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Ensemble successor representations for task generalization in offline-to-online reinforcement learning

Science China(Information Sciences) 2024年第7期67卷 240-255页

作者： Changhong wang Xudong yU Chenjia BAI qiaosheng ZHANG Zhen wang Space Control and Inertial Technology Research Center Harbin Institute of Technology Shanghai Artificial Intelligence Laboratory Shenzhen Research Institute of Northwestern Polytechnical University School of Cybersecurity Northwestern Polytechnical University

In reinforcement learning(RL), training a policy from scratch with online experiences can be inefficient because of the difficulties in exploration. Recently, offline RL provides a promising solution by giving an initialized offline policy, which can be refined through online interactions. However, existing approaches primarily perform offline and online learning in the same task, without considering the task generalization problem in offline-to-online adaptation. In real-world applications, it is common that we only have an offline dataset from a specific task while aiming for fast online-adaptation for several tasks. To address this problem, our work builds upon the investigation of successor representations for task generalization in online RL and extends the framework to incorporate offline-to-online learning. We demonstrate that the conventional paradigm using successor features cannot effectively utilize offline data and improve the performance for the new task by online fine-tuning. To mitigate this, we introduce a novel methodology that leverages offline data to acquire an ensemble of successor representations and subsequently constructs ensemble q functions. This approach enables robust representation learning from datasets with different coverage and facilitates fast adaption of q functions towards new tasks during the online fine-tuning *** empirical evaluations provide compelling evidence showcasing the superior performance of our method in generalizing to diverse or even unseen tasks.

关键词： offline reinforcement learning online fine-tuning task generalization successor representations ensembles

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Deciphering a Million-Plus RSA Integer with Ultralow Local Field Coefficient h and Coupling Coefficient J of the Ising Model by D-Wave 2000q

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Tsinghua Science and Technology 2024年第3期29卷 874-882页

作者： Chao wang qiaoyun Hu Haonan yao Sumin wang Zhi Pei Joint International Research Laboratory of Specialty Fiber Optics and Advanced Communication Shanghai UniversityShanghai 200444China

This work is the first to determine that a real quantum computer(including generalized and specialized)can decipher million-scale RSA relying solely on quantum algorithms,showing the real attack potential of D-Wave *** influence of different column widths on RSA factorization results is studied on the basis of a multiplication table,and the optimal column method is determined by traversal *** traversal experiment of integer factorization within 10000 shows that the local field and coupling coefficients are 75%–93%lower than the research of Shanghai University in 2020 and more than 85%lower than that of Purdue University in *** low Ising model parameters are crucial to reducing the hardware requirements,prompting factoring 1245407 on the D-Wave 2000q real machine.D-Wave advantage already has more than 5000 qubits and will be expanded to 7000 qubits during 2023–2024,with remarkable improvements in decoherence and *** machine is expected to promote the solution of large-scale combinatorial optimization *** of the contributions of this paper is the discussion of the long-term impact of D-Wave on the development of post-quantum cryptography standards.

关键词： quantum annealing RSA D-Wave 2000q post-quantum cryptography

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顾颉刚的边疆史地研究:个人情爱与民族情感的交汇

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社会科学研究 2024年第2期 173-185页

作者：王晴佳美国罗文大学历史系新泽西州葛拉斯堡罗08028-2235

九一八事变之后,顾颉刚的学术生涯出现了一个新的面向,从之前专注上古历史的考证、辨伪转而从事研究中国的历史疆域和边疆民族。1934年《禹贡半月刊》的出版和禹贡学会的成立,便是一个标志。顾颉刚本人指出此乃中日关系恶化、民族危机... 详细信息

九一八事变之后,顾颉刚的学术生涯出现了一个新的面向,从之前专注上古历史的考证、辨伪转而从事研究中国的历史疆域和边疆民族。1934年《禹贡半月刊》的出版和禹贡学会的成立,便是一个标志。顾颉刚本人指出此乃中日关系恶化、民族危机深重所致,但从他当时留下的日记和书信,又可以看出他之从事边疆史地的研究,与他长期爱慕谭慕愚(又名谭惕吾)有着密切的关系。谭慕愚的爱国热忱和行动是促使顾颉刚学术兴趣转向的重要契机,而且顾颉刚与谭慕愚的来往还间接地影响了顾颉刚的古史研究。探讨顾颉刚、谭慕愚及殷履安(顾颉刚妻子)之间的三角关系不仅呈现了顾颉刚学术生涯中民族情感和个人情爱的交互作用,而且有助于展现五四学人婚恋和情感生活的复杂和多面,为从情感史的角度考察中国近代学术变迁提供了一个实例。

关键词：顾颉刚谭慕愚(谭惕吾) 殷履安《禹贡》和禹贡学会边疆史地情感史

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历史和记忆的分与合:一个观念史的分析

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华中师范大学学报（人文社会科学版） 2024年第1期63卷 111-120页

作者：王晴佳上海外国语大学全球文明史研究所上海200083 美国罗文大学历史系新泽西州08028

随着记忆研究在近年的兴起,中文学界出现了“历史记忆”这一名称,含有将两者等同的意思。与之相对照,历史和记忆在西方学术中一直存在某种张力——史学在西方的诞生与对抗记忆的目的相关,之后历史和记忆长期处于一种分离的关系。以兰克... 详细信息

随着记忆研究在近年的兴起,中文学界出现了“历史记忆”这一名称,含有将两者等同的意思。与之相对照,历史和记忆在西方学术中一直存在某种张力——史学在西方的诞生与对抗记忆的目的相关,之后历史和记忆长期处于一种分离的关系。以兰克为代表的近代科学史学,其理论前提是区别“过去”与“现在”,并从后者的立场考察、重构前者,而记忆则常常将两者混为一体。二战之后,兰克史学面临一系列挑战,记忆研究的兴盛便是其中之一。从莫里斯·阿布瓦赫写作《集体记忆》到皮埃尔·诺拉主编《记忆之场》,西方学者试图用记忆来补充和修正历史研究和书写的传统,改进和扩大历史学的方法和范围,促成其内容的更新和革新。但历史研究和记忆研究在近年的合流,仍没有改变两者之间的根本差异。

关键词：近代史学记忆研究历史记忆《记忆之场》莫里斯·阿布瓦赫皮埃尔·诺拉

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Adaptive learning-based optimal tracking control system design and analysis of a disturbed nonlinear hypersonic vehicle model

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Science China(Technological Sciences) 2024年第6期67卷 1893-1906页

作者： AN Kai wang ZhenGuo HUANG Wei Hypersonic Technology Laboratory National University of Defense TechnologyChangsha410073China

We propose an adaptive learning-based optimal control scheme for height-velocity control models considering model uncertainties and external disturbances of hypersonic winged-cone *** longitudinal nonlinear model is first established and transformed into the control-oriented error equations,and the control scheme is organized by a steady-compensation *** overcome and eliminate the impact of model uncertainties and external disturbances,an adaptive radial basis function neural network(RBFNN)is designed by a q-gradient *** the height-velocity error system with estimated uncertainties into account,the adaptive learning-based optimal tracking control(ALOTC)scheme is proposed by combining the critic-only adaptive dynamic programming(ADP)framework and parameter optimization of system settling ***,a novel weight update law is proposed to satisfy the online iteration requirements,and the algorithm convergence and closedloop stability are discussed by the Lyapunov ***,four simulation cases are provided to prove the effectiveness,accuracy,and robustness of the proposed scheme for the hypersonic longitudinal control system.

关键词： optimal tracking control adaptive dynamic programming RBFNN hypersonic vehicle

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由超拍电子伏特加速器产生的超高能伽马射线气泡

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Science Bulletin 2024年第4期69卷 449-457页

作者： LHAASO Collaboration Zhen Cao Chuandong Gao Cong Li Ruo-yu Liu Ruizhi yang 不详 Key Laboratory of Particle Astrophyics&Experimental Physics Division&Computing Center Institute of High Energy PhysicsChinese Academy of SciencesBeijing 100049China University of Chinese Academy of Sciences Beijing 100049China TIANFU Cosmic Ray Research Center ChengduChina Institute of Frontier and Interdisciplinary Science Shandong UniversityQingdao 266237China School of Astronomy and Space Science Nanjing UniversityNanjing 210023China University of Science and Technology of China Hefei 230026China

We report the detection of aγ-ray bubble spanning at least 100deg2 in ultra-high energy(UHE)up to a few PeV in the direction of the star-forming region Cygnus X,implying the presence super PeVatron(s)accelerating protons to at least 10 PeV.A log-parabola form with the photon indexΓ(E)=(2.71±0.02)+(0.11±0.02)×log10(E/10 TeV)is found fitting the gamma-ray energy spectrum of the bubble *** sources,“hot spots”correlated with very massive molecular clouds,and a quasi-spherical amorphousγ-ray emitter with a sharp central brightening are observed in the *** the core of~0.5°,spatially associating with a region containing massive OB association(Cygnus OB2)and a microquasar(Cygnus X-3),as well as previously reported multi-TeV sources,an enhanced concentration of UHEγ-rays is observed with 2 photons at energies above 1 *** general feature of the bubble,the morphology,and the energy spectrum,are reasonably reproduced by the assumption of a particle accelerator in the core,continuously injecting protons into the ambient medium.

关键词： Cosmic rays γ-rays Interstellar medium Star cluster

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Evidence for particle acceleration approaching PeV energies in the W51 complex

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Science Bulletin 2024年第18期69卷 2833-2841页

作者： LHAASO Collaboration Zhen Cao F.Aharonian Axikegu y.X.Bai y.W.Bao D.Bastieri X.J.Bi y.J.Bi W.Bian A.V.Bukevich q.Cao W.y.Cao Zhe Cao J.Chang J.F.Chang A.M.Chen E.S.Chen H.X.Chen Liang Chen Lin Chen Long Chen M.J.Chen M.L.Chen q.H.Chen S.Chen S.H.Chen S.Z.Chen T.L.Chen y.Chen N.Cheng y.D.Cheng M.y.Cui S.W.Cui X.H.Cui y.D.Cui B.Z.Dai H.L.Dai Z.G.Dai Danzengluobu X.q.Dong K.K.Duan J.H.Fan y.Z.Fan J.Fang J.H.Fang K.Fang C.F.Feng H.Feng L.Feng S.H.Feng X.T.Feng y.Feng y.L.Feng S.Gabici B.Gao C.D.Gao q.Gao W.Gao W.K.Gao M.M.Ge L.S.Geng G.Giacinti G.H.Gong q.B.Gou M.H.Gu F.L.Guo X.L.Guo y.q.Guo y.y.Guo y.A.Han M.Hasan H.H.He H.N.He J.y.He y.He y.K.Hor B.W.Hou C.Hou X.Hou H.B.Hu q.Hu S.C.Hu D.H.Huang T.q.Huang W.J.Huang X.T.Huang X.y.Huang y.Huang X.L.Ji H.y.Jia K.Jia K.Jiang X.W.Jiang Z.J.Jiang M.Jin M.M.Kang I.Karpikov D.Kuleshov K.Kurinov B.B.Li C.M.Li Cheng Li Cong Li D.Li F.Li H.B.Li H.C.Li Jian Li Jie Li K.Li S.D.Li W.L.Li W.L.Li X.R.Li Xin Li y.Z.Li Zhe Li Zhuo Li E.W.Liang y.F.Liang S.J.Lin B.Liu C.Liu D.Liu D.B.Liu H.Liu H.D.Liu J.Liu J.L.Liu M.y.Liu R.y.Liu S.M.Liu W.Liu y.Liu y.N.Liu q.Luo y.Luo H.K.Lv B.q.Ma L.L.Ma X.H.Ma J.R.Mao Z.Min W.Mitthumsiri H.J.Mu y.C.Nan A.Neronov L.J.Ou P.Pattarakijwanich Z.y.Pei J.C.qi M.y.q. B.q.qiao J.J.qin A.Raza D.Ruffolo A.Sáiz M.Saeed D.Semikoz L.Shao O.Shchegolev X.D.Sheng F.W.Shu H.C.Song yu.V.Stenkin V.Stepanov y.Su D.X.Sun q.N.Sun X.N.Sun Z.B.Sun J.Takata P.H.T.Tam q.W.Tang R.Tang Z.B.Tang W.W.Tian C.wang C.B.wang G.W.wang H.G.wang H.H.wang J.C.wang Kai wang Kai wang L.P.wang L.y.wang P.H.wang R.wang W.wang X.G.wang X.y.wang y.wang y.D.wang y.J.wang Z.H.wang Z.X.wang Zhen wang Zheng wang D.M.Wei J.J.Wei y.J.Wei T.Wen C.y.Wu H.R.Wu q.W.Wu S.Wu X.F.Wu y.S.Wu S.q.Xi J.Xia G.M.Xiang D.X.Xiao G.Xiao y.L.Xin y.Xing D.R.Xiong Z.Xiong D.L.Xu R.F.Xu R.X.Xu W.L.Xu L.Xue D.H.yan J.Z.yan T.yan C.W.yang C.y.yang F.yang F.F.yang L.L.yang M.J.yang R.Z.yang W.X.yang y.H.yao Z.G.yao L.q.yin N.yin X.H.you Z.y.you y.H.yu q.yuan H.yue H.D.Zeng T.X.Zeng W.Zeng M.Zha B.B.Zhang F.Zhang H.Zhang 不详 Key Laboratory of Particle Astrophysics&Experimental Physics Division&Computing Center Institute of High Energy PhysicsChinese Academy of SciencesBeijing 100049China University of Chinese Academy of Sciences Beijing 100049China TIANFU Cosmic Ray Research Center ChengduChina Dublin Institute for Advanced Studies 31 Fitzwilliam Place2 DublinIreland Max-Planck-Institut for Nuclear Physics P.O.Box 103980Heidelberg 69029Germany School of Physical Science and Technology&School of Information Science and Technology Southwest Jiaotong UniversityChengdu 610031China School of Astronomy and Space Science Nanjing UniversityNanjing 210023China Center for Astrophysics Guangzhou UniversityGuangzhou 510006China Tsung-Dao Lee Institute&School of Physics and Astronomy Shanghai Jiao Tong UniversityShanghai 200240China Institute for Nuclear Research of Russian Academy of Sciences Moscow 117312Russia Hebei Normal University Shijiazhuang 050024China University of Science and Technology of China Hefei 230026China State Key Laboratory of Particle Detection and Electronics China Key Laboratory of Dark Matter and Space Astronomy&Key Laboratory of Radio Astronomy Purple Mountain ObservatoryChinese Academy of SciencesNanjing 210023China Research Center for Astronomical Computing Zhejiang LaboratoryHangzhou 311121China Key Laboratory for Research in Galaxies and Cosmology Shanghai Astronomical ObservatoryChinese Academy of SciencesShanghai 200030China School of Physics and Astronomy Yunnan UniversityKunming 650091China Key Laboratory of Cosmic Rays(Tibet University) Ministry of EducationLhasa 850000China National Astronomical Observatories Chinese Academy of SciencesBeijing 100101China School of Physics and Astronomy(Zhuhai)&School of Physics(Guangzhou)&Sino-French Institute of Nuclear Engineering and Technology(Zhuhai) Sun Yat-sen UniversityZhuhai 519000&Guangzhou 510275GuangdongChina Institute of Frontier and Interdisciplinary Science Shandong UniversityQingdao 266237China APC UniversitéParis Cité

Theγ-ray emission from the W51 complex is widely acknowledged to be attributed to the interaction between the cosmic rays(CRs)accelerated by the shock of supernova remnant(SNR)W51C and the dense molecular clouds in the adjacent star-forming region,***,the maximum acceleration capability of W51C for CRs remains *** on observations conducted with the Large High Altitude Air Shower Observatory(LHAASO),we report a significant detection ofγrays emanating from the W51 complex,with energies from 2 to 200 *** LHAASO measurements,for the first time,extend theγ-ray emission from the W51 complex beyond 100 TeV and reveal a significant spectrum bending at tens of *** combining the"π^(0)-decay bump"featured data from Fermi-LAT,the broadbandγ-ray spectrum of the W51 region can be well-characterized by a simple pp-collision *** observed spectral bending feature suggests an exponential cutoff at~400 TeV or a power-law break at~200 TeV in the CR proton spectrum,most likely providing the first evidence of SNRs serving as CR accelerators approaching the PeV ***,two young star clusters within W51B could also be theoretically viable to produce the most energeticγrays observed by *** findings strongly support the presence of extreme CR accelerators within the W51 complex and provide new insights into the origin of Galactic CRs.

关键词： UHE c-ray Cosmic rays SNR W51C Star clusters

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Determination of the number ofψ(3686)events taken at BESⅢ

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Chinese Physics C 2024年第9期48卷 8-20页

作者： M.Ablikim M.N.Achasov P.Adlarson O.Afedulidis X.C.Ai R.Aliberti A.Amoroso q.An y.Bai O.Bakina I.Balossino y.Ban H.-R.Bao V.Batozskaya K.Begzsuren N.Berger M.Berlowski M.Bertani D.Bettoni F.Bianchi E.Bianco A.Bortone I.Boyko R.A.Briere A.Brueggemann H.Cai X.Cai A.Calcaterra G.F.Cao N.Cao S.A.Cetin J.F.Chang G.R.Che G.Chelkov C.Chen C.H.Chen Chao Chen G.Chen H.S.Chen H.y.Chen M.L.Chen S.J.Chen S.L.Chen S.M.Chen T.Chen X.R.Chen X.T.Chen y.B.Chen y.q.Chen Z.J.Chen Z.y.Chen S.K.Choi G.Cibinetto F.Cossio J.J.Cui H.L.Dai J.P.Dai A.Dbeyssi R.E.de Boer D.Dedovich C.q.Deng Z.y.Deng A.Denig I.Denysenko M.Destefanis F.De Mori B.Ding X.X.Ding y.Ding y.Ding J.Dong L.y.Dong M.y.Dong X.Dong M.C.Du S.X.Du y.y.Duan Z.H.Duan P.Egorov y.H.Fan J.Fang J.Fang S.S.Fang W.X.Fang y.Fang y.q.Fang R.Farinelli L.Fava F.Feldbauer G.Felici C.q.Feng J.H.Feng y.T.Feng M.Fritsch C.D.Fu J.L.Fu y.W.Fu H.Gao X.B.Gao y.N.Gao yang Gao S.Garbolino I.Garzia L.Ge P.T.Ge Z.W.Ge C.Geng E.M.Gersabeck A.Gilman K.Goetzen L.Gong W.X.Gong W.Gradl S.Gramigna M.Greco M.H.Gu y.T.Gu C.y.Guan Z.L.Guan A.q.Guo L.B.Guo M.J.Guo R.P.Guo y.P.Guo A.Guskov J.Gutierrez K.L.Han T.T.Han F.Hanisch X.q.Hao F.A.Harris K.K.He K.L.He F.H.Heinsius C.H.Heinz y.K.Heng C.Herold T.Holtmann P.C.Hong G.y.Hou X.T.Hou y.R.Hou Z.L.Hou B.y.Hu H.M.Hu J.F.Hu S.L.Hu T.Hu y.Hu G.S.Huang K.X.Huang L.q.Huang X.T.Huang y.P.Huang T.Hussain F.Hölzken N.Hüsken N.in der Wiesche J.Jackson S.Janchiv J.H.Jeong q.Ji q.P.Ji W.Ji X.B.Ji X.L.Ji y.y.Ji X.q.Jia Z.K.Jia D.Jiang H.B.Jiang P.C.Jiang S.S.Jiang T.J.Jiang X.S.Jiang y.Jiang J.B.Jiao J.K.Jiao Z.Jiao S.Jin y.Jin M.q.Jing X.M.Jing T.Johansson S.Kabana N.Kalantar-Nayestanaki X.L.Kang X.S.Kang M.Kavatsyuk B.C.Ke V.Khachatryan A.Khoukaz R.Kiuchi O.B.Kolcu B.Kopf M.Kuessner X.Kui N.Kumar A.Kupsc W.Kühn J.J.Lane P.Larin L.Lavezzi T.T.Lei Z.H.Lei M.Lellmann T.Lenz C.Li C.Li C.H.Li Cheng Li D.M.Li F.Li G.Li H.B.Li H.J.Li H.N.Li Hui Li J.R.Li J.S.Li Ke Li L.J.Li L.K.Li Lei Li M.H.Li P.R.Li q.M.Li q.X.Li R.Li S.X.Li T.Li W.D.Li W.G.Li X.Li X.H.Li X.L.Li X.Z.Li Xi Institute of High Energy Physics Beijing 100049China Beihang University Beijing 100191China Bochum Ruhr-University D-44780BochumGermany Budker Institute of Nuclear Physics SB RAS(BINP) Novosibirsk 630090Russia Carnegie Mellon University PittsburghPennsylvania 15213USA Central China Normal University Wuhan 430079China Central South University Changsha 410083China China Center of Advanced Science and Technology Beijing 100190China China University of Geosciences Wuhan 430074China Chung-Ang University Seoul06974Republic of Korea COMSATS University Islamabad Lahore CampusDefence RoadOff Raiwind Road54000LahorePakistan Fudan University Shanghai 200433China GSI Helmholtzcentre for Heavy Ion Research GmbH D-64291DarmstadtGermany Guangxi Normal University Guilin 541004China Guangxi University Nanning 530004China Hangzhou Normal University Hangzhou 310036China Hebei University Baoding 071002China Helmholtz Institute Mainz Staudinger Weg 18D-55099MainzGermany Henan Normal University Xinxiang 453007China Henan University Kaifeng 475004China Henan University of Science and Technology Luoyang 471003China Henan University of Technology Zhengzhou 450001China Huangshan College Huangshan 245000China Hunan Normal University Changsha 410081China Hunan University Changsha 410082China Indian Institute of Technology Madras Chennai 600036India Indiana University BloomingtonIndiana 47405USA INFN Laboratori Nazionali di Frascati (A)INFN Laboratori Nazionali di FrascatiI-00044FrascatiItaly(B)INFN Sezione di PerugiaI-06100PerugiaItaly(C)University of PerugiaI-06100PerugiaItaly INFN Sezione di Ferrara (A)INFN Sezione di FerraraI-44122FerraraItaly(B)University of FerraraI-44122FerraraItaly Inner Mongolia University Hohhot 010021China Institute of Modern Physics Lanzhou 730000China Institute of Physics and Technology Peace Avenue 54BUlaanbaatar 13330Mongolia Instituto de Alta Investigación Universidad de TarapacáCasilla 7DArica 1000000Chile Jilin University Changchun 130012China Joha

The number ofψ(3686)events collected by the BESⅢdetector during the 2021 run period is determined to be(2259.3±11.1)×10~6 by counting inclusiveψ(3686)hadronic *** uncertainty is systematic and the statistical uncertainty is ***,the numbers ofψ(3686)events collected during the 2009 and 2012run periods are updated to be(107.7±0.6)×10~6 and(345.4±2.6)×10~6,*** numbers are consistent with the previous measurements within one standard *** total number ofψ(3686)events in the three data samples is(2712.4±14.3)×10~6.

关键词： ψ(3686) inclusive process Hadronic events BESⅢdetector

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Microstructured Cantilever Probe on Optical Fiber Tip for Microforce Sensor

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Photonic Sensors 2024年第2期14卷 89-99页

作者： Famei wang Changrui LIAO Mengqiang ZOU Dejun LIU Haoqiang HUANG Chao LIU yiping wang Shenzhen Key Laboratory of Ultrafast Laser Micro/Nano Manufacturing Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education/Guangdong ProvinceCollege of Physics and Optoelectronic EngineeringShenzhen UniversityShenzhen 518060China Shenzhen Key Laboratory of Photonic Devices and Sensing Systems for Internet of Things Guangdong and Hong Kong Joint Research Centre for Optical Fibre SensorsState Key Laboratory of Radio Frequency Heterogeneous IntegrationShenzhen UniversityShenzhen 518060China School of Electronics Science Northeast Petroleum UniversityDaqing 163318China

Benefiting from the great advances of the femtosecond laser two-photon polymerization(TPP)technology,customized microcantilever probes can be accurately 3-dimensional(3D)manufactured at the nanoscale size and thus have exhibited considerable potentials in the fields of microforce,micro-vibration,and microforce *** this work,a controllable microstructured cantilever probe on an optical fiber tip for microforce detection is demonstrated both theoretically and *** static performances of the probe are firstly investigated based on the finite element method(FEM),which provides the basis for the structural *** proposed cantilever probe is then 3D printed by means of the TPP *** experimental results show that the elastic constant k of the proposed cantilever probe can be actively tuned from 2.46N/m to 62.35N/*** force sensitivity is 2.5nm/μN,the q-factor is 368.93,and the detection limit is ***,the mechanical properties of the cantilever probe can be flexibly adjusted by the geometric configuration of the ***,it has an enormous potential for matching the mechanical properties of biological samples in the direct contact mode.

关键词： Optical fiber sensor microforce sensing microstructured cantilever two-photon polymerization

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Point defects in 2-D liquid crystals with a singular potential:Profiles and stability

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Science China Mathematics 2024年第11期67卷 2515-2540页

作者： Zhiyuan Geng Wei wang Basque Center for Applied Mathematics School of Mathematical Sciences Zhejiang University

We study radial symmetric point defects with degree k/2 in the 2-D disk or R2in the q-tensor framework with a singular bulk energy,which is defined by Bingham ***,we obtain the existence of solutions for the profiles of radial symmetric point defects with degree k/2 in the 2-D disk or ***,we prove that the solution is stable for |k| = 1 and unstable for |k| > *** identities are derived and utilized throughout the proof of existence and stability/instability.

关键词： radial symmetric point defects singular bulk potential Bingham closure stability

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