Multi-soliton solutions of coupled Lakshmanan-Porsezian-Daniel equations with variable coefficients under nonzero boundary conditions

This paper aims to investigate the multi-soliton solutions of the coupled Lakshmanan–Porsezian–Daniel equations with variable coefficients under nonzero boundary conditions.These equations are utilized to model the phenomenon of nonlinear waves propagating simultaneously in non-uniform optical fibers.By analyzing the Lax pair and the Riemann–Hilbert problem,we aim to provide a comprehensive understanding of the dynamics and interactions of solitons of this system.Furthermore,we study the impacts of group velocity dispersion or the fourth-order dispersion on soliton behaviors.Through appropriate parameter selections,we observe various nonlinear phenomena,including the disappearance of solitons after interaction and their transformation into breather-like solitons,as well as the propagation of breathers with variable periodicity and interactions between solitons with variable periodicities.

Analysis of the Oscillating Mechanism of an Aerial Work Platform Based on ADAMS Hydraulic-Mechanical Coupling Simulation

Rigid model of the aerial work platform and hydraulic model of the oscillating mechanism were established with ADAMS. The simulation of two parameters, cy-linder force and oil chamber pressure, was carried out. The simulation result is useful to the design of the oscillating mechanism.

Consistency Conditions and Constraints on Generalized f(R) Gravity with Arbitrary Geometry-Matter Coupling

We study the consistency conditions of the generalized f （ R） gravity by extending f （ R） gravity with non-minimal coupling to the generalized f（R） with arbitrary geometry-matter coupling. Specifically, we discuss the two particular models of generalized f（R） by means of consistency conditions. It is found that the second model is not physically viable so as to be ruled out. Moreover, we further constrain the first model using the Dolgov- Kawasaki stability criterion, and give the value ranges of the parameters in the first model It is worth stressing that our results include the ones in f（R） gravity with non-minimal coupling as the special case of Q（Lm） = Lm.

On Vector Helmholtz Equation with a Coupling Boundary Condition

The Helmholtz equation is sometimes supplemented by conditions that include the specification of the boundary value of the divergence of the unknown.In this paper, we study the vector Helmholtz problem in domains of both C^(1,1)and Lipschitz.We es- tablish a rigorous variational analysis such as equivalence,existence and uniqueness. And we propose finite element approximations based on the uncoupled solutions.Fi- nally we present a convergence analysis and error estimates.

Free Vibration Analysis of Rectangular Plate with Cutouts under Elastic Boundary Conditions in Independent Coordinate Coupling Method

Based on Kirchhoff plate theory and the Rayleigh-Ritz method,the model for free vibration of rectangular plate with rectangular cutouts under arbitrary elastic boundary conditions is established by using the improved Fourier series in combination with the independent coordinate coupling method(ICCM).The effect of the cutout is taken into account by subtracting the energies of the cutouts from the total energies of the whole plate.The vibration displacement function of the hole domain is based on the coordinate system of the hole domain in this method.From the continuity condition of the vibration displacement function at the cutout,the transition matrix between the two coordinate systems is constructed,and the mass and stiffness matrices are completely obtained.As a result,the calculation is simplified and the computational efficiency of the solution is improved.In this paper,numerical examples and modal experiments are presented to validate the effectiveness of the modeling methods,and parameters related to influencing factors of the rectangular plate are analyzed to study the vibration characteristics.

Determination of Optimum Conditions for X-Ray Fluorescence Analysis Using Coupling Equations

Coupling equations used to calculate the chemical composition of substances by X-ray fluorescence analysis can be classified as empirical, theoretical or semi-empirical based on the method for determining the coefficients of the calibration function. The advantages and disadvantages of each class of equations are discussed. Recommendations for the selecting the optimum conditions for determining empirical correction coefficients and their control during analysis are provided.

Time-dependent behavior and permeability evolution of limestone under hydro-mechanical coupling

Excessively high pore water pressure presents unpredictable risks to the safety of rock tunnels in mountainous regions that are predominantly composed of limestone. Investigating the creep characteristics and permeability evolution of limestone under varying hydrated conditions is crucial for a better understanding of the delayed deformation mechanisms of limestone rock tunnels. To this end, this paper initially conducts a series of multi-stage triaxial creep tests on limestone samples under varying pore water pressures. The experiment examines how pore water pressure affects limestone’s creep strain, strain rate, long-term strength, lifespan, and permeability, all within the context of hydraulicmechanical(HM) coupling. To better describe the creep behavior associated with pore water pressure, this paper proposes a new nonlinear fractional creep constitutive model. This constitutive model depicts the initial, steady-state, and accelerated phases of limestone’s creep behavior. Finally, the proposed model is applied to the numerical realization of deformation in limestone tunnel, validating the effectiveness of the proposed constitutive model in predicting tunnel’s creep deformation. This research enhances our understanding of limestone’s creep characteristics and permeability evolution under HM coupling, laying a foundation for assessing the longterm stability of mountain tunnels.

A STUDY OF A FULLY COUPLED TWO-PARAMETER SYSTEM OF SEQUENTIAL FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLOCAL INTEGRO-MULTIPOINT BOUNDARY CONDITIONS

In this article, we discuss the existence and uniqueness of solutions for a coupled two-parameter system of sequential fractional integro-differential equations supplemented with nonlocal integro-multipoint boundary conditions. The standard tools of the fixed-point theory are employed to obtain the main results. We emphasize that our results are not only new in the given configuration, but also correspond to several new special cases for specific values of the parameters involved in the problem at hand.

Application of the Conditional Nonlinear Local Lyapunov Exponent to Second-Kind Predictability

In order to quantify the influence of external forcings on the predictability limit using observational data,the author introduced an algorithm of the conditional nonlinear local Lyapunov exponent(CNLLE)method.The effectiveness of this algorithm is validated and compared with the nonlinear local Lyapunov exponent(NLLE)and signal-to-noise ratio methods using a coupled Lorenz model.The results show that the CNLLE method is able to capture the slow error growth constrained by external forcings,therefore,it can quantify the predictability limit induced by the external forcings.On this basis,a preliminary attempt was made to apply this method to measure the influence of ENSO on the predictability limit for both atmospheric and oceanic variable fields.The spatial distribution of the predictability limit induced by ENSO is similar to that arising from the initial conditions calculated by the NLLE method.This similarity supports ENSO as the major predictable signal for weather and climate prediction.In addition,a ratio of predictability limit(RPL)calculated by the CNLLE method to that calculated by the NLLE method was proposed.The RPL larger than 1 indicates that the external forcings can significantly benefit the long-term predictability limit.For instance,ENSO can effectively extend the predictability limit arising from the initial conditions of sea surface temperature over the tropical Indian Ocean by approximately four months,as well as the predictability limit of sea level pressure over the eastern and western Pacific Ocean.Moreover,the impact of ENSO on the geopotential height predictability limit is primarily confined to the troposphere.

Evaluation of Haney-Type Surface ThermalBoundary Conditions Using a CoupledAtmosphere and Ocean Model

A coupled atmosphere-ocean model developed at the Institute for Space Studies at NASA Goddard Space Flight Center (Russell et al., 1995) was used to verify the validity of Haney-type surface thermal boundary condition, which linearly connects net downward surface heat fluxQ to air/sea temperature difference ΔT by a relaxation coefficientk. The model was initiated from the National Centers for Environmental Prediction (NCEP) atmospheric observations for 1 December 1977, and from the National Ocean Data Center (NODC) global climatological mean December temperature and salinity fields at 1°x 1° resolution. The time step is 7.5 minutes. We integrated the model for 450 days and obtained a complete model-generated global data set of daily mean downward net surface fluxQ, surface air temperatureT A, and sea surface temperatureT O. Then, we calculated the cross-correlation coefficients (CCC) betweenQ and ΔT. The ensemble mean CCC fields show (a) no correlation betweenQ and ΔT in the equatiorial regions, and (b) evident correlation (CCC≥0.7) betweenQ and ΔT in the middle and high latitudes. Additionally, we did the variance analysis and found that whenk=120 W m?2K?1, the two standard deviations, σQ and σκδT , are quite close in the middle and high latitudes. These results agree quite well with a previous research (Chu et al., 1998) on analyzing the NCEP re-analyzed surface data, except that a smaller value ofk (80 W m?2K?1) was found in the previous study. Key words Air-sea coupled system - Ocean surface fluxes - Surface thermal boundary condition

Analysis of convergence for initial condition estimation of coupled map lattices based on symbolic dynamics

A novel approach to the inverse problem of diffusively coupled map lattices is systematically investigated by utilizing the symbolic vector dynamics. The relationship between the performance of initial condition estimation and the structural feature of dynamical system is proved theoretically. It is found that any point in a spatiotemporal coupled system is not necessary to converge to its initial value with respect to sufficient backward iteration, which is directly relevant to the coupling strength and local mapping function. When the convergence is met, the error bound in estimating the initial condition is proposed in a noiseless environment, which is determined by the dimension of attractors and metric entropy of the system. Simulation results further confirm the theoretic analysis, and prove that the presented method provides the important theory and experimental results for better analysing and characterizing the spatiotemporal complex behaviours in an actual system.

A method of estimating initial conditions of coupled map lattices based on time-varying symbolic dynamics

A novel computationally efficient algorithm in terms of the time-varying symbolic dynamic method is proposed to estimate the unknown initial conditions of coupled map lattices （CMLs）. The presented method combines symbolic dynamics with time-varying control parameters to develop a time-varying scheme for estimating the initial condition of multi-dimensional spatiotemporal chaotic signals. The performances of the presented time-varying estimator in both noiseless and noisy environments are analysed and compared with the common time-invariant estimator. Simulations are carried out and the obtained results show that the proposed method provides an efficient estimation of the initial condition of each lattice in the coupled system. The algorithm cannot yield an asymptotically unbiased estimation due to the effect of the coupling term, but the estimation with the time-varying algorithm is closer to the Cramer-Rao lower bound （CRLB） than that with the time-invariant estimation method, especially at high signal-to-noise ratios （SNRs）.

The effects of process conditions on the plasma characteristic in radio-frequency capacitively coupled SiH_4/NH_3/N_2 plasmas: Two-dimensional simulations

A two-dimensional （2D） fluid model is presented to study the behavior of silicon plasma mixed with SiH4 , N2 , and NH3 in a radio-frequency capacitively coupled plasma （CCP） reactor. The plasma–wall interaction （including the deposition） is modeled by using surface reaction coefficients. In the present paper we try to identify, by numerical simulations, the effect of variations of the process parameters on the plasma properties. It is found from our simulations that by increasing the gas pressure and the discharge gap, the electron density profile shape changes continuously from an edge-high to a center-high, thus the thin films become more uniform. Moreover, as the N2 /NH3 ratio increases from 6/13 to 10/9, the hydrogen content can be significantly decreased, without decreasing the electron density significantly.

Coupled pile soil interaction analysis in undrained condition

The effective stress method is developed to predict the axial capacity of piles in clay. The effective stress state changes due to the resulting pore pressure change and therefore, the strength and stiffness of the soil will change. In this work, the finite element method is utilized as a tool for the analysis of pile-soil systems in undrained condition. The computer program CRISP was developed to suit the problem requirements. CRISP uses the finite element technique and allows predictions to be made of ground deformation using critical state theories. Eight-node isoparametric element was added to the program in addition to the slip element. A pile loading problem was solved in which the pile-soil system is analyzed in undrained condition. The pile is modelled as elastic-plastic material, while the soil is assumed to follow the modified Cam clay model. During undrained loading condition, the settlement values increase by 22% when slip elements are used. The surface settlement increases by about three times when the load is doubled and the surface settlement at all points increases when using slip elements due to the mode of motion which allows smooth movement of the adjacent soil with respect to the pile. The vertical displacement increases as the distance decreases from the pile and negligible values are obtained beyond 10D (where D is the pile diameter) from the center of the pile and these values are slightly increased when slip elements are used. The vertical effective stress along a section at a distance D from the pile center is approximately the same for all load increments and lower values of effective vertical stress can be obtained when slip elements are used.

Sliding Mode Control of Coupled Tank Systems Using Conditional Integrators

For the problem of set point regulation of the liquid level in coupled tank systems, we present a continuous sliding mode control(SMC) with a "conditional integrator", which only provides integral action inside the boundary layer. For a special choice of the controller parameters, our design can be viewed as a PID controller with anti-windup and achieves robust regulation.The proposed controller recovers the transient response performance without control chattering. Both full-state feedback as well as output-feedback designs are presented in this work. Our output-feedback design uses a high-gain observer(HGO) which recovers the performance of a state-feedback design where plant parameters are assumed to be known. We consider both interacting as well as non-interacting tanks and analytical results for stability and transient performance are presented in both the cases. The proposed controller continuous SMC with conditional integrators(CSMCCI) provides superior results in terms of the performance measures as well as performance indices than ideal SMC, continuous SMC(CSMC) and continuous SMC with conventional integrator(CSMCI). Experimental results demonstrate good tracking performance in spite of unmodeled dynamics and disturbances.

Analysis of high-frequency local coupling instability induced by multi- transmitting formula - P-SV wave simulation in a 2D waveguide

Local coupling instability will occur when the numerical scheme of absorbing boundary condition and that of the field wave equation allow energies to spontaneously enter into the computational domain. That is, the two schemes support common wave solutions with group velocity pointed into the computation domain. The key to eliminate local coupling instability is to avoid such wave solutions. For lumped-mass finite element simulation of P-SV wave motion in a 2D waveguide, an approach for stable implementation of high order multi-transmitting formula is provided. With a uniform rectangular mesh, it is proven and validated that high-freqaency local coupling instability can be eliminated by setting the ratio of the element size equal to or greater than x/2 times the ratio of the P wave velocity to the S wave velocity. These results can be valuable for dealing instability problems induced by other absorbing boundary conditions.

Stiffness Degradation of Undisturbed Saturated Soft Clay in the Yangtze Estuary Under Complex Stress Conditions

Stiffness degradation will occur due to the generation of accumulated pore pressure in saturated soft clays under cyclic loading. The soil static-dynamic multi-purpose triaxial and torsional shear apparatus in Dalian University of Technology was employed to perform different types of test on the saturated soft marine clay in the Yangtze Estuary. Undisturbed samples of the clay were subjected to undrained cyclic vertical and torsional coupling shear and cyclic torsional shear after three-directional anisotropic consolidation with different initial consolidation parameters. Investigated were the effects of the initial orientation angle of the major principal stress, initial ratio of deviatoric stress, initial coefficient of intermediate principal stress and continuous rotation of principal stress axes on the stiffness degradation. It is found that the degradation index decreases （or degradation degree increases） significantly with increasing initial orientation angle of the major principal stress and initial ratio of deviatoric stress. Compared with the effects of the initial orientation angle of the major principal stress and initial ratio of deviatoric stress, the effect of initial coefficient of intermediate principal stress is less evident and this trend is more clearly reflected by the results of the cyclic torsional shear tests than those of the cyclic coupling shear tests. At the same cycle number, the degradation index obtained from the cyclic torsional shear test is higher than that from the cyclic coupling shear test. The main reason is that the continuous rotation in principal stress directions during cyclic coupling shear damages the original structure of the soil more than the cyclic torsional shear does.Based on a series of experiments, a mathematical model for stiffness degradation is proposed and the relevant parameters are determined.

On vibration analysis of functionally graded carbon nanotube reinforced magneto-electro-elastic plates with different electro-magnetic conditions using higher order finite element methods

This article deals with evaluating the frequency response of functionally graded carbon nanotube reinforced magneto-electro-elastic(FG-CNTMEE)plates subjected to open and closed electro-magnetic circuit conditions.In this regard finite element formulation has been derived.The plate kinematics adjudged via higher order shear deformation theory(HSDT)is considered for evaluation.The equations of motion are obtained with the help of Hamilton’s principle and solved using condensation technique.It is found that the convergence and accuracy of the present FE formulation is very good to address the vibration problem of FG-CNTMEE plate.For the first time,frequency response analysis of FG-CNTMEE plates considering the effect of various circuit conditions associated with parameters such as CNT distributions,volume fraction,skew angle,aspect ratio,length-to-thickness ratio and coupling fields has been carried out.The results of this article can serve as benchmark for future development and analysis of smart structures.

Mechanistic Drifting Forecast Model for A Small Semi-Submersible Drifter Under Tide–Wind–Wave Conditions

Understanding the drifting motion of a small semi-submersible drifter is of vital importance regarding monitoring surface currents and the floating pollutants in coastal regions. This work addresses this issue by establishing a mechanistic drifting forecast model based on kinetic analysis. Taking tide–wind–wave into consideration, the forecast model is validated against in situ drifting experiment in the Radial Sand Ridges. Model results show good performance with respect to the measured drifting features, characterized by migrating back and forth twice a day with daily downwind displacements. Trajectory models are used to evaluate the influence of the individual hydrodynamic forcing. The tidal current is the fundamental dynamic condition in the Radial Sand Ridges and has the greatest impact on the drifting distance. However, it loses its leading position in the field of the daily displacement of the used drifter. The simulations reveal that different hydrodynamic forces dominate the daily displacement of the used drifter at different wind scales. The wave-induced mass transport has the greatest influence on the daily displacement at Beaufort wind scale 5–6; while wind drag contributes mostly at wind scale 2–4.

GaN-based heterostructures： electric-static equilibrium and boundary conditions

In the GaN-based heterostructures, this paper reports that the strong electric fields induced by polarization effects at the structure boundaries complicate the electric-static equilibrium and the boundary conditions. The basic requirements of electric-static equilibrium for the heterostructure systems are discussed first, and it is deduced that in the application of the coupled Schroedinger-Poisson model to the heterostructures of electric static equilibrium state, zero external electric field guarantees the overall electric neutrality, and there is no need to introduce the charge balance equation. Then the relation between the screening of the polar charges in GaN-based heterostructures and the possible boundary conditions of the Poisson equation is analysed, it is shown that the various boundary conditions are equivalent to each other, and the surface charge, which can be used in studying the screening of the polar charges, can be precisely solved even if only the conduction band energy is correctly known at the surface. Finally, through the calculations on an AlGaN/GaN heterostructure with typical structure parameters by the coupled Schroedinger-Poisson model under the various boundary conditions, the correctness of the above analyses are validated.