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Nonlocal symmetries,soliton-cnoidal wave solution and soliton molecules to a(2+1)-dimensional modified KdV system

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Communications in Theoretical Physics 2024年第4期76卷 14-21页

作者： Jianyong Wang bo ren Department of Mathematics and Physics Quzhou UniversityQuzhou 324000China Department of Mathematics Zhejiang University of TechnologyHangzhou 310014China

A(2+1)-dimensional modified KdV(2DmKdV)system is considered from several ***,residue symmetry,a type of nonlocal symmetry,and the Bäcklund transformation are obtained via the truncated Painlevéexpansion ***,the residue symmetry is localized to a Lie point symmetry of a prolonged system,from which the finite transformation group is ***,the integrability of the 2DmKdV system is examined under the sense of consistent tanh expansion ***,explicit soliton-cnoidal wave solutions are ***,abundant patterns of soliton molecules are presented by imposing the velocity resonance condition on the multiple-soliton solution.

关键词： soliton-cnoidal wave solution nonlocal symmetry soliton molecule (2+1)-dimensional modified KdV system

Phase Transformation and Carbide Precipitation of Functional Gradient Semi-solid 9Cr18 Steel

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Acta Metallurgica Sinica(English Letters) 2018年第8期31卷 823-830页

作者： Yong-Jin Wang ren-bo Song ren-Feng Song School of Materials Science and Engineering University of Science and Technology BeijingBeijing 100083China Institute of Industrial Science The University of TokyoKomaba 4-6-1MeguroTokyo 153-8505Japan Ansteel Mining Engineering Corporation Anshan 114004China

The unique phase transformation and carbide evolution in 9Cr18 steel were investigated during semi-solid forming and subsequent heat treatment. The functional gradient thixoforging 9Cr18 component was divided into inner area and edge area. Microstructure evolution was different at each area. After semi-solid cooling, the solid particles in the inner area were retained as meta-austenite. During annealing, M_（23）C_6 carbide began to precipitate when temperature reached 700 °*** transformation occurred when temperature reached 800 °C. The occurrence of M_（23）C_6 carbide and martensite structure would be harmful to the mechanical properties of inner area. In the edge area, the liquid underwent eutectic transformation to form bar-shape M_7C_3 carbide and secondary austenite after semi-solid cooling. The width of bar-shape carbide would decrease during annealing. By controlling the carbide evolution, we could tailor the functional gradient material with required property.

关键词： Semi-solid forming Solid/liquid phase Annealing Carbide precipitation

A novel method for importance measure analysis in the presence of epistemic and aleatory uncertainties

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Chinese Journal of Aeronautics 2014年第3期27卷 568-576页

作者： ren bo Lu Zhenzhou Zhou Changcong School of Aeronautics Northwestern Polytechnical University

For structural systems with both epistemic and aleatory uncertainties, research on quantifying the contribution of the epistemic and aleatory uncertainties to the failure probability of the systems is conducted. Based on the method of separating epistemic and aleatory uncertainties in a variable, the core idea of the research is firstly to establish a novel deterministic transition model for auxiliary variables, distribution parameters, random variables, failure probability, then to propose the improved importance sampling （IS） to solve the transition model. Furthermore, the distribution parameters and auxiliary variables are sampled simultaneously and independently;therefore, the inefficient sampling procedure with an＇＇inner-loop＇＇ for epistemic uncertainty and an＇＇outer-loop＇＇ for aleatory uncertainty in traditional methods is avoided. Since the proposed method combines the fast convergence of the proper estimates and searches failure samples in the interesting regions with high efficiency, the proposed method is more efficient than traditional methods for the variance-based failure probability sensitivity measures in the presence of epistemic and aleatory uncertainties. Two numerical examples and one engineering example are introduced for demonstrating the efficiency and precision of the proposed method for structural systems with both epistemic and aleatory uncertainties.

关键词： Aleatory uncertainty Epistemic uncertaintyImportance sampling Sensitivity analysis Uncertainty system

A New (2+1)-Dimensional Integrable Equation

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Communications in Theoretical Physics 2009年第1期51卷 13-16页

作者： ren bo LIN Ji Institute of Nonlinear Physics Zhejiang Normal University Jinhua 321004 China Abdus Salam International Centre for Theoretical Physics Trieste 34139 Italy

A new nonlinear partial differential equation （PDE） in 2＋1 dimensions is obtained from the mKP equation by means of an asymptotically exact reduction method based on Fourier expansion and spatio-temporal resealing. In order to demonstrate integrability property of the new equation, the corresponding Lax pair is obtained by applying the reduction technique to the Lax pair of the mKP equation.

关键词： mKP equation asymptotically exact reduction method Lax pair

半导体量子点分子-腔光机械耦合系统中光学双稳及多稳态的形成及调控

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原子与分子物理学报 2025年第5期42卷 115-122页

作者：曾莹任波徐名琪杨红佘彦超吉首大学物理与机电工程学院吉首416000 铜仁学院物理与电子工程系铜仁554300

本研究探讨了外部磁场对半导体量子点分子与腔光机械耦合系统中光学双稳态行为的影响.研究结果显示,外部磁场、量子点之间的隧穿耦合以及探测光单光子的失谐可以有效地调控系统的光学双稳态.在弱隧穿和弱磁场条件下,系统的光学双稳态阈... 详细信息

本研究探讨了外部磁场对半导体量子点分子与腔光机械耦合系统中光学双稳态行为的影响.研究结果显示,外部磁场、量子点之间的隧穿耦合以及探测光单光子的失谐可以有效地调控系统的光学双稳态.在弱隧穿和弱磁场条件下,系统的光学双稳态阈值和磁滞回线宽度随着外部磁场和点间隧穿耦合强度的增加而增大.随着磁场强度和隧穿耦合强度的进一步增加,系统的双稳态将演变为多稳态.有趣的是,在强隧穿和强磁场作用下,系统的光学双稳态阈值和磁滞回线宽度随着外部磁场和点间隧穿耦合强度的增加而减小.这种对耦合腔光机械系统中光学双稳态的灵活调控将在可控光开关方面具有潜在的广泛应用前景.

关键词：双稳态多稳态点间隧穿耦合光力耦合

Real Interpolation between Martingale Hardy and BMO Spaces

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Acta Mathematica Sinica,English Series 2013年第1期29卷 65-74页

作者： Yan bo ren Tie Xin GUO School of Mathematics and Statistics He'nan University of Science and Technology School of Mathematics and Systems Science Beihang University

In this paper, we consider the real interpolation with a function parameter between martingale Hardy and BMO spaces. An interpolation theorem for martingale Hardy and BMO spaces is formulated. As an application, real interpolation between martingale Lorentz and BMO spaces is given. Keywords Martingale space, BMO space, Lorentz space, real interpolation, function parameter

关键词： Martingale space BMO space Lorentz space real interpolation function parameter

A New Characterization of p-Smoothable Banach Spaces

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Acta Mathematica Sinica,English Series 2011年第5期27卷 1005-1010页

作者： Yan bo ren You Liang HOU School of Mathematics and Statistics He 'nan University of Science and Technology Luoyang 471003 P. R. China School of Mathematics and Statistics Wuhan University Wuhan 430072 P. R. China

In this paper an atomic decomposition theorem for Banach-space-valued weak Hardy regular martingale space wpHα^s（X） is given. As an application, p-smoothable Banach spaces are characterized in terms of bounded sublinear operators defined on Banach-space-valued weak Hardy regular martingale space wpHa^s（X）. Keywords Martingale, weak Hardy space, atomic decomposition, p-smoothable Banach space

关键词： Martingale weak Hardy space atomic decomposition p-smoothable Banach space

Dynamic Deformation Behavior of Dual Phase Ferritic-Martensitic Steel at Strain Rates From 10^(-4)to 2000 s^(-1)

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Journal of Iron and Steel Research International 2013年第8期20卷 48-53页

作者： SONG ren-bo DAI Qi-feng School of Materials Science and Engineering University of Science and Technology Beijing

The deformation behavior of the dual phase steel （DP1000 steel） was studied by the quasi-static tensile ex-periment and the dynamic tensile experiment. The experiments were carried out at strain rates ranging from 10^-4 to 2 000 s^-1 at room temperature. Then the stress-strain curves of DP1000 steel in the strain rate range of 10^-4-2000 s^-1 were measured. By introducing the strain rate sensitivity factor m, Zerilli Armstrong model was optimized. The con- stitutive equation parameters which formulate the mechanical behavior of DP1000 steel were fitted based on the John-son-Cook （JC） constitutive model and the optimized Zerilli-Armstrong （ZA） constitutive model, respectively. By comparing indicators of ＂accuracy-of-fit＂, Rz terms, for the two models, the optimized Zerilli-Armstrong constitu-tive model can reflect plastic deformation behavior both at the low and high strain rates more accurately. The reasons why the optimized Zerilli-Armstrong constitutive model is more advantageous than the Johnson Cook model were discussed by using the yield strength and ultimate tensile strength （UTS） versus strain rates, and strain hardening rate versus effective plastic strain analytical methods.

关键词： DP steel dynamic deformation behavior split Hopkinson tensile bar constitutive model strain ratesensitivity

Soliton molecules and the CRE method in the extended mKdV equation

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Communications in Theoretical Physics 2020年第5期72卷 41-45页

作者： bo ren Ji Lin Ping Liu Institute of Nonlinear Science Shaoxing UniversityShaoxing312000China Department of Physics Zhejiang Normal UniversityJinhua321004China College of Electron and Information Engineering University of Electronic Science and Technology of China Zhongshan InstituteZhongshan528402China

The soliton molecules of the(1+1)-dimensional extended modified Korteweg–de Vries(mKdV)system are obtained by a new resonance condition,which is called velocity *** soliton molecule and interaction between a soliton molecule and one-soliton are displayed by selecting suitable *** soliton molecules including the bright and bright soliton,the dark and bright soliton,and the dark and dark soliton are exhibited in figures 1–3,***,the nonlocal symmetry of the extended mKdV equation is derived by the truncated Painlevé*** consistent Riccati expansion(CRE)method is applied to the extended mKdV *** demonstrates that the extended mKdV equation is a CRE solvable system.A nonauto-B?cklund theorem and interaction between one-soliton and cnoidal waves are generated by the CRE method.

关键词： extended mKdV equation soliton molecule CRE method nonlocal symmetry