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Soliton resolution and asymptotic stability of N-solutions for the defocusing Kundu–Eckhaus equation with nonzero boundary conditions

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Communications in Theoretical Physics 2024年第1期76卷 1-6页

作者： Engui Fan Yanxi Zhang School of Mathematical sciences and Key laboratory of mathematics for nonlinear science Fudan UniversityShanghai200433China Tianjin Xinhua High School No.99 machang RoadTianjin300204China

In this paper,we address interesting soliton resolution,asymptotic stability of N-soliton solutions and the Painleve asymptotics for the Kundu-Eckhaus(KE)equation with nonzero boundary conditions iq_(t)+q_(xx)-2(l|q|^(2)-1)q+4β^(2)(lql^(4)-1)q+4iβ(lql^(2))_(x)q=0,q(x,0)=q_(0)(x)-±1,x→±∞.The key to proving these results is to establish the formulation of a Riemann-Hilbert(RH)problem associated with the above Cauchy problem and find its connection with the RH problem of the defocusing NLS *** the■-steepest descent method and the results of the defocusing NLS equation,we find complete leading order approximation formulas for the defocusing KE equation on the whole(x,t)half-plane including soliton resolution and asymptotic stability of N-soliton solutions in a solitonic region,Zakharov-Shabat asymptotics in a solitonless region and the Painlevéasymptotics in two transition regions.

关键词： defocusing Kundu-Eckhaus equation Riemann-Hilbert problems steepest descent method soliton resolution asymptotic stability Painleve transcendents

Q-homotopy analysis method for time-fractional Newell–Whitehead equation and time-fractional generalized Hirota–Satsuma coupled KdV system

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Communications in Theoretical Physics 2024年第3期76卷 70-83页

作者： Di Liu Qiongya Gu Lizhen Wang Center for nonlinear Studies School of MathematicsNorthwest UniversityXi'an710127China

In this paper,two types of fractional nonlinear equations in Caputo sense,time-fractional Newell–Whitehead equation(FNWE)and time-fractional generalized Hirota–Satsuma coupled KdV system(HS-cKdVS),are investigated by means of the q-homotopy analysis method(q-HAM).The approximate solutions of the proposed equations are constructed in the form of a convergent series and are compared with the corresponding exact *** to the presence of the auxiliary parameter h in this method,just a few terms of the series solution are required in order to obtain better *** the sake of visualization,the numerical results obtained in this paper are graphically displayed with the help of Maple.

关键词： fractional Newell-Whitehead equation fractional generalized Hirota-Satsuma coupled KdV system approximate solution q-homotopy analysis method

Ultra-wide band gap and wave attenuation mechanism of a novel star-shaped chiral metamaterial

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Applied mathematics and Mechanics(English Edition) 2024年第7期45卷 1261-1278页

作者： Shuo WANG Anshuai WANG Yansen WU Xiaofeng LI Yongtao SUN Zhaozhan ZHANG Qian DING G.D.AYALEW Yunxiang MA Qingyu LIN Department of Mechanics Tianjin University Tianjin Key laboratory of nonlinear Dynamics and Control Tianjin University State Key laboratory of Metastable Materials science and Technology Yanshan University

A novel hollow star-shaped chiral metamaterial(SCM) is proposed by incorporating chiral structural properties into the standard hollow star-shaped metamaterial, exhibiting a wide band gap over 1 500 Hz. To broaden the band gap,solid single-phase and two-phase SCMs are designed and simulated, which produce two ultra-wide band gaps(approximately 5 116 Hz and 6 027 Hz, respectively). The main reason for the formation of the ultra-wide band gap is that the rotational vibration of the concave star of two novel SCMs drains the energy of an elastic wave. The impacts of the concave angle of a single-phase SCM and the resonator radius of a two-phase SCM on the band gaps are studied. Decreasing the concave angle leads to an increase in the width of the widest band gap, and the width of the widest band gap increases as the resonator radius of the two-phase SCM increases. Additionally,the study on elastic wave propagation characteristics involves analyzing frequency dispersion surfaces, wave propagation directions, group velocities, and phase velocities. Ultimately, the analysis focuses on the transmission properties of finite periodic structures. The solid single-phase SCM achieves a maximum vibration attenuation over 800, while the width of the band gap is smaller than that of the two-phase SCM. Both metamaterials exhibit high vibration attenuation capabilities, which can be used in wideband vibration reduction to satisfy the requirement of ultra-wide frequencies.

关键词： metamaterial ultra-wide band gap wave propagation vibration suppression O421 + .5 74H45

Time-dependent Global Attractors for the Nonclassical Diffusion Equations with Fading Memory

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Acta Mathematicae Applicatae Sinica 2024年

作者： Yu-ming QIN Xiao-ling CHEN Department of mathematics Donghua University Department of mathematics Institute for Nonlinear Science Donghua University

In this paper, we discuss the long-time behavior of solutions to the nonclassical diffusion equation with fading memory when the nonlinear term f satisfies critical exponential growth and the external force g(x)∈L2(Ω). In the framework of time-dependent spaces, we verify the existence of absorbing sets and the asymptotic compactness of the process, then we obtain the existence of the time-dependent global attractor A={At}t∈Rin Mt. Furthermore, we achieve the regularity of A, that is, Atis bounded in Mt1with a bound independent of t.

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Prediction of chemical short-range order in high-/medium-entropy alloys

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Journal of Materials science & Technology 2024年第2期169卷 115-123页

作者： Pei-Yu Cao Jing Wang Ping Jiang Yun-Jiang Wang Fu-Ping Yuan Xiao-Lei Wu State Key laboratory of nonlinear Mechanics Institute of MechanicsChinese Academy of ScienceBeijing 100190China School of Engineering science University of Chinese Academy of SciencesBeijing 100049China

Chemical short-range orders(CSROs),as the built-in sub-nanoscale entities in a high-/medium-entropy alloy(H/MEA),have aroused an ever-increasing *** multi-principal elements in an H/MEA to form a complex concentrated solution,a variety of sub-systems of species exist to induce the metastable ordered compounds as candidates for ultimate *** issues remain pending on the origin of CSROs as to how to judge if CSRO will form in an H/MEA and particularly,what kind of CSROs would be stably produced if there were multiple ***,the first-principles method,along with the proposed local formation energy calculation in allusion to the atomic-scale chemical heterogeneities,is used to predict the CSRO formation based on the mechanical stability,thermodynamic formation energy,and electronic *** simulations are detailed in an equiatomic ternary VCoNi MEA with three kinds of potential compounds,i.e.,L1_(1),L1_(2),and B2,in the face-centered cubic *** turns out that L1_(1)is stable but hard to grow up so as to become the final CSRO.L1_(1)is further predicted as CSROs in CrCoNi,but unable to form in FeCoNi and CrMnFeCoNi *** predictions are consistent with the experimental *** findings shed light on understanding the formation of *** method is applicable to other H/MEAs to design and tailor CSROs by tuning chemical species/contents and thermal processing for high performance.

关键词： Short-range order High-entropy alloy Microstructure First-principles calculation Gibbs free energy Local electronic density of states

Discontinuous phase diagram of amorphous carbons

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National science Review 2024年第4期11卷 164-171页

作者： YinBo Zhu ZhouYu Fang ZhongTing Zhang HengAn Wu CAS Key laboratory of Mechanical Behavior and Design of Materials Department of Modern MechanicsUniversity of Science and Technology of China State Key laboratory of nonlinear Mechanics Institute of Mechanics Chinese Academy of Sciences

The short-range order and medium-range order of amorphous carbons demonstrated in experiments allow us to rethink whether there exist intrinsic properties hidden by atomic disordering. Here we presented six representative phases of amorphous carbons（0.1–3.4 g/cm3）, namely, disordered graphene network（DGN）, high-density amorphous carbon（HDAC）, amorphous diaphite（a-DG）, amorphous diamond（a-D）, paracrystalline diamond（p-D）, and nano-polycrystalline diamond（NPD）, respectively, classified by their topological features and microstructural characterizations that are comparable with experiments. To achieve a comprehensive physical landscape for amorphous carbons, a phase diagram was plotted in the sp3/sp2versus density plane, in which the counterintuitive discontinuity originates from the inherent difference in topological microstructures, further guiding us to discover a variety of phase transitions among different amorphous carbons. Intriguingly, the power law, log（sp3/sp2） ∝ ρn, hints at intrinsic topology and hidden order in amorphous carbons, providing an insightful perspective to reacquaint atomic disorder in non-crystalline carbons.

关键词： amorphous carbons disordered carbons phase diagram microstructural topology phase transition

Long-time asymptotic behavior for the nonlocal nonlinear Schro¨dinger equation in the solitonic region

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science China mathematics 2024年

作者： Gaozhan Li Yiling Yang Engui Fan School of Mathematical sciences and Key laboratory of mathematics for nonlinear sciences Fudan University

In this paper, we extend the ■-steepest descent method to study the Cauchy problem for the nonlocal nonlinear Schr?dinger（NNLS） equation with weighted Sobolev initial data iqt+qxx+2σ■2（x, t）q（-x, t） = 0,q（x, 0） = q0（x）,where q0∈ H1,1（R）. Based on the spectral analysis of the Lax pair, the solution of the Cauchy problem is expressed in terms of the solution of a Riemann-Hilbert problem, which is transformed into a solvable model after a series of deformations. We further obtain the asymptotic expansion of the solution to the Cauchy problem for the NNLS equation in the solitonic region. The leading term is soliton solutions, the second term is the interaction between solitons and dispersion, and the error term comes from a corresponding?ˉ-*** with the asymptotic results on the classical NLS equation, the major difference is the second and third terms of the asymptotic expansion for the NNLS equation, which were affected by a function depending on the scattering data and the stationary phase point.

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A vibration isolator with a controllable quasi-zero stiffness region based on nonlinear force design

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Applied mathematics and Mechanics(English Edition) 2024年第8期45卷 1279-1294页

作者： Xinyu LIAN Bing LIU Huaxia DENG Xinglong GONG CAS Key laboratory of Mechanical Behavior and Design of Materials Department of Modern Mechanics University of Science and Technology of China State Key laboratory of nonlinear Mechanics Institute of MechanicsChinese Academy of Sciences State Key laboratory of Fire science University of Science and Technology of China

To achieve stability optimization in low-frequency vibration control for precision instruments, this paper presents a quasi-zero stiffness(QZS) vibration isolator with adjustable nonlinear stiffness. Additionally, the stress-magnetism coupling model is established through meticulous theoretical derivation. The controllable QZS interval is constructed via parameter design and magnetic control, effectively segregating the high static stiffness bearing section from the QZS vibration isolation section. Furthermore, a displacement control scheme utilizing a magnetic force is proposed to regulate entry into the QZS working range for the vibration isolation platform. Experimental results demonstrate that the operation within this QZS region reduces the peak-to-peak acceleration signal by approximately 66.7% compared with the operation outside this region, thereby significantly improving the low frequency performance of the QZS vibration isolator.

关键词： 70K20 low frequency nonlinear O328 quasi-zero stiffness (QZS) vibration isolator

Physics-Informed Neural Networks with Two Weighted Loss Function Methods for Interactions of Two-Dimensional Oceanic Internal Solitary Waves

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Journal of Systems science & Complexity 2024年第2期37卷 545-566页

作者： SUN Junchao CHEN Yong TANG Xiaoyan School of Mathematical sciences Key Laboratory of Mathematics and Engineering Applications(Ministry of Education)&Shanghai Key Laboratory of PMMPEast China Normal UniversityShanghai 200241China College of mathematics and Systems science Shandong University of Science and TechnologyQingdao 266590China

The multiple patterns of internal solitary wave interactions(ISWI)are a complex oceanic *** remote sensing techniques indirectly detect these ISWI,but do not provide information on their detailed structure and ***,the author. considered a three-layer fluid with shear flow and developed a(2+1)Kadomtsev-Petviashvili(KP)model that is capable of describing five types of oceanic ISWI,including O-type,P-type,TO-type,TP-type,and *** learning models,particularly physics-informed neural networks(PINN),are widely used in the field of fluids and internal solitary ***,the author. find that the amplitude of internal solitary waves is much smaller than the wavelength and the ISWI occur at relatively large spatial scales,and these characteristics lead to an imbalance in the loss function of the PINN *** solve this problem,the author. introduce two weighted loss function methods,the fixed weighing and the adaptive weighting methods,to improve the PINN *** successfully simulated the detailed structure and dynamics of ISWI,with simulation results corresponding to the satellite *** particular,the adaptive weighting method can automatically update the weights of different terms in the loss function and outperforms the fixed weighting method in terms of generalization ability.

关键词： Internal solitary wave interactions KP equation PINN method weighted loss function method

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