Calculation of the Coupling Coefficient of Twin-Core Fiber Based on the Supermode Theory with Finite Element Method

Currently, coupled mode theory (CMT) is widely used for calculating the coupling coefficient of twin-core fibers (TCFs) that are used in a broad range of important applications. This approach is highly accurate for scenarios with weak coupling between the cores but shows significant errors in the strong coupling scenarios, necessitating the use of a more accurate method for coupling coefficient calculations. Therefore, in this work, we calculate the coupling coefficients of TCFs using the supermode theory with finite element method (FEM) that has higher accuracy than CMT, particularly for the strong coupling TCF. To investigate the origin of the differences between the results obtained by these two methods, the modal field distributions of the supermodes of TCF are simulated and analyzed in detail.

THE COUPLING DYNAMICAL MODELING THEORY OF FLEXIBLE MULTIBODY SYSTEM

Based on the deformation theory of elastic beams, the coupling effect between the coupling displacements of a point on the middle line of beam and large overall motion is presented. The 'coupling matrix library' and Jourdain's variation principle and single direction recursive formulation method are used to establish the general coupling dynamical equations of flexible multibody system. Two typical examples show the coupling effect between coupling displacements and large overall motion on the dynamics of flexible multibody system consisting of beams.

A High-Precision Calculation of Bond Length and Spectroscopic Constants of Hg2 Based on the Coupled-Cluster Theory with Spin-Orbit Coupling

Based on the two-component relativistic effective core potential and matched basis sets cc-pwcvnz-pp （n=Q, 5）, combining the completed basis-set extrapolation of electronic correlation energy and the fourth-order polynomial fitting technique, the bond length and spectroscopic constants of Hg2 are studied by the coupled cluster theory with spin-orbit coupling. Spin-orbit coupling is included in the post Hartree-Fock procedure, i.e., in the coupled- cluster iteration, to obtain more reliable theoretical results. The results show that our theoretical values agree with the experimental values very well and will be helpful to understand the spectral character of Hg2.

Antiplane shear crack in a prestressed elastic medium based on the couple stress theory

A prestressed elastic medium containing a mode-Ⅲcrack is studied by means of the couple stress theory(CST).Based on the CST under initial stresses,a governing differential equation along with a mixed boundary value problem is established.The singularities of the couple stress and force stress near the crack tips are analyzed through the asymptotic crack-tip fields resulting from the characteristic expansion method.To determine their intensity,a hypersingular integral equation is derived and numerically solved with the help of the Chebyshev polynomial.The obtained results show a strong size-dependence of the out-of-plane displacement on the crack and the couple stress intensity factor(CSIF)and the force stress intensity factor(FSIF)around the crack tips.The symmetric part of the shear stress has no singularity,and the skew-symmetric part related to the couple stress exhibits an r^(-3/2)singularity,in which r is the distance from the crack tip.The initial stresses also affect the crack tearing displacement and the CSIF and FSIF.

Multi-mode coupling analysis of a sub-terahertz band planar corrugated Bragg reflector

Planar Bragg reflector operating in the sub-terahertz wavelength installed at the upstream end of a sheet beam back- ward wave oscillator （BWO） is very promising to minimize the whole circuit structure and make it more compact. In this paper, a sub-terahertz wavelength （0.18-0.22 THz） tunable planar Bragg reflector is numerically analyzed by using multi-mode coupling theory （MCT）. The operating mode TE10 and dominant coupling mode TE01 are mainly considered in this theory. Reflection and transmission performance of the reflector are demonstrated in detail and the results, in excellent agreement with the theoretical analysis and simulation, are also presented in this paper. Self- and cross-coupling coefficients between these two modes are presented as well. The reflector behaviors with different Bragg dimensions are discussed and analyzed in the 0.16-0.22 THz range. The analysis in this paper can be of benefit to the design and fabrication of the whole BWO circuit.

Size dependent free vibration analysis of functionally graded piezoelectric micro/nano shell based on modified couple stress theory with considering thickness stretching effect

Higher-order shear and normal deformation theory is used in this paper to account thickness stretching effect for free vibration analysis of the cylindrical micro/nano shell subjected to an applied voltage and uniform temperature rising.Size dependency is included in governing equations based on the modified couple stress theory.Hamilton’s principle is used to derive governing equations of the cylindrical micro/nano shell.Solution procedure is developed using Navier technique for simply-supported boundary conditions.The numerical results are presented to investigate the effect of significant parameters such as some dimensionless geometric parameters,material properties,applied voltages and temperature rising on the free vibration responses.

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CON-TINUUM THEORIES (Ⅱ)—MICROMORPHIC CONTINUUM THEORY AND COUPLE STRESS THEORY

The purpose is to reestablish the balance laws of momentum, angular momentum and energy and to derive the corresponding local and nonlocal balance equations for micromorphic continuum mechanics and couple stress theory. The desired results for micromorphic continuum mechanics and couple stress theory are naturally obtained via direct transitions and reductions from the coupled conservation law of energy for micropolar continuum theory, respectively. The basic balance laws and equations for micromorphic continuum mechanics and couple stress theory are constituted by combining these results derived here and the traditional conservation laws and equations of mass and microinertia and the entropy inequality. The incomplete degrees of the former related continuum theories are clarified. Finally, some special cases are conveniently derived.

Linear and nonlinear torsional free vibration of functionally graded micro/nano-tubes based on modified couple stress theory

The linear and nonlinear torsional free vibration analyses of functionMly graded micro/nuno-tubes （FGMTs） are analytically investigated based on the couple stress theory. The employed non-classical continuum theory contains one material length scale parameter, which can capture the small scale effect. The FGMT model accounts for the through-radius power-law variation of a two-constituent material. Hamilton＇s principle is used to develop the non-classical nonlinear governing equation. To study the effect of the boundary conditions, two types of end conditions, i.e., fixed-fixed and fixed-free, are considered. The derived boundary value governing equation is of the fourthorder, and is solved by the homotopy analysis method （HAM）. This method is based on the Taylor series with an embedded parameter and is capable of providing very good approximations by means of only a few terms, if the initial guess and the auxiliary linear operator are properly selected. The analytical expressions are developed for the linear and nonlinear natural frequencies, which can be conveniently used to investigate the effects of the dimensionless length scale parameter, the material gradient index, and the vibration amplitude on the natural frequencies of FGMTs.

Nonlinearity analysis of piezoelectric micromachined ultrasonic transducers based on couple stress theory

This paper studies the static deformation behavior of a piezoelectric micromachined ultrasonic transducer （PMUT） actuated by a strong external electric field. The transducer membrane consists of a piezoelectric layer, a passive layer and two electrode layers. The nonlinearities of the piezoelectric layer caused by electrostriction under a strong electric field are analyzed. Because the thickness of the transducer membrane is on the microscale, the size dependence of the deformation behavior is evaluated using the couple stress theory. The results show that the optimal ratio of the top electrode diameter and the membrane diameter is around 0.674. It is also found that this optimal value does not depend on any other parameters if the thicknesses of the two electrodes are negligible compared with those of the piezo- electric and passive layers. In addition, the nonlinearities of the piezoelectric layer will become stronger along with the increase of the electric field, which means that softening of the membrane stiffness occurs when a strong external electric field is applied. Meanwhile, the optimal thickness ratio for the passive layer and the piezoelectric layer is not equal to 1.0 which is usually adopted by previous researchers. Because there exists size dependence of membrane deforma-tion, the optimal value of this thickness ratio needs to be greater than 1.0 on the microscale.

Sensitivity analysis of pull-in voltage for RF MEMS switch based on modified couple stress theory

An approximate analytical model for calculating the pull-in voltage of a stepped cantilever-type radio frequency （RF） micro electro-mechanical system （MEMS） switch is developed based on the Euler-Bernoulli beam and a modified couple stress theory, and is validated by comparison with the finite element results. The sensitivity functions of the pull-in voltage to the designed parameters are derived based on the proposed model. The sensitivity investigation shows that the pull-in voltage sensitivities increase/decrease nonlinearly with the increases in the designed parameters. For the stepped cantilever beam, there exists a nonzero optimal dimensionless length ratio, where the pull-in voltage is insensitive. The optimal value of the dimensionless length ratio only depends on the dimensionless width ratio, and can be obtained by solving a nonlinear equation. The determination of the designed parameters is discussed, and some recommendations are made for the RF MEMS switch optimization.

A Size-Dependent Functionally Graded Higher Order Plate Analysis Based on Modified Couple Stress Theory and Moving Kriging Meshfree Method

A size-dependent computational approach for bending,free vibration and buckling analyses of isotropic and sandwich functionally graded(FG)microplates is in this study presented.We consider both shear deformation and small scale effects through the generalized higher order shear deformation theory and modified couple stress theory(MCST).The present model only retains a single material length scale parameter for capturing properly size effects.A rule of mixture is used to model material properties varying through the thickness of plates.The principle of virtual work is used to derive the discrete system equations which are approximated by moving Kriging interpolation(MKI)meshfree method.Numerical examples consider the inclusions of geometrical parameters,volume fraction,boundary conditions and material length scale parameter.Reliability and effectiveness of the present method are confirmed through numerical results.

Size-dependent thermoelastic initially stressed micro-beam due to a varying temperature in the light of the modified couple stress theory

The bending of the Euler-Bernoulli micro-beam has been extensively modeled based on the modified couple stress(MCS)theory.Although many models have been incorporated into the literature,there is still room for introducing an improved model in this context.In this work,we investigate the thermoelastic vibration of a micro-beam exposed to a varying temperature due to the application of the initial stress employing the MCS theory and generalized thermoelasticity.The MCS theory is used to investigate the material length scale effects.Using the Laplace transform,the temperature,deflection,displacement,flexure moment,and stress field variables of the micro-beam are derived.The effects of the temperature pulse and couple stress on the field distributions of the micro-beam are obtained numerically and graphically introduced.The numerical results indicate that the temperature pulse and couple stress have a significant effect on all field variables.

Gravitational constant in f(R) theories of gravity with non-minimal coupling between matter and geometry

We study the effect of the non-minimal coupling between matter and geometry on the gravitational constant in the context of f(R) theories of gravity on cosmic scales. For a class of f(R) models,the result shows that the value of the gravitational constant not only changes over time but also has the dampened oscillation behavior.Compared with the result of the standard ACDM model, the consequence suggests that the coupling between matter and geometry should be weak.

A Spin-orbit Coupling Study on the Quinoline-and Porphyrin-based Photosensitizers

The spin-orbit coupling（SOC） of four porphyrin- and quinoline-based compounds has been studied using Pauli-Breit SOC operator with one- and two-electron terms. The results revealed that the yield of singlet oxygen is affected by the spin-orbit coupling matrix element involving the emitting triplet and the perturbing singlet state. Investigated quinoline-based compounds have more high SOC values than those porphyrin-based compounds due to spin parallel electron pairs of oxygen. The open shell d8 of metal Pt can induce the stronger exchange interactions than the closed shell p6 of metal Mg, resulting in bigger SOC matrix element in quinoline-based Pt complex than in the quinoline-based Mg complex. Simultaneously, potential energy curves of the first excited sate and the first triplet sate have been calculated, which proves that all investigated complexes can induce singlet oxygen. These computational findings support quinolin-based compounds have high singlet oxygen yields and provide a rigorous basis for predicting the probability of singlet oxygen yields in plane-type molecules.

Pressure control method and device innovative design for deep oil in-situ exploration and coring

Deep oil exploration coring technology cannot accurately maintain the in-situ pressure and temperature of samples, which leads to a distortion of deep oil and gas resource reserve evaluations based on conventional cores and cannot guide the development of deep oil and gas resources on Earth. The fundamental reason is the lack of temperature and pressure control in in-situ coring environments. In this paper, a pressure control method of a coring device is studied. The theory and method of deep intelligent temperature-pressure coupling control are innovatively proposed, and a multifield coupling dynamic sealing model is established. The optimal cardinality three term PID (Proportional-Integral-Differential) intelligent control algorithm of pressure system is developed. The temperature-pressure characteristic of the gas-liquid two-phase cavity is analyzed, and the pressure intelligent control is carried out based on three term PID control algorithms. An in-situ condition-preserved coring (ICP-Coring) device is developed, and an intelligent control system for the temperature and pressure of the coring device is designed and verified by experiments. The results show that the temperature-pressure coupling control system can effectively realize stable sealing under temperature-pressure fields of 140 MPa and 150 °C. The temperature-pressure coupling control method can accurately realize a constant pressure inside the coring device. The maximum working pressure is 140 MPa, and the effective pressure compensation range is 20 MPa. The numerical simulation experiment of pressure system control algorithm is carried out, and the optimal cardinality and three term coefficients are obtained. The pressure steady-state error is less than 0.01%. The method of temperature-pressure coupling control has guiding significance for coring device research, and is also the basis for temperature-pressure decoupling control in ICP-Coring.

Stress-induced potential barriers and charge distributions in a piezoelectric semiconductor nanofiber

The performance of a piecewise-stressed ZnO piezoelectric semiconductor nano?ber is studied with the multi-?eld coupling theory. The ?elds produced by equal and opposite forces as well as sinusoidally distributed forces are examined. Speci?c distributions of potential barriers, wells, and regions with effective polarization charges are found. The results are fundamental for the mechanical tuning on piezoelectric semiconductor devices and piezotronics.

Fiber core mode leakage induced by refractive index variation in high-power fiber laser

This paper presents an investigation of specific optical fiber core mode leakage behavior that occurs in high-power double-clad fiber lasers as a result of thermally-induced refractive index variations. A model of the power transfer between the core modes and the cladding modes during thermally-induced refractive index variations is established based on the mode coupling theory. The results of numerical simulations based on actual laser parameters are presented. Experimental measurements were also carried out, the results showed good agreement with the corresponding simulation results.

Independently tunable dual resonant dip refractive index sensor based on metal–insulator–metal waveguide with Q-shaped resonant cavity

A plasmonic resonator system consisting of a metal–insulator–metal waveguide and a Q-shaped resonant cavity is proposed in this paper. The transmission properties of surface plasmon polaritons in this structure are investigated by using the finite difference in time domain(FDTD) method, and the simulation results contain two resonant dips. The physical mechanism is studied by the multimode interference coupled mode theory(MICMT), and the theoretical results are in highly consistent with the simulation results. Furthermore, the parameters of the Q-shaped cavity can be controlled to adjust the two dips, respectively. The refractive index sensor proposed in this paper, with a sensitivity of 1578 nm/RIU and figure of merit(FOM) of 175, performs better than most of the similar structures. Therefore, the results of the study are instructive for the design and application of high sensitivity nanoscale refractive index sensors.

Effects of memory on scaling behaviour of Kardar-Parisi-Zhang equation

In order to describe the time delay in the surface roughing process the Kardar Parisis-Zhang （KPZ） equation with memory effects is constructed and analysed using the dynamic renormalization group and the power counting mode coupling approach by Chattopadhyay [2009 Phys. Rev. E 80 011144]. In this paper, the scaling analysis and the classical self-consistent mode-coupling approximation are utilized to investigate the dynamic scaling behaviour of the KPZ equation with memory effects. The values of the scaling exponents depending on the memory parameter are calculated for the substrate dimensions being 1 and 2, respectively. The more detailed relationship between the scaling exponent and memory parameter reveals the significant influence of memory effects on the scaling properties of the KPZ equation.

Urbanization and eco-environment coupling circle theory and coupler regulation

A near-distance,nonlinear coupling relationship objectively exists between urbanization and the eco-environment.The issue of how to coordinate the relationship between them has become a global strategic and scientific issue.This study reveals the nature,relationship and intensity of coupling between urbanization and the eco-environment from a theoretical perspective.Based on the strength of coupling,relationships can be characterized as having very-low,low,medium,high,very-high or full coupling intensity,which correspond to the categories of random coupling,indirect coupling,loose coupling,cooperative coupling,close coupling,and controlled coupling.Together,these make up an urbanization and eco-environment"coupling tower."This study also develops an urbanization and eco-environment coupling circle theory and generates 45 coupling graphs(including linear,exponential-curve,logarithmic-curve,double exponential-curve and S-curve graphs)per 10°of rotation of the coupling circle,with different graphs corresponding to different urban development stages and development models.Of the various coupling graphs,the S-curve graph is considered the optimum,as it reflects the best interactivity scenario between urbanization and the eco-environment.Using an S-curve coupling graph,and with the help of an SD model and based on the complex one-to-one,one-to-many,and many-to-many relationships between the variables,this study develops the Urbanization and Eco-environment Coupler(UEC).The UEC is composed of 11 regulating elements and 201 variables.If one variable changes,it changes the whole,affecting the structure,function and regulation of the entire coupler.The UEC includes three spatio-temporal scales:static regulation between multiple urbanization areas and eco-environment areas at the same time,dynamic regulation between the same urbanization area and eco-environment area at different times,and dynamic regulation between multiple urbanization areas and eco-environment areas at different times.Regulation gradually promotes evolution from low-level coupling to high-level coupling between urbanization and the eco-environment.