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Liouville Type Results for a p-Laplace Equation with Negative Exponent

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Acta Mathematica Sinica,English Series 2016年第12期32卷 1515-1540页

作者： Zong ming guo Lin Feng MEI Department of Mathematics He'nan Normal University

Positive entire solutions of the equation where 1 〈 p ≤ N, q 〉 0, are classified via their Morse indices. It is seen that there is a critical power q = qc such that this equation has no positive radial entire solution that has finite Morse index when q 〉 qc but it admits a family of stable positive radial entire solutions when 0 〈 q ≤ qc- Proof of the stability of positive radial entire solutions of the equation when 1 〈 p 〈 2 and 0 〈 q ≤ qc relies on Caffarelli-Kohn Nirenberg＇s inequality. Similar Liouville type result still holds for general positive entire solutions when 2 〈 p ≤ N and q 〉 qc. The case of 1 〈 p 〈 2 is still open. Our main results imply that the structure of positive entire solutions of the equation is similar to that of the equation with p = 2 obtained previously. Some new ideas are introduced to overcome the technical difficulties arising from the p-Laplace operator.

关键词： Positive entire solutions p-Laplacian morse index negative exponent critical value,liouville type results

Transition-layer Solutions of Quasilinear Elliptic Boundary Blow-up Problems and Dirichlet Problems

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Acta Mathematica Sinica,English Series 2011年第11期27卷 2177-2190页

作者： Zong ming guo Yao Yong YAN Department of Mathematics He＇nan Normal University Xinxiang 453007 P. R. China

We study profiles of positive solutions for quasilinear elliptic boundary blow-up problems and Dirichlet problems with the same equation：where ω 〉 0, a（x） is a continuous function satisfying 0 〈 a（x）〈 1 for x ∈Ω, Ω is a bounded smooth domain in R^N. We will see that the profile of a minimal positive boundary blow-up solution of the equation shares some similarities to the profile of a positive minimizer solution of the equation with homogeneous Dirichlet boundary condition.

关键词： Quasilinear elliptic boundary blow-up problems quasilinear elliptic Dirichlet problems transition-layer solutions minimizer solutions

Generation of multiphoton quantum states on silicon

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Light(Science & Applications) 2019年第1期8卷 811-817页

作者： ming Zhang Lan-Tian Feng Zhi-Yuan Zhou Yang Chen Hao Wu ming Li Shi-ming Gao guo-Ping guo Guang-Can guo Dao-Xin Dai Xi-Feng Ren State Key Laboratory for Modern Optical Instrumentation Centre for Optical and Electromagnetic ResearchZhejiang Provincial Key Laboratory for Sensing TechnologiesCollege of Optical Science and EngineeringZhejiang UniversityZijingang CampusHangzhou 310058China Ningbo Research Institute Zhejiang UniversityNingbo 315100China Key Laboratory of Quantum Information CASUniversity of Science and Technology of ChinaHefeiAnhui 230026China Synergetic Innovation Center of Quantum Information&Quantum Physics University of Science and Technology of ChinaHefeiAnhui 230026China

Multiphoton quantum states play a critical role in emerging quantum technologies and greatly improve our fundamental understanding of the quantum *** photonics is well recognized as an attractive technology offering great promise for the generation of photonic quantum states with high-brightness,tunability,stability,and ***,we demonstrate the generation of multiphoton quantum states using a single-silicon nanophotonic *** detected four-photon rate reaches 0.34 Hz even with a low-pump power of 600μ*** multiphoton quantum state is also qualified with multiphoton quantum interference,as well as quantum state *** the generated four-photon states,the quantum interference visibilities are greater than 95%,and the fidelity is 0.78±***,such a multiphoton quantum source is fully compatible with the on-chip processes of quantum manipulation,as well as quantum detection,which is helpful for the realization of large-scale quantum photonic integrated circuits(QPICs)and shows great potential for research in the area of multiphoton quantum science.

关键词： quantum multiphoton realization

Laser-induced microjet-assisted ablation for high-quality microfabrication

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International Journal of Extreme Manufacturing 2022年第3期4卷 122-130页

作者： Yang guo Pei Qiu Shaolin Xu gary J Cheng School of Mechatronics Engineering Harbin Institute of TechnologyHarbin 150001People’s Republic of China Department of Mechanical and Energy Engineering Southern University of Science and TechnologyShenzhen 518055People’s Republic of China School of Industrial Engineering Purdue UniversityWest LafayetteIN 47906United States of America

Liquid-assisted laser ablation has the advantage of relieving thermal effects of common laser ablation processes, whereas the light scattering and shielding effects by laser-induced cavitation bubbles, suspended debris, and turbulent liquid flow generally deteriorate laser beam transmission stability, leading to low energy efficiency and poor surface quality. Here, we report that a continuous and directional high-speed microjet will form in the laser ablation zone if laser-induced primary cavitation bubbles asymmetrically collapse sequentially near the air-liquid interface under a critical thin liquid layer. The laser-induced microjet can instantaneously and directionally remove secondary bubbles and ablation debris around the laser ablation region, and thus a very stable material removal process can be obtained. The shadowgraphs of high-speed camera reveal that the average speed of laser-induced continuous microjet can be as high as 1.1 m sin its initial 500 μm displacement. The coupling effect of laser ablation, mechanical impact along with the collapse of cavitation bubbles and flushing of high-speed microjet helps achieve a high material removal rate and significantly improved surface quality. We name this uncovered liquid-assisted laser ablation process as laser-induced microjet-assisted ablation(LIMJAA) based on its unique characteristics. High-quality microgrooves with a large depth-to-width ratio of 5.2 are obtained by LIMJAA with a single-pass laser scanning process in our experiments. LIMJAA is capable of machining various types of difficult-to-process materials with high-quality arrays of micro-channels, square and circle microscale through-holes. The results and disclosed mechanisms in our work provide a deep understanding of the role of laser-induced microjet in improving the processing quality of liquid-assisted laser micromachining.

关键词： liquid-assisted laser ablation laser-induced microjet cavitation bubbles laser microfabrication

Improvement of proof-ultimate strength difference in laser additive manufactured Ti-6Al-2V-1.5Mo-0.5Zr-0.3Si alloy by tuning basketweave structure

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Journal of Iron and Steel Research International 2019年第6期26卷 631-636页

作者： guo-chao Li Xu Cheng Hua-ming Wang National Engineering Laboratory of Additive Manufacturing for Large Metallic Components and Engineering Research Center of Ministry of Education on Laser Direct Manufacturing for Large Metallic Components School of Materials Science and Engineering Beihang University Beijing 100191 China Beijing Yuding Additive Manufacturing Research Institute Co. Ltd. Beijing 102206 China

After annealed at 1000 ℃, a special basket-weave structure is obtained in laser additive manufactured Ti-6Al-2V-1.5Mo- 0.5Zr-0.3Si alloy. The unit of the special basket-weave structure is a lamellas clusters, which consist of lamellar primary ot (otp), crab-like structures at the edges of otp and lamellar secondary a (as) on both sides of otp. As the units of basket-weave structures, the width of the clusters is much larger than that of a lamellas in as-deposited alloy. The formation temperature and process of the special basket-weave structure are studied, and the room temperature properties are tested and compared with the as-deposited alloy. The results show that the formation of the special basket-weave structure finishes within about 30 s and crab-like structures form earlier than lamellar as. The yield strength of the alloy is decreased by about 75 MPa compared to that of the as-deposited alloy. Besides, the proof-ultimate strength difference of the alloy is two times higher than that of the as-deposited alloy with about 34% improvement for the impact toughness. It is because ot colony size shows a positive correlation to the width of the unit forming basket-weave structure. The enhancement in proof-ultimate strengthdifference could significantly improve the toughness of the alloy, and thus effectively increase the safety of the alloy.

关键词： Titanium alloy Basket-weave structure Formation process a colony size Yield strength

Burr formation mechanism and morphological transformation critical conditions in grinding of nickel-based superalloy honeycomb cores

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Chinese Journal of Aeronautics 2023年第11期36卷 434-451页

作者： Haihang WANG Jie CHEN Chenguang WANG guoqiang guo Qinglong AN Weiwei ming ming CHEN State Key Laboratory of Mechanical System and Vibration School of Mechanical EngineeringShanghai Jiao Tong UniversityShanghai 200240China AVIC Chengdu Aircraft Industrial(Group)Co. Ltd.Chengdu 610092China Shanghai Spaceflight Precision Machinery Institute Shanghai 201600China

Nickel-based Superalloy Honeycomb(NBSH) is widely used in aerospace field due to the high temperature resistance, high specific strength and light weight. However, the NBSH is extremely prone to form burrs during processing. The unreasonable burr morphology causes insufficient welding strength or false welding between NBSH and skin, resulting in premature failure of the parts. Hence, the burr formation mechanism and morphological transformation critical conditions in grinding NBSH were investigated based on finite element method(FEM) and experiments. Furthermore, the orthogonal experiments were carried out to investigate the effects of grinding parameters on burr and obtain the suitable parameter intervals to restrain the flash burr formation. The results indicate that due to the absence of supporting material, the extruded material of edge transforms into the Fourth Deformation Zone(FDZ). The FDZ rotates a certain angle due to the extrusion of abrasive particle, which leads to the fact that the FDZ cannot be removed and remains on the honeycomb wall, thus forming micro burr. If the material removal per unit time is large, the chip is not removed from FDZ. The parts that should have been chips are bonded with micro burr to form a flash burr. To restrain the flash burr formation, the suitable intervals of grinding depth,grinding speed and feed speed are 5–15 μm, 60–70 m/min and 500–1000 mm/min, respectively.

关键词： Burr Grinding Honeycomb Mechanism Nickel-based superalloy

FOURIER-CHEBYSHEV PSEUDOSPECTRAL METHOD FOR THREE-DIMENSIONAL VORTICITY EQUATION

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Journal of Computational Mathematics 1998年第5期16卷 417-436页

作者： Li, Jian guo, Ben-yu Cao, Wei-ming Chinese Acad Sci ICMSEC State Key Lab Sci & Engn Comp Beijing 100080 Peoples R China Shanghai Univ Dept Math Shanghai 201800 Peoples R China

In this paper, a Fourier-Chebyshev pseudospectral scheme with mixed filtering is proposed for three-dimensional vorticity equation. The generalized stability and convergence are proved. The numerical results show the ... 详细信息

关键词： Pseudospectral method vorticity equation error estimates

A spherical cavity expansion model for penetration of ogival-nosed projectiles into concrete targets with shear-dilatancy

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Acta Mechanica Sinica 2011年第6期27卷 1001-1012页

作者： Tao He He-ming Wen Xiao-Jun guo CAS Key Laboratory for Mechanical Behavior and Design of Materials University of Science and Technology of China 230027 Hefei China

A dynamic spherical cavity-expansion penetration model is suggested herein to predict the penetration and perforation of concrete targets struck normally by ogivalnosed *** dilatancy as well as compressibility of the material in comminuted region are considered in the paper by introducing a dilatant-kinematic relation.A procedure is first presented to compute the radial stress at the cavity surface and then a numerical method is used to calculate the results of penetration and perforation with friction being taken into *** influences of various target parameters such as shear strength,bulk modulus,density,Poisson＇s ratio and tensile strength on the depth of penetration are *** is shown that the model predictions are in good agreement with available experimental *** is also shown that the shear strength plays a dominant role in the target resistance to penetration.

关键词： Spherical cavity expansion Shear dilatancy Ogival-nosed projectile Concrete target Penetration Perforation

Semiconductor quantum computation

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National Science Review 2019年第1期6卷 32-54页

作者： Xin Zhang Hai-Ou Li Gang Cao ming Xiao Guang-Can guo guo-Ping guo Key Laboratory of Quantum Information CAS University of Science and Technology of China Synergetic Innovation Center of Quantum Information & Quantum Physics University of Science and Technology of China

Semiconductors, a significant type of material in the information era, are becoming more and more powerful in the field of quantum information. In recent decades, semiconductor quantum computation was investigated thoroughly across the world and developed with a dramatically fast speed. The research varied from initialization, control and readout of qubits, to the architecture of fault-tolerant quantum ***, we first introduce the basic ideas for quantum computing, and then discuss the developments of single-and two-qubit gate control in semiconductors. Up to now, the qubit initialization, control and readout can be realized with relatively high fidelity and a programmable two-qubit quantum processor has even been demonstrated. However, to further improve the qubit quality and scale it up, there are still some challenges to resolve such as the improvement of the readout method, material development and scalable designs. We discuss these issues and introduce the forefronts of progress. Finally, considering the positive trend of the research on semiconductor quantum devices and recent theoretical work on the applications of quantum computation, we anticipate that semiconductor quantum computation may develop fast and will have a huge impact on our lives in the near future.

关键词： semiconductor quantum dot qubit quantum computation spin manipulation