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A New Method for Solving Nonlinear Partial Differential Equations Based on Liquid Time-Constant Networks

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Journal of Systems Science & Complexity 2024年第2期37卷 480-493页

作者： SUN Jiuyun dong Huanhe fang Yong College of Mathematics and Systems Science Shandong University of Science and TechnologyQingdao 266590China

In this paper,physics-informed liquid networks(PILNs)are proposed based on liquid time-constant networks(LTC)for solving nonlinear partial differential equations(PDEs).In this approach,the network state is controlled via ordinary differential equations(ODEs).The significant advantage is that neurons controlled by ODEs are more expressive compared to simple activation *** addition,the PILNs use difference schemes instead of automatic differentiation to construct the residuals of PDEs,which avoid information loss in the neighborhood of sampling *** this method draws on both the traveling wave method and physics-informed neural networks(PINNs),it has a better physical ***,the KdV equation and the nonlinear Schr¨odinger equation are solved to test the generalization ability of the *** the best of the authors’knowledge,this is the first deep learning method that uses ODEs to simulate the numerical solutions of PDEs.

关键词： Nonlinear partial differential equations numerical solutions physics-informed liquid networks physics-informed neural networks

Equilibria and Stability Analysis of Cohen-Grossberg BAM Neural Networks on Time Scale

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Journal of Systems Science & Complexity 2022年第4期35卷 1348-1373页

作者： LIU Mingshuo fang Yong dong Huanhe College of Mathematics and Systems Science Shandong University of Science and TechnologyQingdao266590China

This paper considers the Cohen-Grossberg BAM neural networks(CG-BAMNNs) on time scale, which can unify and generalize the continuous and discrete systems. First, the criteria for the existence and uniqueness of the equilibrium of CG-BAMNNs are derived on time scale. Then based on that, the authors give the criteria for the stability and estimation of equilibrium of the CG-BAMNNs on time scale. The method proposed in this paper unifies and generalizes the continuous and discrete CGBAMNNs systems, and is applicable to some other neural network systems on time scale with practical meaning. The effectiveness of the proposed criteria for delayed CG-BAMNNs is demonstrated by numerical simulation.

关键词： Cohen-Grossberg BAM neural networks existence numerical simulation stability uniqueness

Comparison of Different Methods for Determining the Imidization Degree of Polyimide Fibers

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Chinese Journal of Polymer Science 2016年第2期34卷 209-220页

作者： Wen-ke Yang fang-fang Liu Guo-min Li En-song Zhang Yan-hu Xue Zhi-xin dong 邱雪鹏姬相玲 State Key Laboratory of Polymer Physics and Chemistry Changchun Institute of Applied Chemistry Chinese Academy of Sciences University of Chinese Academy of Sciences Laboratory of Polymer Composites and Engineering Changchun Institute of Applied Chemistry Chinese Academy of Sciences

In this study, polyimide fibers at different stages of imidization were characterized by TGA, DSC, and FTIR. The imidization degree （ID） calculated by TGA was based on the weight loss of each sample, which was caused by the imidization of residual amic acid groups. The results of TGA showed good regularity with the thermal treatment temperature of the PI fibers. For DSC, the ID was calculated based on the area of endothermal peak of each sample. Compared with TGA, DSC showed a relatively higher value because the endothermal peak was reduced by the exothermic re-formation of polyamic acid which may be partially degraded during thermal treatment. The IDs obtained by the FTIR spectra generally showed poorer regularities than those obtained by both TGA and DSC, especially for the results calculated using the 730 cm^-1 band. Based on the 1350 cm^-1 band, the obtained IDs showed better agreement with the TGA or DSC results. The results obtained by these three methods were compared and analyzed. The ID obtained by TGA showed much more reliability among these three methods.

关键词： Imidization degree Polyimide fibers Polyamic acid Polyimide Characterization.

抗癌灵Ⅰ、Ⅱ号对S_(180)荷瘤小鼠肿瘤抑制作用的研究

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时珍国医国药 2004年第3期15卷 136-137页

作者：谷东方宋维华师晶玉李宝馨哈尔滨医科大学黑龙江哈尔滨150086

目的 :探讨中药抗癌灵、号对 S180 荷瘤小鼠肿瘤的影响。方法 :建立 S180 荷瘤小鼠动物模型 ,采用体内实验方法 ,通过观察给药 14 d的瘤重来考察药物的抗肿瘤效果。结果 :大、中、小剂量抗癌灵 (5.0 g/kg,3 .2 g/kg,2 .0 g/kg)溶液治... 详细信息

目的 :探讨中药抗癌灵、号对 S180 荷瘤小鼠肿瘤的影响。方法 :建立 S180 荷瘤小鼠动物模型 ,采用体内实验方法 ,通过观察给药 14 d的瘤重来考察药物的抗肿瘤效果。结果 :大、中、小剂量抗癌灵 (5.0 g/kg,3 .2 g/kg,2 .0 g/kg)溶液治疗 2周后 ,对小鼠肉瘤 S180 抑瘤率分别为 3 3 .89%～ 53 .62 %和 2 3 .2 8%～ 44.13 % ,且大剂量组疗效更佳 (P<0 .0 1)。结论 :中药抗癌灵 , 号对小鼠肉瘤 S180 的生长具有抑制作用。

关键词：抗癌灵Ⅰ号抗癌灵Ⅱ号抑瘤率 S_(180)荷瘤小鼠抑制肿瘤作用

Correlation Between Energy Transfer Rate and Atomization Energy of Some Trinitro Aromatic Explosive Molecules

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Chinese Journal of Chemical Physics 2008年第3期21卷 250-254页

作者： Su-hong Ge Xin-lu Cheng Zheng-lai Liu Xiang-dong Yang fang-fang dong Department of Physics Hexi University Zhangye 734000 China Institute of Atomic and Molecular Physics Sichuan University Chengdu 610065 China

An assumptive theoretical relationship is suggested to describe the property of molecular atomization energy and energy transfer rate in the initiation of explosions. To investigate the relationship between atomization energy and energy transfer rate, the number of doorway modes of explosives is estimated by the theory of Dlott and Fayer in which the rate is proportional to the number of normal mode vibrations. It was evaluated frequencies of normal mode vibrations of eight molecules by means of density functional theory （DFT） at the b3p86/6-31G（d,p） level. It is found that the number of doorway modes shows a linear correlation to the atomization energies of the molecules, which were also calculated by means of the same method. A mechanism of this correlation is discussed. It is also noted that in those explosives with similar molecular structure and molecular weight, the correlation between the atomization energy and the number of doorway modes is higher.

关键词： Secondary explosive Atomization energy Normal mode vibration Doorway region

复式钢管混凝土墩柱轴压性能及承载力提高分析

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Bottlenecks and Countermeasures of High-Penetration Renewable Energy Development in China

工程力学 2025年第1期42卷 209-222页

作者：张玉芬郝圣旺李栋磊方永坚燕山大学建筑工程与力学学院秦皇岛066099 河北工业大学土木与交通学院天津300401 河北省土木工程绿色建造与智能运维重点实验室秦皇岛066099

为提升矩形钢管混凝土独柱墩的工作性能，在其截面内套异心双圆钢管形成新型复式钢管混凝土墩柱。该文进行了7个墩柱轴压荷载试验，通过对比空钢管柱、矩形墩柱和夹层墩柱分析了新型墩柱的破坏形态、钢管应变发展及承载力和延性差异，... 详细信息

为提升矩形钢管混凝土独柱墩的工作性能，在其截面内套异心双圆钢管形成新型复式钢管混凝土墩柱。该文进行了7个墩柱轴压荷载试验，通过对比空钢管柱、矩形墩柱和夹层墩柱分析了新型墩柱的破坏形态、钢管应变发展及承载力和延性差异，最后利用钢管和混凝土的组合效应原理进行组合墩柱轴压承载力提高分析。研究得出新型复式钢管混凝土墩柱轴压破坏形态为鼓曲破坏，其极限承载力较夹层墩柱提高20%，较矩形墩柱提高22%，延性提高效果更为明显;新型墩柱内、外钢管应变发展充分，说明钢管较好地发挥了竖向承载和横向约束混凝土的能力;根据钢板的正则化宽厚比和屈曲后强度计算得出，内、外钢管在混凝土的支撑下承载力提高15%，混凝土在钢管的约束下承载力提高49%;根据约束组合效应得出，新型墩柱整体承载力提高31%;采用等效套箍系数计算的新型墩柱承载力与试验值绝对误差在4%以内，说明新型复式钢管混凝土墩柱符合钢管混凝土统一理论。研究结果表明，新型复式钢管混凝土墩柱在约束混凝土效应方面明显提高，构件的承载力较高、延性较好，具有较强的工程应用前景。

关键词：新型复式钢管混凝土墩柱轴压性能破坏形态承载力套箍系数

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Engineering 2021年第11期7卷 1611-1622页

作者： Jizhen Liu Qinghua Wang Ziqiu song fang fang State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources North China Electric Power UniversityBeijing 102206China School of Control and Computer Engineering North China Electric Power UniversityBeijing 102206China

China has become the world’s largest producer and consumer of energy,and ranks first in its wind and solar power installation ***,serious wind and solar curtailment in China has significantly hindered the development and utilization of renewable *** address problems in the consumption of renewable energy,this paper analyzes four key factors affecting the capacity of power generated from renewable energy sources:power balance,power regulation performance,transmission capacity,and load *** on these bottlenecks,we propose seven solutions:centralized and distributed development of renewable energy,improving the peak-load regulation flexibility of thermal power,increasing the proportion of gas turbines and pumped-hydropower storage,construction of transmission channels and a flexible smart grid developing demand response and virtual power plants,adopting new energy active support and energy storage,and establishing appropriate policies and market *** Chinese Government and energy authorities have issued a series of policies and measures,and in the past three years,China has had remarkable achievements in the adoption of renewable *** rate of idle wind capacity decreased from 17%in 2016 to 7%in 2018,and that of solar decreased from 10%in 2016 to 3%in 2018.

关键词： Bottlenecks Countermeasures Idle wind and solar power Renewable energy

Design Optimization of Irregular Cellular Structure for Additive Manufacturing

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Chinese Journal of Mechanical Engineering 2017年第5期30卷 1184-1192页

作者： Guo-Hua song Shi-Kai Jing fang-Lei Zhao Ye-dong Wang Hao Xing Jing-Tao Zhou School of Mechanical Engineering Beijing Institute of Technology Key Lab of Contemporary Design and Integrated Manufacturing Technology Ministry of EducationNorthwestern Polytechnical University

Irregularcellular structurehas great potential to be considered in light-weight design field. However, the research on optimizing irregular cellular structures has not yet been reporteddue to the difficulties in their modeling technology. Based on the variable density topology opti- mization theory, an efficient method for optimizing the topology of irregular cellular structures fabricated through additive manufacturing processes is proposed. The pro- posed method utilizes tangent circles to automatically generate the main outline of irregular cellular structure. The topological layoutof each cellstructure is optimized using the relative density informationobtained from the proposed modified SIMP method. A mapping relationship between cell structure and relative densityelement is builtto determine the diameter of each cell structure. The results show that the irregular cellular structure can be optimized with the proposed method. The results of simulation and experimental test are similar for irregular cellular structure, which indicate that the maximum deformation value obtained using the modified Solid Isotropic Microstructures with Penalization （SIMP） approach is lower 5.4× 10-5 mm than that using the SIMP approach under the same under the same external load. The proposed research provides the instruction to design the other irregular cellular structure.

关键词： Irregular cellular structure Additivemanufacturing Topology optimization Relative densitymapping

Design of Lattice Structures Using Local Relative Density Mapping Method

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Chinese Journal of Mechanical Engineering 2018年第5期31卷 110-118页

作者： Guo-Hua song Shi-Kai Jing fang-Lei Zhao Ye-dong Wang Hao Xing Long-Fei Qie Beijing Xinghang Mechanical-electrical Equipment Co.Ltd. Beijing 100074 China School of Mechanical Engineering Beijing Institute of Technology Beijing 100081 China

In order to solve the problem of substantial computational resources of lattice structure during optimization, a local relative density mapping(LRDM) method is proposed. The proposed method uses solid isotropic microstructures with penalization to optimize a model at the macroscopic scale. The local relative density information is obtained from the topology optimization result. The contour lines of an optimized model are extracted using a density contour approach, and the triangular mesh is generated using a mesh generator. A local mapping relationship between the elements’ relative density and the struts’ relative cross?sectional area is established to automatically determine the diameter of each individual strut in the lattice structures. The proposed LRDM method can be applied to local finite element meshes and local density elements, but it is also suitable for global ones. In addition, some cases are con?sidered in order to test the e ectiveness of the LRDM method. The results show that the solution time of the LRDM is lower than the RDM method by approximately 50%. The proposed method provides instructions for the design of more complex lattice structures.

关键词： Lattice structures Local relative density mapping Topology optimization Additive manufacturing