nonlinear

摘要： In this paper, an optimization model is proposed to simulate and predict the current situation of smog. The model takes the interval grey number sequence with the known possibility function as the original data, and constructs a time-delay nonlinear multivariable grey model MGM based on the new kernel and degree of greyness sequences considering its time-delay and nonlinearity. The time-delay parameter is determined by the maximum value of the grey time-delay absolute correlation degree, and the nonlinear parameter is determined by the minimum value of average relative error. In order to verify the feasibility of the model, this paper uses the smog related data of Nanjing city for simulation and prediction. Compared with the other four models, the new model has higher simulation and prediction accuracy.

摘要： Road material constitutive model is the essential condition of pavement structure design,calculation,and maintenance decision.Experts have conducted in-depth studies on the problems and proposed many meaningful constitutive models.However,these constitutive models have not been summarized and no uniform conclusion on the applicability of them is reported in the academic circle.The linear elastic model based on Hooke's law is still used in pavement structure design.This paper systematically reviewed the existing constitutive models that reflect the materials'mechanical properties and used for pavement structure calculation.These constitutive models were divided into three categories:linear,nonlinear,and damage models under repeated loads.The applicable conditions,parameter determination methods,advantages,and disadvantages of each model were introduced.Moreover,the model's feasibility in structural design and calculation was analyzed.Follow-up studies should focus on the parameter determination standard of viscoelastic constitutive models,the extension of the 1D constitutive model to 3D state,and the nonlinear constitutive models related to stress-strain state to drive the application of the constitutive models in pavement structure calculation and design.Furthermore,to evaluate the life cycle service performance of road materials and structures,establishing the pavement damage model from the structure perspective will be the future direction.

摘要： Optical antennas play an important role in optical field manipulation.Among them,nanoscale bowtie antennas have been extensively studied for its high confinement and enhancement.In this mini-review,we start with a brief introduction of bowtie antennas and underlying physics.Then we review the applications with respect to optically and electrically excited nanoscale bowtie antennas.Optically driven bowtie antennas enable a set of optical applications such as near-field imaging/trapping,nonlinear response,nanolithography,photon generation and detection.Finally,we put emphasis on the principle and applications of electrically driven bowtie antennas,an emerging method of generating ultrafast and broadband tunable nanosources.In a word,nanoscale bowtie antennas still have great potential research value to explore.

摘要： The circumferential vibration of a gear pair is a parametric excitation caused by nonlinear tooth stiffness,which fluctuates with meshing.In addition,the vibration characteristics of the gear pair become complicated owing to the tooth profile error and backlash.It is considered that the circumferential vibration of the gear pair is affected by the torsional vibration of the shafts.It is important to understand quantitatively the vibration characteristics of the gear system considering the shafts.Therefore,the purpose of this research was to clarify the nonlinear vibration characteristics of a gear pair considering the influence of the shafts using theoretical methods.To achieve this objective,calculations were performed using equations of motion in which the circumferential vibration of the gear pair and the torsional vibration of the shafts were coupled.The nonlinear tooth stiffness was represented by a sine wave.The influence of tooth separation was considered by defining a nonlinear function using backlash and the tooth profile error.For the numerical calculations,both stable and unstable periodic solutions were obtained by using the shooting method.The effect of the shafts on the gear system vibration were clarified by comparing the results in the cases in which the shaft was not considered,one shaft was considered,and both shafts were considered.

摘要： With the fast evolution of wireless and networking communication technology,applications of surface acoustic wave(SAW),or Rayleigh wave,resonators are proliferating with fast shrinking sizes and increasing frequencies.It is inevitable that the smaller resonators will be under a strong electric field with induced large deformation,which has to be described in wave propagation equations with the consideration of nonlinearity.In this study,the formal nonlinear equations of motion are constructed by introducing the nonlinear constitutive relation and strain components in a standard procedure,and the equations are simplified by the extended Galerkin method through the elimination of harmonics.The wave velocity of the nonlinear SAW is obtained from approximated nonlinear equations and boundary conditions through a rigorous solution procedure.It is shown that if the amplitude is small enough,the nonlinear results are consistent with the linear results,demonstrating an alternative procedure for nonlinear analysis of SAW devices working in nonlinear state.

摘要： This paper is concerned with the coordinative control problem of networked nonlinear multi-agents(NNM)with communication delays.A high-order fully actuated(HOFA)model is introduced to describe the nonlinear multi-agents.Based on this model,a HOFA predictive coordination method is proposed to compensate for the communication delays actively and achieve simultaneous stability and consensus.This method largely simplifies the design of networked nonlinear multi-agents and makes the control performance be same for networked nonlinear multi-agents with and without communication delays.The analysis on the closed-loop systems derives the simultaneous stability and consensus criteria of networked nonlinear multiagents using the HOFA predictive coordination method.With the presented way of designing HOFA predictive coordination controllers,a simulated example demonstrates the advantages of the proposed method.

摘要： The effects of electron nonlocal heat transport (NLHT) on the two-dimensional single-mode ablative Rayleigh–Taylor instability (ARTI) upto the highly nonlinear phase are reported for the first time through numerical simulations with a multigroup diffusion model. It is found thatas well as its role in the linear stabilization of ARTI growth, NLHT can also mitigate ARTI bubble nonlinear growth after the first saturationto the classical terminal velocity, compared with what is predicted by the local Spitzer–Härm model. The key factor affecting the reductionin the linear growth rate is the enhancement of the ablation velocity Va by preheating. It is found that NLHT mitigates nonlinear bubblegrowth through a mechanism involving reduction of vorticity generation. NLHT enhances ablation near the spike tip and slows down thespike, leading to weaker vortex generation as the pump of bubble reacceleration in the nonlinear stage. NLHT more effectively reduces thenonlinear growth of shorter-wavelength ARTI modes seeded by the laser imprinting phase in direct-drive laser fusion.

摘要： This work aims to study the nonlinear ordinary differential equations(ODEs)system of magnetohydrodynamic(MHD)past over an inclined plate using Levenberg-Marquardt backpropagation neural networks(LMBNNs).The stochastic procedures LMBNNs are provided with three categories of sample statistics,testing,training,and verification.The nonlinear MHD system past over an inclined plate is divided into three profiles,dimensionless momentum,species(salinity),and energy(heat)conservations.The data is applied 15%,10%,and 75%for validation,testing,and training to solve the nonlinear system of MHD past over an inclined plate.A reference data set is designed to compare the obtained and proposed solutions for the MHD system.The plots of the absolute error(AE)are provided to check the accuracy and precision of the considered nonlinear system of MHD.The obtained numerical solutions of the nonlinear magnetohydrodynamic system have been considered to reduce the mean square error(MSE).For the capability,dependability,and aptitude of the stochastic LMBNNs procedure,the numerical performances are provided to authenticate the relative arrangements of MSE,error histograms(EHs),state transitions(STs),correlation,and regression.

摘要： As inferred from earthquake engineering literature,considering soil structure interaction(SSI)effects is important in evaluating the response of transmission line towers(TLT)to dynamic loads such as impulse loads.The proposed study investigates the dynamic effects of SSI on TLT behavior.Linear and non-linearmodels are studied.In the linearmodel,the soil is represented by complex impedances,dependent of dynamic frequency,determined from numerical simulations.The nonlinearmodel considers the soil non-linear behavior in its material constitutive law and foundation uplift in a non-linear time history analysis.The simplified structure behavior of a typical lattice transmission tower is assessed.The analysis of frequency and time domain are followed through varying soil stiffness and damping values.Three different shock durations are investigated.The soil-structure system with equivalent dynamic properties is determined.The behaviors achieved utilizing a rigid and a flexible base for the structures is compared to estimate the impact of taking SSI into account in the calculation.The current mainstream approach in structural engineering,emphasizing the importance of the SSI effect,is illustrated using an example where the SSI effect could be detrimental to the structure.Furthermore,the non-linear analysis results are analyzed to show the linear approach’s limitations in the event of grand deformations.

摘要： A novel design of the computational intelligent framework is presented to solve a class of host-vector-predator nonlinear model governed with set of ordinary differential equations.The host-vector-predator nonlinear model depends upon five groups or classes,host plant susceptible and infected populations,vectors population of susceptible and infected individuals and the predator population.An unsupervised artificial neural network is designed using the computational framework of local and global search competencies of interior-point algorithm and genetic algorithms.For solving the hostvector-predator nonlinear model,a merit function is constructed using the differential model and its associated boundary conditions.The optimization of this merit function is performed using the computational strength of designed integrated heuristics based on interior point method and genetic algorithms.For the comparison,the obtained numerical solutions of networks models optimized with efficacy of global search of genetic algorithm and local search with interior point method have been compared with the Adams numerical solver based results or outcomes.Moreover,the statistical analysis will be performed to check the reliability,robustness,viability,correctness and competency of the designed integrated heuristics of unsupervised networks trained with genetic algorithm aid with interior point algorithm for solving the biological based host-vector-predator nonlinear model for sundry scenarios of paramount interest.