored underlying activity in the brain by measuring electroencephalography(EEG)in people with depression.However,the consistency of findings on EEG microstates in patients with depression is poor,and few studies have reported the relationship between EEG microstates,cognitive scales,and depression severity scales.AIM To investigate the EEG microstate characteristics of patients with depression and their association with cognitive functions.METHODS A total of 24 patients diagnosed with depression and 32 healthy controls were included in this study using the Structured Clinical Interview for Disease for The Diagnostic and Statistical Manual of Mental Disorders,Fifth Edition.We collected information relating to demographic and clinical characteristics,as well as data from the Repeatable Battery for the Assessment of Neuropsychological Status(RBANS;Chinese version)and EEG.RESULTS Compared with the controls,the duration,occurrence,and contribution of microstate C were significantly higher[depression(DEP):Duration 84.58±24.35,occurrence 3.72±0.56,contribution 30.39±8.59;CON:Duration 72.77±10.23,occurrence 3.41±0.36,contribution 24.46±4.66;Duration F=6.02,P=0.049;Occurrence F=6.19,P=0.049;Contribution F=10.82,P=0.011]while the duration,occurrence,and contribution of microstate D were significantly lower(DEP:Duration 70.00±15.92,occurrence 3.18±0.71,contribution 22.48±8.12;CON:Duration 85.46±10.23,occurrence 3.54±0.41,contribution 28.25±5.85;Duration F=19.18,P<0.001;Occurrence F=5.79,P=0.050;Contribution F=9.41,P=0.013)in patients with depression.A positive correlation was observed between the visuospatial/constructional scores of the RBANS scale and the transition probability of microstate class C to B(r=0.405,P=0.049).CONCLUSION EEG microstate,especially C and D,is a possible biomarker in depression.Patients with depression had a more frequent transition from microstate C to B,which may relate to more negative rumination and visual processing.
基金supported by the Key Research Program of Frontier Sciences,Chinese Academy of Sciences(Grant No.QYZD-SSW-SYS019)。
文摘Emergence refers to the existence or formation of collective behaviors in complex systems.Here,we develop a theoretical framework based on the eigen microstate theory to analyze the emerging phenomena and dynamic evolution of complex system.In this framework,the statistical ensemble composed of M microstates of a complex system with N agents is defined by the normalized N×M matrix A,whose columns represent microstates and order of row is consist with the time.The ensemble matrix A can be decomposed as■,where r=min(N,M),eigenvalueσIbehaves as the probability amplitude of the eigen microstate U_I so that■and U_I evolves following V_I.In a disorder complex system,there is no dominant eigenvalue and eigen microstate.When a probability amplitudeσIbecomes finite in the thermodynamic limit,there is a condensation of the eigen microstate UIin analogy to the Bose–Einstein condensation of Bose gases.This indicates the emergence of U_I and a phase transition in complex system.Our framework has been applied successfully to equilibrium threedimensional Ising model,climate system and stock markets.We anticipate that our eigen microstate method can be used to study non-equilibrium complex systems with unknown orderparameters,such as phase transitions of collective motion and tipping points in climate systems and ecosystems.
文摘Macrostate and microstate characteristics of interregional nonlinear interdependence of brain dynamics are investigated for Zen-meditation and normal resting EEG. Evaluation of nonlinear interdependence based on nonlinear dynamic theory and phase space reconstruction is employed in the 30-channel electroencephalographic (EEG) signals to characterize the functioning interactions among different local neuronal networks. This paper presents a new scheme for exploring the microstate and macrostate of interregional brain neural network interactivity. Nonlinear interdependence quantified by similarity index is applied to the phase trajectory reconstructed from multi-channel EEG. The microstate similarity-index matrix (miSIM) is evaluated every 5 millisecond. The miSIMs are classified by K-means clustering. The cluster center corresponds to the macrostate SIM (maSIM) evaluated by conventional scheme. Zen-meditation EEG exhibits rather stationary and stronger interconnectivity among frontal midline regional neural oscillators, whereas resting EEG appears to drift away more often from the midline and extend to the inferior brain regions.
基金financially supported by the Key Project of the Equipment Pre-Research Field Fund of China(No.6140922010302)the National Natural Science Foundation of China(No.51690164)。
文摘Entropy-stabilized multi-component alloys have been considered to be prospective structural materials attributing to their impressive mechanical and functional properties.The local chemical complexions,microstates and configurational transformations are essential to reveal the structure–property relationship,thus,to promote the development of advanced multicomponent alloys.In the present work,effects of local lattice distortion(LLD)and microstates of various configurations on the equilibrium volume(V0),total energy,Fermi energy,magnetic moment(μMag)and electron work function(Φ)and bonding structures of the Fe–Mn–Al medium entropy alloy(MEA)have been investigated comprehensively by first-principles calculations.It is found that theΦandμMag of those MEA are proportional to the V 0,which is dominated by lattice distortion.In terms of bonding charge density,both the strengthened clusters or the so-called short-range order structures and the weakly bonded spots or weak spots are characterized.While the presence of weakly bonded Al atoms implies a large LLD/mismatch,the Fe–Mn bonding pairs result in the formation of strengthened clusters,which dominate the local microstates and the configurational transitions.The variations ofμMag are associated with the enhancement of the nearest neighbor magnetic Fe and Mn atoms,attributing to the LLD caused by Al atoms,the local changes in the electronic structures.This work provides an atomic and electronic insight into the microstate-dominated solid-solution strengthening mechanism of Fe–Mn–Al MEA.
文摘Unlike other groups of elements, Group 3 constituency remains unsettled. This article argues that ground level microstates and atomic number parity suggest Sc-Y-Lu-Lr Group 3 membership.
基金supported by the National Natural Science Foundation of China(Grant Nos.12135003,71731002,and 12471141)the Postdoctoral Fellowship Program of CPSF(Grant No.GZC20231179)+1 种基金the China Postdoctoral Science Foundation-Tianjin Joint Support Program(Grant No.2023T001TJ)the Tianjin Education Commission scientific Research Project(Grant No.2023SK070)。
文摘The Kuramoto model is one of the most profound and classical models of coupled phase oscillators.Because of the global couplings between oscillators,its precise critical exponents can be obtained using the mean-field approximation(MFA),where the time average of the modulus of the mean-field is defined as the order parameter.Here,we further study the phase fluctuations of oscillators from the mean-field using the eigen microstate theory(EMT),which was recently developed.The synchronization of phase fluctuations is identified by the condensation and criticality of eigen microstates with finite eigenvalues,which follow the finite-size scaling with the same critical exponents as those of the MFA in the critical regime.Then,we obtain the complete critical behaviors of phase oscillators in the Kuramoto model.We anticipate that the critical behaviors of general phase oscillators can be investigated by using the EMT and different critical exponents from those of the MFA will be obtained.
基金supported by the Key Research Program of Frontier Sciences,Chinese Academy of Sciences(Grant No.QYZD-SSW-SYS019)supported by the HPC Cluster of ITP-CAS
文摘In a statistical ensemble with M microstates, we introduce an M × M correlation matrix with correlations among microstates as its elements. Eigen microstates of ensemble can be defined using eigenvectors of the correlation matrix. The eigenvalue normalized by M represents weight factor in the ensemble of the corresponding eigen microstate. In the limit M →∞, weight factors drop to zero in the ensemble without localization of the microstate. The finite limit of the weight factor when M →∞ indicates a condensation of the corresponding eigen microstate. This finding indicates a transition into a new phase characterized by the condensed eigen microstate. We propose a finite-size scaling relation of weight factors near critical point, which can be used to identify the phase transition and its universality class of general complex systems. The condensation of eigen microstate and the finite-size scaling relation of weight factors are confirmed using Monte Carlo data of one-dimensional and two-dimensional Ising models.
文摘随着智慧水利建设的推进,水利水电高边坡工程面临着信息反馈滞后、现场监控不足、施工质量控制不到位等状况。基于这些问题,提出了一种结合建筑信息模型(building information modeling,BIM)、有限元分析与混合现实(mixed reality,MR)的数字化解决方案。基于MicroStation软件,通过钻孔数据创建BIM模型,导入ABAQUS进行三维地应力平衡以及二维边坡降雨入渗分析,通过部署现场监测系统,结合进行二次开发,将分析结果和监测数据反馈至MicroStation中,实现了数值计算结果与BIM环境的互通;同时将BIM模型导入Unity3D平台中,并借助HoloLens2头戴式MR设备,将虚拟的三维模型、分析结果和监测数据与现实环境叠加,实现了工程现场的可视化和交互式分析。通过迈湾水利枢纽工程的案例,展示了该技术的实际应用效果,有效提升了水利水电高边坡工程的数字化管理水平和安全保障能力。这些技术的融合不仅促进了信息模型在实际工程中的优化和协同,还为工程安全性、可靠性和效率性提供了新的支持和解决方案。
