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Isometric Immersions of Lightlike Warped Product Manifolds
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作者 Domitien Ndayirukiye Cyriaque Atindogbe Gilbert Nibaruta 《Journal of Applied Mathematics and Physics》 2024年第7期2490-2505,共16页
In this paper, we deal with isommetric immersions of globally null warped product manifolds into Lorentzian manifolds with constant curvature c in codimension k≥3. Under the assumptions that the globally null warped ... In this paper, we deal with isommetric immersions of globally null warped product manifolds into Lorentzian manifolds with constant curvature c in codimension k≥3. Under the assumptions that the globally null warped product manifold has no points with the same constant sectional curvature c as the Lorentzian ambient, we show that such isometric immersion splits into warped product of isometric immersions. 展开更多
关键词 Lightlike Warped Product Manifolds Globally Null Warped Products Manifolds Lightlike Warped Product Isometric immersions
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ON THE REFLECTION OF IMMERSIONS IN EUCLIDEAN SPACES~*
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作者 李邦河 U.Kaiser 《Acta Mathematica Scientia》 SCIE CSCD 1991年第3期301-307,共7页
We calculate the first obstruction to regular homotopy of an immersion f: M(n) --> R(n + k) into r-degrees-f for a reflection r of R(n + k). In the case of k = n - 1 we give necessary and sufficient conditions for ... We calculate the first obstruction to regular homotopy of an immersion f: M(n) --> R(n + k) into r-degrees-f for a reflection r of R(n + k). In the case of k = n - 1 we give necessary and sufficient conditions for f to be regularly homotopic to r-degrees-f in terms of obstructions to the existence of a normal vectorfield of f. 展开更多
关键词 TH ON THE REFLECTION OF immersions IN EUCLIDEAN SPACES 刁刀
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SLANT IMMERSIONS OF COMPLEX SPACE FORMS AND CHEN'S INEQUALITY 被引量:10
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作者 李光汉 吴传喜 《Acta Mathematica Scientia》 SCIE CSCD 2005年第2期223-232,共10页
A submanifold in a complex space form is called slant if it has constant Wirtinger angles. B. Y. Chen and Y. Tazawa proved that there do not exist minimal proper slant surfaces in CP2 and CH2. So it seems that the sla... A submanifold in a complex space form is called slant if it has constant Wirtinger angles. B. Y. Chen and Y. Tazawa proved that there do not exist minimal proper slant surfaces in CP2 and CH2. So it seems that the slant immersion has some interesting properties. The authors have great interest to consider slant immersions satisfying some additional conditions, such as unfull first normal bundles or Chen’s equality holding. They prove that there do not exist n-dimensional Kaehlerian slant immersions in CPn and CHn with unfull first normal bundles. Next, it is seen that every Kaehlerian slant submanifold satisfying an equality of Chen is minimal which is similar to that of Lagrangian immersions. But in contrast, it is shown that a large class of slant immersions do not exist thoroughly. Finally, they give an application of Chen’s inequality to general slant immersions in a complex projective space, which generalizes a result of Chen. 展开更多
关键词 Slant immersion IDEAL Chen's inequality complex space form
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MULTIPLE POINTS OF IMMERSIONS OF M^6■R^7
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作者 Mohammad A.Asadi-Golmankhaneh 《Acta Mathematica Scientia》 SCIE CSCD 2011年第1期259-267,共9页
In this article, we determine the multiple point set of immersions of 6-dimensional manifolds into 7-dimensional Euclidean space R7. The method is to evaluate the characteristic numbers of these manifolds. By a certai... In this article, we determine the multiple point set of immersions of 6-dimensional manifolds into 7-dimensional Euclidean space R7. The method is to evaluate the characteristic numbers of these manifolds. By a certain method, these numbers can be read of from the Hurewicz image ofh : π7QMO(1) → H7QMO(1).In particular, we show that for any immersion of P 6 in R7 the double, 4-fold and 6-fold point manifolds are cobordant to boundaries and triple point manifolds cobordant to P 4, 5-fold point manifolds cobordant to P 2 and 7-fold point manifold are odd number. 展开更多
关键词 IMMERSION Hurewicz homomorphism spherical classes Stiefel-Whitney number
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ON MINIMAL IMMERSIONS OF R^2 INTO THE NEARLY KAHLER S^6
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作者 沈一兵 贺群 《Acta Mathematica Scientia》 SCIE CSCD 2004年第3期349-360,共12页
In terms of the almost complex affine connection and moving unitary frames, all totally rael minimal immersions from R-2 into the nearly Kahler S-6 axe determine explicitly. Moreover, the complete flat almost complex ... In terms of the almost complex affine connection and moving unitary frames, all totally rael minimal immersions from R-2 into the nearly Kahler S-6 axe determine explicitly. Moreover, the complete flat almost complex curves in the nearly Kahler S-6 are determined completely. 展开更多
关键词 minimal immersion the nearly Kahler S-6 flat totally real surface
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An MPI parallel DEM-IMB-LBM framework for simulating fluid-solid interaction problems 被引量:2
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作者 Ming Xia Liuhong Deng +3 位作者 Fengqiang Gong Tongming Qu Y.T.Feng Jin Yu 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2024年第6期2219-2231,共13页
The high-resolution DEM-IMB-LBM model can accurately describe pore-scale fluid-solid interactions,but its potential for use in geotechnical engineering analysis has not been fully unleashed due to its prohibitive comp... The high-resolution DEM-IMB-LBM model can accurately describe pore-scale fluid-solid interactions,but its potential for use in geotechnical engineering analysis has not been fully unleashed due to its prohibitive computational costs.To overcome this limitation,a message passing interface(MPI)parallel DEM-IMB-LBM framework is proposed aimed at enhancing computation efficiency.This framework utilises a static domain decomposition scheme,with the entire computation domain being decomposed into multiple subdomains according to predefined processors.A detailed parallel strategy is employed for both contact detection and hydrodynamic force calculation.In particular,a particle ID re-numbering scheme is proposed to handle particle transitions across sub-domain interfaces.Two benchmarks are conducted to validate the accuracy and overall performance of the proposed framework.Subsequently,the framework is applied to simulate scenarios involving multi-particle sedimentation and submarine landslides.The numerical examples effectively demonstrate the robustness and applicability of the MPI parallel DEM-IMB-LBM framework. 展开更多
关键词 Discrete element method(DEM) Lattice Boltzmann method(LBM) Immersed moving boundary(IMB) Multi-cores parallelization Message passing interface(MPI) CPU Submarine landslides
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Comparative Analysis of ARIMA and LSTM Model-Based Anomaly Detection for Unannotated Structural Health Monitoring Data in an Immersed Tunnel
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作者 Qing Ai Hao Tian +4 位作者 Hui Wang Qing Lang Xingchun Huang Xinghong Jiang Qiang Jing 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第5期1797-1827,共31页
Structural Health Monitoring(SHM)systems have become a crucial tool for the operational management of long tunnels.For immersed tunnels exposed to both traffic loads and the effects of the marine environment,efficient... Structural Health Monitoring(SHM)systems have become a crucial tool for the operational management of long tunnels.For immersed tunnels exposed to both traffic loads and the effects of the marine environment,efficiently identifying abnormal conditions from the extensive unannotated SHM data presents a significant challenge.This study proposed amodel-based approach for anomaly detection and conducted validation and comparative analysis of two distinct temporal predictive models using SHM data from a real immersed tunnel.Firstly,a dynamic predictive model-based anomaly detectionmethod is proposed,which utilizes a rolling time window for modeling to achieve dynamic prediction.Leveraging the assumption of temporal data similarity,an interval prediction value deviation was employed to determine the abnormality of the data.Subsequently,dynamic predictive models were constructed based on the Autoregressive Integrated Moving Average(ARIMA)and Long Short-Term Memory(LSTM)models.The hyperparameters of these models were optimized and selected using monitoring data from the immersed tunnel,yielding viable static and dynamic predictive models.Finally,the models were applied within the same segment of SHM data,to validate the effectiveness of the anomaly detection approach based on dynamic predictive modeling.A detailed comparative analysis discusses the discrepancies in temporal anomaly detection between the ARIMA-and LSTM-based models.The results demonstrated that the dynamic predictive modelbased anomaly detection approach was effective for dealing with unannotated SHM data.In a comparison between ARIMA and LSTM,it was found that ARIMA demonstrated higher modeling efficiency,rendering it suitable for short-term predictions.In contrast,the LSTM model exhibited greater capacity to capture long-term performance trends and enhanced early warning capabilities,thereby resulting in superior overall performance. 展开更多
关键词 Anomaly detection dynamic predictive model structural health monitoring immersed tunnel LSTM ARIMA
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Simulation of wave scattering over a floating platform in the ocean with a coupled CFD-IBM model
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作者 Pengxuan Luo Jingxin Zhang +1 位作者 Yongyong Cao Shaohong Song 《Theoretical & Applied Mechanics Letters》 CAS CSCD 2024年第3期157-161,共5页
A numerical study of linear wave scattering over a floating platform has been simulated by an efficient numericalmodel in this letter.The non-hydrostatic model is used to simulate the free surface and the uneven botto... A numerical study of linear wave scattering over a floating platform has been simulated by an efficient numericalmodel in this letter.The non-hydrostatic model is used to simulate the free surface and the uneven bottom.For thesolid body modelling,the immersed boundary method(IBM)is implemented by introducing a virtual boundaryforce into the momentum equations to emulate the boundary conditions.This implementation enhances theability of the model to simulate interactions between waves and floating structures.A numerical case involvingwave interactions with a floating platform is studied to validate the numerical model.By simulating the wavepropagation,the numerical model captures the variation of the wave scattering very well,which verifies theperformance of the numerical model and the robust strategy of the IBM. 展开更多
关键词 Non-hydrostatic model Immersed boundary method Wave structure interaction Floating platform
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A High-Accuracy Curve Boundary Recognition Method Based on the Lattice Boltzmann Method and Immersed Moving Boundary Method
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作者 Jie-Di Weng Yong-Zheng Jiang +2 位作者 Long-Chao Chen Xu Zhang Guan-Yong Zhang 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第9期2533-2557,共25页
Applying numerical simulation technology to investigate fluid-solid interaction involving complex curved bound-aries is vital in aircraft design,ocean,and construction engineering.However,current methods such as Latti... Applying numerical simulation technology to investigate fluid-solid interaction involving complex curved bound-aries is vital in aircraft design,ocean,and construction engineering.However,current methods such as Lattice Boltzmann(LBM)and the immersion boundary method based on solid ratio(IMB)have limitations in identifying custom curved boundaries.Meanwhile,IBM based on velocity correction(IBM-VC)suffers from inaccuracies and numerical instability.Therefore,this study introduces a high-accuracy curve boundary recognition method(IMB-CB),which identifies boundary nodes by moving the search box,and corrects the weighting function in LBM by calculating the solid ratio of the boundary nodes,achieving accurate recognition of custom curve boundaries.In addition,curve boundary image and dot methods are utilized to verify IMB-CB.The findings revealed that IMB-CB can accurately identify the boundary,showing an error of less than 1.8%with 500 lattices.Also,the flow in the custom curve boundary and aerodynamic characteristics of the NACA0012 airfoil are calculated and compared to IBM-VC.Results showed that IMB-CB yields lower lift and drag coefficient errors than IBM-VC,with a 1.45%drag coefficient error.In addition,the characteristic curve of IMB-CB is very stable,whereas that of IBM-VC is not.For the moving boundary problem,LBM-IMB-CB with discrete element method(DEM)is capable of accurately simulating the physical phenomena of multi-moving particle flow in complex curved pipelines.This research proposes a new curve boundary recognition method,which can significantly promote the stability and accuracy of fluid-solid interaction simulations and thus has huge applications in engineering. 展开更多
关键词 Fluid-solid interaction curve boundary recognition method Lattice Boltzmann method immersed moving boundary method
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A Computational Framework for Parachute Inflation Based on Immersed Boundary/Finite Element Approach
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作者 HUANG Yunyao ZHANG Yang +3 位作者 PU Tianmei JIA He WU Shiqing ZHOU Chunhua 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI CSCD 2024年第4期502-514,共13页
A computational framework for parachute inflation is developed based on the immersed boundary/finite element approach within the open-source IBAMR library.The fluid motion is solved by Peskin's diffuse-interface i... A computational framework for parachute inflation is developed based on the immersed boundary/finite element approach within the open-source IBAMR library.The fluid motion is solved by Peskin's diffuse-interface immersed boundary(IB)method,which is attractive for simulating moving-boundary flows with large deformations.The adaptive mesh refinement technique is employed to reduce the computational cost while retain the desired resolution.The dynamic response of the parachute is solved with the finite element approach.The canopy and cables of the parachute system are modeled with the hyperelastic material.A tether force is introduced to impose rigidity constraints for the parachute system.The accuracy and reliability of the present framework is validated by simulating inflation of a constrained square plate.Application of the present framework on several canonical cases further demonstrates its versatility for simulation of parachute inflation. 展开更多
关键词 parachute inflation fluid-structure interaction immersed boundary method finite element method adaptive mesh refinement
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Parallelization strategies for resolved simulations of fluid-structure-particle interactions
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作者 Jianhua QIN Fei LIAO +1 位作者 Guodan DONG Xiaolei YANG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2024年第5期857-872,共16页
Fluid-structure-particle interactions in three spatial dimensions happen in many environmental and engineering flows.This paper presents the parallel algorithms for the hybrid diffuse and sharp interface immersed boun... Fluid-structure-particle interactions in three spatial dimensions happen in many environmental and engineering flows.This paper presents the parallel algorithms for the hybrid diffuse and sharp interface immersed boundary(IB)method developed in our previous work.For the moving structure modeled using the sharp interface IB method,a recursive box method is developed for efficiently classifying the background grid nodes.For the particles modeled using the diffuse interface IB method,a‘master-slave’approach is adopted.For the particle-particle interaction(PPI)and particle-structure interaction(PSI),a fast algorithm for classifying the active and inactive Lagrangian points,which discretize the particle surface,is developed for the‘dry’contact approach.The results show that the proposed recursive box method can reduce the classifying time from 52seconds to 0.3 seconds.Acceptable parallel efficiency is obtained for cases with different particle concentrations.Furthermore,the lubrication model is utilized when a particle approaches a wall,enabling an accurate simulation of the rebounding phenomena in the benchmark particle-wall collision problem.At last,the capability of the proposed computational framework is demonstrated by simulating particle-laden turbulent channel flows with rough walls. 展开更多
关键词 particle-resolved direct numerical simulation particle-laden flow complex geometry resolved fluid-structure-particle interaction(RFSPI) immersed boundary(IB)method
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The Combination of Achnatherum inebrians Extracts and Soil Microorganisms Inhibited Seed Germination and Seedling Growth in Elymus nutans
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作者 Rui Zhang Taixiang Chen +4 位作者 Zhenjiang Chen Hao Chen Xuekai Wei Malik Kamran Chunjie Li 《Phyton-International Journal of Experimental Botany》 SCIE 2024年第3期567-580,共14页
In a greenhouse experiment,the effects of soil microorganisms and extracts of Achnatherum inebrians on the seed germination and seedling growth of Elymus nutans were studied.The results showed that both the extracts f... In a greenhouse experiment,the effects of soil microorganisms and extracts of Achnatherum inebrians on the seed germination and seedling growth of Elymus nutans were studied.The results showed that both the extracts from aboveground and belowground parts of A.inebrians significantly inhibited the germination rate,germination potential,germination index,vigor index,seedling height,root length,and fresh weight of E.nutans,but increased malondialdehyde content,catalase,peroxidase and superoxide dismutase activity of E.nutans seedlings(p<0.05).The allelopathy of aqueous extracts of the aboveground parts of A.inebrians was stronger than that of the pre-cipitates.Aqueous extracts of the aboveground parts of A.inebrians decreased seed germination rate,germination potential,germination index,vigor index,seedling length,root length,and seedling fresh weight by 10.45%-74.63%,24.18%-32.50%,19.03%-73.36%,37.83%-88.41%,21.42%-53.14%,2.65%-40.21%,and 20.45%-61.36%,respectively,and malondialdehyde content,peroxidase,catalase,and superoxide dismutase activity increased by 8.09%-62.24%,27.83%-86.47%,22.90%-93.17%,and 11.15%-75.91%,respectively.The above indexes were higher in live soil than in sterilized soil.Soil microorganisms increased the allelopathy of A.inebrians.The seed germination rate,germination potential,germination index,vigor index,seedling length,and seedling fresh weight of E.nutans planted in live soil decreased by 8.22%-48.48%,10.00%-51.85%,8.19%-53.26%,16.43%-60.03%,12.91%-28.81%,and 9.09%-22.86%compared with sterilized soil,respectively.Malondialdehyde content,peroxidase,catalase,and superoxide dismutase activity of E.nutans planted in live soil increased by 53.91%-81.06%,15.71%-57.34%,33.33%-86.31%,and 9.78%-52.51%compared with sterilized soil,respectively.The existence of soil microorganisms enhanced the allelopathy of the secondary metabolites of A.inebrians.A combination of microorganisms and aqueous extracts from the aboveground parts of A.inebrians had the strongest allelopathic effect on E.nutans. 展开更多
关键词 Achnatherum inebrians water immersion liquid aqueous leachate precipitate ALLELOPATHY Elymus nutans soil microorganisms
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Effects of virtual agents on interaction efficiency and environmental immersion in MR environments
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作者 Yihua BAO Jie GUO +2 位作者 Dongdong WENG Yue LIU Zeyu TIAN 《虚拟现实与智能硬件(中英文)》 EI 2024年第2期169-179,共11页
Background Physical entity interactions in mixed reality(MR)environments aim to harness human capabilities in manipulating physical objects,thereby enhancing virtual environment(VEs)functionality.In MR,a common strate... Background Physical entity interactions in mixed reality(MR)environments aim to harness human capabilities in manipulating physical objects,thereby enhancing virtual environment(VEs)functionality.In MR,a common strategy is to use virtual agents as substitutes for physical entities,balancing interaction efficiency with environmental immersion.However,the impact of virtual agent size and form on interaction performance remains unclear.Methods Two experiments were conducted to explore how virtual agent size and form affect interaction performance,immersion,and preference in MR environments.The first experiment assessed five virtual agent sizes(25%,50%,75%,100%,and 125%of physical size).The second experiment tested four types of frames(no frame,consistent frame,half frame,and surrounding frame)across all agent sizes.Participants,utilizing a head mounted display,performed tasks involving moving cups,typing words,and using a mouse.They completed questionnaires assessing aspects such as the virtual environment effects,interaction effects,collision concerns,and preferences.Results Results from the first experiment revealed that agents matching physical object size produced the best overall performance.The second experiment demonstrated that consistent framing notably enhances interaction accuracy and speed but reduces immersion.To balance efficiency and immersion,frameless agents matching physical object sizes were deemed optimal.Conclusions Virtual agents matching physical entity sizes enhance user experience and interaction performance.Conversely,familiar frames from 2D interfaces detrimentally affect interaction and immersion in virtual spaces.This study provides valuable insights for the future development of MR systems. 展开更多
关键词 Mixed reality Virtual agents Interaction performance Environmental immersion Virtual environments
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Performance Analysis of Plant Shells/PVC Composites under Corrosion and Aging Conditions
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作者 Haoping Yao Xinyu Zhong Chunxia He 《Journal of Renewable Materials》 EI CAS 2024年第5期993-1006,共14页
To make full use of plant shellfibers(rice husk,walnut shell,chestnut shell),three kinds of wood-plastic com-posites of plant shellfibers and polyvinyl chloride(PVC)were prepared.X-ray diffraction analysis was carried o... To make full use of plant shellfibers(rice husk,walnut shell,chestnut shell),three kinds of wood-plastic com-posites of plant shellfibers and polyvinyl chloride(PVC)were prepared.X-ray diffraction analysis was carried out on three kinds of plant shellfibers to test their crystallinity.The aging process of the composites was conducted under 2 different conditions.One was artificial seawater immersion and xenon lamp irradiation,and the other one was deionized water spray and xenon lamp irradiation.The mechanical properties(tensile strength,flexural strength,impact strength),changes in color,water absorption,Fourier transform infrared spectroscopy(FTIR),and microstructures of the composites before and after the two aging experiments were analyzed.The results showed that the chestnut shell had the highest crystallinity,which was 42%.The chestnut shell/PVC composites had the strongest interface bonding,the least internal defects,and the best general mechanical properties among the three composites.Its tensile strength,bending strength and impact strength were 23.81 MPa,34.12 MPa,and 4.32 KJ·m^(-2),respectively.Comparing the two aging conditions,artificial seawater immersion and xenon lamp irradiation destroyed the quality of the combination of plant shellfibers and PVC,making the internal defects of the composites increase.This made the water absorption ability and changes in the color of the composites more obvious and led to a great decrease in the mechanical properties.The general mechanical properties of the chestnut shell/PVC composites were the best,but their water absorption ability changed more obviously. 展开更多
关键词 Plant shellfibers polyvinyl chloride wood-plastic composites artificial seawater immersion deionized water spray xenon lamp irradiation
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Numerical Sensitivity Studies on Effects of Ice Nucleating Processes on Electrification in Thunderstorms
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作者 师正 曲凯悦 +5 位作者 李璐滢 管啸林 孙京 崔雪东 胡佳瑞 吴子珉 《Journal of Tropical Meteorology》 SCIE 2024年第2期149-167,共19页
This study employed numerical simulations to explore the impact of varying ice nucleation processes on the microphysics and electrification within thunderstorm clouds.A two-dimensional cumulus model,incorporating both... This study employed numerical simulations to explore the impact of varying ice nucleation processes on the microphysics and electrification within thunderstorm clouds.A two-dimensional cumulus model,incorporating both noninductive and inductive charge separation schemes,was utilized.The findings revealed that the freezing nucleation mechanism significantly influenced the microphysical development,electrification,and charge structure of thunderstorms.Homogeneous freezing generated a large quantity of small ice crystals near the cloud tops,which were primarily responsible for the development of positive charge regions through a non-inductive charging process.Conversely,heterogeneous freezing resulted in larger ice crystals,enhancing graupel formation and leading to a more rapid and intense charge separation rate of around-15°C.Ice crystals formed heterogeneously and charged negatively during the development stage,resulting in an inverted dipole charge structure.When both immersion and homogeneous freezing processes were considered,the competition between these two distinct freezing processes resulted in reduced cloud water content and weaker electrification.Under conditions of low cloud water content at lower storm levels,graupel particles were negatively charged through non-inductive charging,causing the charge structure to quickly revert to a normal dipole structure. 展开更多
关键词 homogeneous freezing heterogeneous freezing immersion freezing non-inductive charging charge structure
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Numerical Investigation on Thermal Performance of Two-Phase Immersion Cooling Method for High-Power Electronics
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作者 Liqun Zhou Weilin Yang +1 位作者 Chaojie Li Shi Lin 《Frontiers in Heat and Mass Transfer》 EI 2024年第1期157-173,共17页
The power density of electronic components grows continuously,and the subsequent heat accumulation and temperature increase inevitably affect electronic equipment’s stability,reliability and service life.Therefore,ac... The power density of electronic components grows continuously,and the subsequent heat accumulation and temperature increase inevitably affect electronic equipment’s stability,reliability and service life.Therefore,achieving efficient cooling in limited space has become a key problem in updating electronic devices with high performance and high integration.Two-phase immersion is a novel cooling method.The computational fluid dynamics(CFD)method is used to investigate the cooling performance of two-phase immersion cooling on high-power electronics.The two-dimensional CFD model is utilized by the volume of fluid(VOF)method and Reynolds StressModel.Lee’s model was employed to calculate the phase change rate.The heat transfer coefficient along the heatedwalls and the shear-lift force on bubbles are calculated.The simulation data are verified with the literature results.The cooling performance of different coolants has been studied.The results indicate that the boiling heat transfer coefficient can be enhanced by using a low boiling point coolant.The methanol is used as the cooling medium for further research.In addition,the mass flow rate and inlet temperature are investigated to assess the thermal performance of twophase immersion cooling.The average temperature of the high-power electronics is 80℃,and the temperature difference can be constrained to 8℃.Meanwhile,the convective heat transfer coefficient reaches 2740 W/(m2・℃)when the inlet temperature is 50℃,and the mass flow rate is 0.3 kg/s.In conclusion,the results demonstrated that two-phase immersion cooling has provided an effective method for the thermal management of high-power electronics. 展开更多
关键词 Immersion cooling operating condition high-power electronics thermal management
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Integrating Chinese Culture Into Language Curriculum:Teaching Chinese Culture to International Students in China
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作者 ZHANG Wen 《Cultural and Religious Studies》 2024年第3期158-163,共6页
This paper explores the integration of Chinese culture into language education for German students at the University of Shanghai for Science and Technology(USST).Focusing on USST’s Chinese curriculum and pedagogical ... This paper explores the integration of Chinese culture into language education for German students at the University of Shanghai for Science and Technology(USST).Focusing on USST’s Chinese curriculum and pedagogical strategies,the study emphasizes the importance of cultural immersion,experiential learning,and authentic materials.Drawing on Byram’s Intercultural Communicative Competence(ICC)model,the Cultural Studies Approach,and Task-Based Language Teaching(TBLT),the paper presents a case study on incorporating Chinese calligraphy into regular classes.This hands-on approach not only enriches cultural understanding but also enhances language skills.The findings stress the need for tailored,multifaceted pedagogical approaches to prepare international students for cross-cultural interactions in a globalized context. 展开更多
关键词 Chinese culture language education cultural immersion Intercultural Communicative Competence
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CODIMENSION 1 AND 2 IMMERSIONS OF DOLD MANIFOLDS IN COMPLEX PROJECTIVE SPACES
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作者 李贵松 《Systems Science and Mathematical Sciences》 SCIE EI CSCD 1990年第3期286-288,共3页
In this paper the following problem has been completely solved:when is a map f:P(m‘n)→CP<sup>?</sup> homotopic to an immersion with codimension one or
关键词 Dold MANIFOLD COMPLEX PROJECTIVE space CODIMENSION 1 and 2 immersions
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ON EXISTENCE OF HIGHER ORDER IMMERSIONS
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作者 李贵松 《Chinese Science Bulletin》 SCIE EI CAS 1991年第1期12-16,共5页
Ⅰ. INTRODUCTIONThroughout this note, all manifolds are assumed to be smooth and closed. We refer to [1]—[3] for the definitions and basic properties of higher order tangent bundles and pth order nonsingular immersio... Ⅰ. INTRODUCTIONThroughout this note, all manifolds are assumed to be smooth and closed. We refer to [1]—[3] for the definitions and basic properties of higher order tangent bundles and pth order nonsingular immersions (p-immersions). Let M be an n-manifold. We denote 展开更多
关键词 HIGHER order immersions EXISTENCE CODIMENSION n-2.
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Recovery of Immersions from Their Metric Tensors and Nonlinear Korn Inequalities:A Brief Survey
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作者 Philippe G.CIARLET Cristinel MARDARE Sorin MARDARE 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2017年第1期253-280,共28页
The authors discuss the existence and uniqueness up to isometries of Enof immersions φ : Ω  R^n→ E^n with prescribed metric tensor field(g ij) : Ω→ S^n>, and discuss the continuity of the mapping(gij) →φ d... The authors discuss the existence and uniqueness up to isometries of Enof immersions φ : Ω  R^n→ E^n with prescribed metric tensor field(g ij) : Ω→ S^n>, and discuss the continuity of the mapping(gij) →φ defined in this fashion with respect to various topologies. In particular, the case where the function spaces have little regularity is considered. How, in some cases, the continuity of the mapping(gij) →φ can be obtained by means of nonlinear Korn inequalities is shown. 展开更多
关键词 Isometric immersions Nonlinear Korn inequalities Metric tensor
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