Nonlinear analysis on electrical properties in a bended composite piezoelectric semiconductor beam

In this paper,the interactions between the transverse loads and the electrical field quantities are investigated based on the nonlinear constitutive relation.By considering a composite beam consisting of a piezoelectric semiconductor and elastic layers,the nonlinear model is established based on the phenomenological theory and Euler’s beam theory.Furthermore,an iteration procedure based on the differential quadrature method(DQM)is developed to solve the nonlinear governing equations.Before analysis,the convergence and correctness are surveyed.It is found that the convergence of the proposed iteration is fast.Then,the transverse pressure induced electrical field quantities are investigated in detail.From the calculated results,it can be found that the consideration of nonlinear constitutive relation is necessary for a beam undergoing a large load.Compared with the linear results,the consideration of the nonlinear constitutive relation breaks the symmetry for the electric potential,the electric field,and the perturbation carrier density,and has little influence on the electric displacement.Furthermore,the non-uniform pressures are considered.The results show that the distributions of the electric field quantities are sensitively altered.It indicates that the electrical properties can be manipulated with the design of different transverse loads.The conclusions in this paper could be the guidance on designing and manufacturing electronic devices accurately.

Nonlinear Dispersion Effect on Wave Transformation

—A new nonlinear dispersion relation is given in this paper.which can overcome the limitationof the intermediate minimum value in the dispersion relation proposed by Kirby and Dalrymple(1986).and which has a better approximation to Hedges'empirical relation than the modified relations by Hedges(1987).Kirby and Dalrymple(1987)for shallow waters.The new dispersion relation is simple in form.thusit can be used easily in practice.Meanwhile,a general explicit approximation to the new dispersion rela-tion and other nonlinear dispersion relations is given.By use of the explicit approximation to the newdispersion relation along with the mild slope equation taking into account weakly nonlinear effect.amathematical model is obtained,and it is applied to laboratory data.The results show that the model de-veloped with the new dispersion relation predicts wave transformation over complicated topography quitewell.

Nonlinear Inverse Relations of the Bell Polynomials via the Lagrange Inversion Formula (Ⅱ)

In this paper,by means of the classical Lagrange inversion formula,the authors establish a general nonlinear inverse relation as the solution to the problem proposed in the paper[J.Wang,Nonlinear inverse relations for the Bell polynomials via the Lagrange inversion formula,J.Integer Seq.,Vol.22(2019),Article 19.3.8].As applications of this inverse relation,the authors not only find a short proof of another nonlinear inverse relation due to Birmajer,et al.(2012),but also set up a few convolution identities concerning the Mina polynomials.

Numerical simulation of hypersonic thermochemical nonequilibrium flows using nonlinear coupled constitutive relations

To predict aeroheating performance of hypersonic vehicles accurately in thermochemical nonequilibrium flows accompanied by rarefaction effect,a Nonlinear Coupled Constitutive Relations(NCCR)model coupled with Gupta’s chemical models and Park’s two-temperature model is firstly proposed in this paper.Three typical cases are intensively investigated for further validation,including hypersonic flows over a two-dimensional cylinder,a RAM-C II flight vehicle and a type HTV-2 flight vehicle.The results predicted by NCCR solution,such as heat flux coefficient and electron number densities,are in better agreement with those of direct simulation Monte Carlo or flight data than Navier-Stokes equations,especially in the extremely nonequilibrium regions,which indicates the potential of the newly-developed solution to capture both thermochemical and rarefied nonequilibrium effects.The comparisons between the present solver and NCCR model without a two-temperature model are also conducted to demonstrate the significance of vibrational energy source term in the accurate simulation of high-Mach flows.

Analytical method of nonlinear coupled constitutive relations for rarefied non-equilibrium flows

It is well known that Navier-Stokes equations are not valid for those high-Knudsen and high-Mach flows, in which the local thermodynamically non-equilibrium effects are dominant. To extend the non-equilibrium describing the ability of macroscopic equations, Nonlinear Coupled Constitutive Relation(NCCR) model was developed from Eu’s generalized hydrodynamic equations to substitute linear Newton’s law of viscosity and Fourier’s law of heat conduction in conservation laws. In the NCCR model, how to solve the decomposed constitutive equations with reasonable computational cost is a key ingredient of this scheme. In this paper, an analytic method is proposed firstly. Compared to the iterative procedure in the conventional NCCR model, the analytic method not only obtains exact roots of the decomposed constitutive polynomials, but also preserves the nonlinear constitutive relations in the original framework of NCCR methods. Numerical tests to assess the efficiency and accuracy of the proposed method are conducted for argon shock structures, Couette flows, two-dimensional hypersonic flows over a cylinder and threedimensional supersonic flows over a three-dimensional sphere. These superior advantages of the current method are expected to render itself a powerful tool for simulating the hypersonic rarefied flows and microscale flows of high Knudsen number for engineering applications.

New Numerical Scheme for Simulation of Hyperbolic Mild-Slope Equation

The original hyperbolic mild-slope equation can effectively take into account the combined effects of wave shoaling,refraction, diffraction and reflection, but does not consider the nonlinear effect of waves, and the existing numericalschemes for it show some deficiencies. Based on the original hyperbolic mild-slope equation, a nonlinear dispersion rela-tion is introduced in present paper to effectively take the nonlinear effect of waves into account and a new numericalscheme is proposed. The weakly nonlinear dispersion relation and the improved numerical scheme are applied to thesimulation of wave transformation over an elliptic shoal. Numerical tests show that the improvement of the numericalscheme makes efficient the solution to the hyperbolic mild-slope equation. A comparison of numerical results with experi-mental data indicates that the results obtained by use of the new scheme are satisfactory.

Impacts of parameter uncertainties on deep chlorophyll maximum simulation revealed by the CNOP-P approach

Parameter uncertainty is a primary source of uncertainty in ocean ecosystem simulations.The deep chlorophyll maximum(DCM)is a ubiquitous ecological phenomenon in the ocean.Using a theoretical nutrients-phytoplankton model and the conditional nonlinear optimal perturbation approach related to parameters,we investigated the eff ects of parameter uncertainties on DCM simulations.First,the sensitivity of single parameter was analyzed.The sensitivity ranking of 10 parameters was obtained by analyzing the top four specifi cally.The most sensitive parameter(background turbidity)aff ects the light supply for DCM formation,whereas the other three parameters(nutrient content of phytoplankton,nutrient recycling coeffi cient,and vertical turbulent diff usivity)control nutrient supply.To explore the interactions among diff erent parameters,the sensitivity of multiple parameters was further studied by examining combinations of four parameters.The results show that background turbidity is replaced by the phytoplankton loss rate in the optimal parameter combination.In addition,we found that interactions among these parameters are responsible for such diff erences.Finally,we found that reducing the uncertainties of sensitive parameters could improve DCM simulations remarkably.Compared with the sensitive parameters identifi ed in the single parameter analysis,reducing parameter uncertainties in the optimal combination produced better model performance.This study shows the importance of nonlinear interactions among various parameters in identifying sensitive parameters.In the future,the conditional nonlinear optimal perturbation approach related to parameters,especially optimal parameter combinations,is expected to greatly improve DCM simulations in complex ecosystem models.

Ensemble Forecast for Tropical Cyclone Based on CNOP-P Method:A Case Study of WRF Model and Two Typhoons

In this paper,we set out to study the ensemble forecast for tropical cyclones.The case study is based on the Conditional Nonlinear Optimal Perturbation related to Parameter(CNOP-P)method and the WRF model to improve the prediction accuracy for track and intensity,and two different typhoons are selected as cases for analysis.We first select perturbed parameters in the YSU and WSM6 schemes,and then solve CNOP-Ps with simulated annealing algorithm for single parameters as well as the combination of multiple parameters.Finally,perturbations are imposed on default parameter values to generate the ensemble members.The whole proposed procedures are referred to as the PerturbedParameter Ensemble(PPE).We also conduct two experiments,which are control forecast and ensemble forecast,termed Ctrl and perturbed-physics ensemble(PPhyE)respectively,to demonstrate the performance for contrast.In the article,we compare the effects of three experiments on tropical cyclones in aspects of track and intensity,respectively.For track,the prediction errors of PPE are smaller.The ensemble mean of PPE filters the unpredictable situation and retains the reasonably predictable components of the ensemble members.As for intensity,ensemble mean values of the central minimum sea-level pressure and the central maximum wind speed are closer to CMA data during most of the simulation time.The predicted values of the PPE ensemble members included the intensity of CMA data when the typhoon made landfall.The PPE also shows uncertainty in the forecast.Moreover,we also analyze the track and intensity from physical variable fields of PPE.Experiment results show PPE outperforms the other two benchmarks in track and intensity prediction.

MODAL DISCONTINUOUS GALERKIN METHOD FOR SHOCK WAVE STRUCTURES

The discontinuous Galerkin(DG)finite element method has been popular as a numerical technique for solving the conservation laws.In the present study,in order to investigate the shock wave structures in highly thermal nonequilibrium,an explicit modal cell-based DG scheme is developed for solving the conservation laws in conjunction with nonlinear coupled constitutive relations(NCCR).Convergent iterative methods for solving algebraic constitutive relations are also implemented in the DG scheme.It is shown that the new scheme works well for all Mach numbers,for example,Ma=15.