Communications in Nonlinear Science and Numerical Simulation最新文献

{"title":"Optimal error estimates of conservative virtual element method for the coupled nonlinear Schrödinger–Helmholtz equation","authors":"Jixiao Guo ,&nbsp;Yanping Chen ,&nbsp;Jianwei Zhou ,&nbsp;Qin Liang","doi":"10.1016/j.cnsns.2025.108680","DOIUrl":"10.1016/j.cnsns.2025.108680","url":null,"abstract":"<div><div>In this work, we propose a novel class of mass- and energy-conserving schemes formulated on arbitrary polygonal meshes for the coupled nonlinear Schrödinger–Helmholtz system. This approach leverages the Crank–Nicolson time discretization and the virtual element method for spatial discretization. To establish the theoretical foundation, we use the duality argument to estimate the difference quotient of the error in the <span><math><mrow><msup><mrow><mi>H</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></math></span>-norm and the classical Schaefer’s fixed point theorem to demonstrate the existence, uniqueness, and convergence of the numerical solutions when <span><math><mi>h</mi></math></span> and <span><math><mi>τ</mi></math></span> are sufficiently small. Specifically, we rigorously derive an optimal error estimate of the form <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>h</mi></mrow><mrow><mi>r</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span> in the <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>;</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>-norm without restriction on the grid ratio, where <span><math><mi>τ</mi></math></span> and <span><math><mi>h</mi></math></span> represent the temporal and spatial mesh sizes, respectively, and <span><math><mi>r</mi></math></span> is the degree of approximation. Compared to conventional theoretical analysis techniques, our methodology does not require temporal–spatial splitting arguments and avoids cumbersome mathematical induction. Finally, numerical examples on a set of polygonal meshes confirm the accuracy and efficacy of our proposed method, underscoring its conservation properties over long-time simulations.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"145 ","pages":"Article 108680"},"PeriodicalIF":3.4,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143463314","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Research on reliability and dynamic characteristics of planar complex multi-bar mechanism considering clearance and irregular wear effect","authors":"Dong Liang ,&nbsp;Tao Lv ,&nbsp;Zhimin Wang","doi":"10.1016/j.cnsns.2025.108708","DOIUrl":"10.1016/j.cnsns.2025.108708","url":null,"abstract":"<div><div>To study the motion reliability and dynamic characteristics of a planar multi-bar mechanism with clearance, this paper takes the R-2RRP-RRR mechanism with single clearance as the research object, establishes its dynamic model based on the Newton-Euler method, and the effectiveness of the dynamic model is verified through both the numerical computation and multibody dynamics simulation. A method for motion reliability analysis using failure rate as a reliability metric based on Monte Carlo algorithm is proposed, which is simple and highly accurate, and the influence rule of mechanism motion reliability under the interaction of multiple factors is revealed using the proposed method. Based on Archard's model and Lankarani-Nikravesh nonlinear contact force model, a method for analyzing and quantifying irregular wear effects of multi-bar mechanism with clearance is presented, and the influence on the mechanism of crank speed, clearance size, coefficient of friction and coefficient of restitution on irregular wear of mechanism with clearance are investigated systematically. The factors affecting the behavior of the nonlinear characteristics of multi-bar mechanism are studied, and the obtained conclusions provide sound foundation for the life prediction and optimal design of multi-bar mechanism with single clearance as well as multi-clearance in practical application.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"145 ","pages":"Article 108708"},"PeriodicalIF":3.4,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143507508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Parametric resonance and stochastic stability of a vibro-impact system under bounded noise excitation","authors":"Dongliang Hu ,&nbsp;Jianfeng Zhang ,&nbsp;Huatao Chen ,&nbsp;Juan LG Guirao ,&nbsp;Xianbin Liu","doi":"10.1016/j.cnsns.2025.108715","DOIUrl":"10.1016/j.cnsns.2025.108715","url":null,"abstract":"<div><div>The vibro-impact system has more complex and variable dynamic behavior, and its research has attracted the attention of many scholars. However, the effect of resonance on the dynamic characteristics of vibro-impact systems is rarely explored. In this paper, the parametric resonance and stochastic stability of a vibro-impact system excited by bounded noise parameters are investigated. For weak noise excitations, the approximate analytical results of the moment Lyapunov exponent and the largest Lyapunov exponent are calculated by using the method of singular perturbation and Fourier series expansion, which are in good agreement with those obtained by Monte Carlo numerical simulation. Then, based on the moment Lyapunov exponent and the largest Lyapunov exponent, the effects of parametric resonance and different parameters on the stochastic stability of the vibro-impact system are investigated in detail.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"145 ","pages":"Article 108715"},"PeriodicalIF":3.4,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143478842","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal control for a reaction–diffusion model with tumor-immune interactions","authors":"Fang Li ,&nbsp;Bo You","doi":"10.1016/j.cnsns.2025.108677","DOIUrl":"10.1016/j.cnsns.2025.108677","url":null,"abstract":"<div><div>The main objective of this paper is to consider an optimal distributed control problem for a reaction–diffusion model with tumor-immune interactions, which consists of a coupled system of reaction–diffusion equations for normal cells, tumor cells, immune cells and chemotherapeutic drug. Moreover, a suitable distributed control variable representing the concentration of cytotoxic drugs in medical treatment is introduced into the equation of chemotherapeutic drug. We first establish the well-posedness of the state system by combining of truncation method, Faedo–Galerkin method and maximum principle of second-order parabolic equations. Then we prove the existence of an optimal control, the Fréchet differentiability of the control-to-state operator in a suitable functional analytic framework, and finally deduce the corresponding first-order necessary conditions of optimality by studying the corresponding linearized system and the backward adjoint system.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"145 ","pages":"Article 108677"},"PeriodicalIF":3.4,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143463309","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modulational instability in PT-symmetric Bragg grating structures with four-wave mixing","authors":"I. Inbavalli ,&nbsp;K. Tamilselvan ,&nbsp;A. Govindarajan ,&nbsp;T. Alagesan ,&nbsp;M. Lakshmanan","doi":"10.1016/j.cnsns.2025.108679","DOIUrl":"10.1016/j.cnsns.2025.108679","url":null,"abstract":"<div><div>We explore the dynamics of modulational instability (MI) in <span><math><mi>PT</mi></math></span>-symmetric fiber Bragg gratings, focusing on the intermodulation phenomenon known as four-wave mixing (FWM). While the role of FWM has been already studied in conventional systems, introducing equal amount of gain and loss, which are the key elements of <span><math><mi>PT</mi></math></span>-symmetric notion, leads to intriguing new outcomes. Notably, it results in an unprecedented double-loop structure in the dispersion curve, a feature which is not observed in any conventional periodic Bragg system. In our investigation of MI which is achieved by applying small perturbations to the continuous wave and performing a linear stability analysis, we identify many peculiar MI spectra in a range of regimes spanning conventional to broken <span><math><mi>PT</mi></math></span>-symmetry. Among these, we uncover a remarkable MI pattern resembling two oppositely tilted conical structures. Furthermore, we examine the influence of key system parameters such as pump power, gain and loss, and self-phase modulation across two critical domains including normal and anomalous dispersion regimes. Particularly, we find that the impact of pump power enhances the MI spectra in all the regimes irrespective of the stand-alone effect of system parameters.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"145 ","pages":"Article 108679"},"PeriodicalIF":3.4,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143463310","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Torsional vibration analysis and suppression for integrated electric drive system considering nonlinear excitations","authors":"Zhicheng Sun ,&nbsp;Jianjun Hu ,&nbsp;Qi Guo","doi":"10.1016/j.cnsns.2025.108695","DOIUrl":"10.1016/j.cnsns.2025.108695","url":null,"abstract":"<div><div>Integrated Electric Drive Systems (IEDS) are widely used in electric vehicles due to its compact design and high-power density. To address the issue where nonlinear excitations and variable, complex operating conditions of IEDS can exacerbate high and low-frequency torsional vibrations, leading to decreased reliability of the IEDS. The active dual-layer suppression method is proposed based on analyzing inherent properties and the influence of nonlinear excitations, including time-varying meshing stiffness, backlash, meshing error, and dead-zone, on the dynamic performance of IEDS, which can simultaneously suppress high and low-frequency torsional vibration of the IEDS. In the upper-layer, a torsional vibration suppression method based on pole placement is proposed to optimize the motor's reference torque. Then, a current harmonic suppression method based on active disturbance rejection control is proposed in the lower-ayer to compensate for the voltage errors caused by nonlinear excitations and decoupling errors, thereby reducing current harmonics and torque ripple. The simulation and experimental results show that the method can effectively reduce current harmonics and torque ripple, while also decreasing high and low frequency torsional vibrations of IEDS. This enhances the reliability of IEDS and improves the vehicle stability.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"145 ","pages":"Article 108695"},"PeriodicalIF":3.4,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143463315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multi-scale modeling of Snail-mediated response to hypoxia in tumor progression","authors":"Giulia Chiari ,&nbsp;Martina Conte ,&nbsp;Marcello Delitala","doi":"10.1016/j.cnsns.2025.108673","DOIUrl":"10.1016/j.cnsns.2025.108673","url":null,"abstract":"<div><div>Tumor cell migration within the microenvironment is a crucial aspect for cancer progression and, in this context, hypoxia has a significant role. An inadequate oxygen supply acts as an environmental stressor inducing migratory bias and phenotypic changes. In this paper, we propose a novel multi-scale mathematical model to analyze the pivotal role of Snail protein expression in the cellular responses to hypoxia. Starting from the description of single-cell dynamics driven by the Snail protein, we construct the corresponding kinetic transport equation that describes the evolution of the cell distribution. Subsequently, we employ proper scaling arguments to formally derive the equations for the statistical moments of the cell distribution, which govern the macroscopic tumor dynamics. Numerical simulations of the model are performed in various scenarios with biological relevance to provide insights into the role of the multiple tactic terms, the impact of Snail expression on cell proliferation, and the emergence of hypoxia-induced migration patterns. Moreover, quantitative comparisons with experimental data show the model’s reliability in measuring the impact of Snail transcription on cell migratory potential. Through our findings, we shed light on the potential of our mathematical framework in advancing the understanding of the biological mechanisms driving tumor progression.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"145 ","pages":"Article 108673"},"PeriodicalIF":3.4,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143463311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multilayer heterostructure power-law inhomogeneous model for the functionally graded cylinders and annular disks with rotation effect for arbitrarily material property with the parametric uncertainty","authors":"Hui Li ,&nbsp;Jun Xie ,&nbsp;Wenshuai Wang ,&nbsp;Xing Li ,&nbsp;Pengpeng Shi","doi":"10.1016/j.cnsns.2025.108689","DOIUrl":"10.1016/j.cnsns.2025.108689","url":null,"abstract":"<div><div>This study comprehensively investigates the influence of the rotation effect on the elastic field of functionally graded (FG) hollow cylinders and annular disks with considering uncertainty and fluctuation in material parameters. The multilayer heterostructure power-law inhomogeneous (MHPI) model is introduced, where the radial change in Young's modulus and density are approximated by multiple sublayers with power-law functionally graded materials (FGMs). The analytical solutions for rotating FG hollow cylinders and annular disks are derived by considering continuity between the layers and six different boundary conditions. Numerical examples are conducted using various classical gradient assumptions, including property profile gradient models (power, linear, and exponential laws, etc.) and the volume fractional gradient model (volume fractional gradient and homogenization schemes). Comparison of the MHPI model with the finite difference method (FDM) and the multilayer heterostructure homogeneous (MHH) model demonstrates its validity. Additionally, the study analyzes the impact of the gradient parameter, rotation effect, and elastic foundation effect on the elastic field of rotating FG hollow cylinders and annular disks. The results show that the MHPI model effectively overcomes the oscillation problem of the circumferential stress calculated by the MHH model, and the accuracy is very high, with an error of about 5‰ in the case of the number of sublayers <em>N</em> = 10. The solution of the problem for different boundary conditions such as stress-free or displacement-fixed can be obtained by adjusting the elastic foundation parameters. In addition, based on the reliable and efficient MHPI model, how the uncertainties in the material parameters <em>E</em> and <em>ρ</em> affect the mechanical response of rotating FG hollow cylinders and annular disks is analyzed, which contributes to a deeper understanding of their mechanical behavior.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"145 ","pages":"Article 108689"},"PeriodicalIF":3.4,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143463313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Finite and fixed time synchronization of multi-link complex-valued complex networks with time delay via hybrid control","authors":"Jie Wei,&nbsp;Zhihuan Chen","doi":"10.1016/j.cnsns.2025.108678","DOIUrl":"10.1016/j.cnsns.2025.108678","url":null,"abstract":"<div><div>This paper investigates the problem of finite and fixed time synchronization for multi-link complex-valued complex networks (MLCCNs) with time delay. In contrast to the existing works, the finite and fixed time synchronization of MLCCNs is conducted in the complex field, which is more general. In order to reduce the control costs, two hybrid control strategies, with finite time and fixed time, are proposed to address the synchronization process of MLCCNs. Based on the Lyapunov stability theory as well as inequality technique of complex field, sufficient criteria are established by theoretical proof. Numerical simulations are presented to validate the effectiveness and superiority of the proposed theoretical results.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"144 ","pages":"Article 108678"},"PeriodicalIF":3.4,"publicationDate":"2025-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143444749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A hybrid energy harvester with bistable mechanism based on flapping-wing structure","authors":"Jiwen Fang,&nbsp;Mingwei Jiang,&nbsp;Bo Fan,&nbsp;Chong Li,&nbsp;Jiang Shao","doi":"10.1016/j.cnsns.2025.108705","DOIUrl":"10.1016/j.cnsns.2025.108705","url":null,"abstract":"<div><div>The utilization of low-frequency vibrations distributed in nature to provide energy supply for microelectronic devices has drawn greater attention. Based on the principle of flapping wings of insects, a bionic flapping wing bistable energy harvester (BFBEH) for low-frequency vibration is proposed by using a symmetrical flexible cantilever beam mounted with piezoelectric fibers to simulate the wings of insects, and the lifting and lowering motions of the center unit constructed by a magnetic inductor coil and a levitating magnet to simulate the muscle motions of insects. In consideration of broadening the energy harvesting frequency band, nonlinear magnetic force is introduced to realize bistability. When excited by vibration, the magnetic induction coil and the suspended magnet generate relative motion to realize electromagnetic energy harvesting, while the cantilever beam unit connected to the induction coil frame realizes piezoelectric energy harvesting. In particular, the coupling of a permanent magnet as a mass block at the end of the cantilever beam with a fixed steady state magnet can construct the bistable characteristics of the flapping wing. Theoretical modeling of the bionic energy harvester is established. The focus is on the theoretical modeling of the bistable mechanism and the numerical simulation of its potential energy. The electromagnetic simulation results show that the structure has an effective energy harvesting capability in a low frequency environment. An experimental system is set up to analyze the effects of excitation frequency, limit height, and the number of permanent magnet groups at the end of the flexible cantilever beam on the output performance of the bistable energy harvesting device. The experimental results show that the excitation frequency, limit height, and magnetically coupled bistable mechanism have a large influence on the output power of the collector, and the output power of the BFBEH under low-frequency vibration is greater than 0 .2W.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"144 ","pages":"Article 108705"},"PeriodicalIF":3.4,"publicationDate":"2025-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143429370","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}