Fully analytical evaluation of optical gain coefficient in bulk semiconductors in quasi-equilibrium free-carrier approximation

In this letter, a new analytical method is presented to calculate of the semiconductor optical gain coefficient. This method is particularly suitable for theoretical analyses to determine the dependence of semiconductor gain on the total carrier density and temperature in the semiconductor lasers. Also, the optical gain functions for semiconductor optical gain coefficient are presented analytically. The analytical evaluation is verified with numerical methods, which illustrates the accuracy of these obtained analytical expressions.     

Analytical Model of Doppler Spectra of Light Backscattered from Rotating Convex Bodies of Revolution in the Global Cartesian Coordinate System

We present an analytical model of Doppler spectra in backscattering from arbitrary rough convex bodies of revolution rotating around their axes in the global Cartesian coordinate system. This analytical model is applied to analyse Doppler spectra in backseatter from two cones and two cylinders, as well as two ellipsoids of revolution. We numerically analyse the influences of attitude and geometry size of objects on Doppler spectra. The analytical model can give contribution of the surface roughness, attitude and geometry size of convex bodies of revolution to Doppler spectra and may contribute to laser Doppler velocimetry as well as ladar applications.     

Analytical and statistical calculation of gamma dose rate for the accident of losing the shield for Tehran Research Reactor

In this paper we study the analytical and statistical results of estimating the gamma dose rate at pool access floor in TRR when the core shield accidentally decreases to some non-permitted levels. Due to the risk of experimental techniques, we use the analytical and statistical methods. In normal conditions (no risk), the discrepancies between experiment and two methods are justified and it is found that for such problems we have to normalize these methods to experimental results as follows: the analytical method by factor 0.13 and MCNP by 1.7.     

Controlling hyperchaotic complex systems with unknown parameters based on adaptive passive method

The aim of this paper is to study the control of hyperchaotic complex nonlinear systems with unknown parameters using passive control theory.An approach is stated to design the passive controller and estimate the unknown parameters based on the property of the passive system.The feasibility and effectiveness of the proposed approach is demonstrated through its application to the hyperchaotic complex Lü system,as an example.The estimated values of the unknown parameters are calculated.The analytical form of the complex controller is derived and used in the numerical simulation to control the hyperchaotic attractors of this example.Block diagrams of this example using Matlab/Simulink are constructed after and before the control to ensure the validity of the analytical results.Other examples of hyperchaotic complex nonlinear systems can be similarly treated.     

Potential Energy of the Di-nuclear System

We perform the calculation of the nucleus-nucleus interaction potential of the dinuclear system with deformed nuclei. Based on the calculated results by properly treating the double-folding method, some results from the analytical expressions for calculating both the nuclear and the Coulomb interactions are investigated. It is concluded that the analytical formula to calculate the Coulomb interaction by Wong [Phys. Rev. Lett. 31 (1973) 766] can reproduce good double folding results. However the results by the parametrized Morse formula, which are used to calculate the nuclear interaction, greatly deviate from the double folding results, unless the distance of nuclei is adjusted to be shifted to a smaller relative distance determined by the same distance between the nuclear surfaces as one of them pertains to the deformed nuclei. Using the double folding method to calculate the nuclear interaction and employing Wong‘s analytical formula to calculate the Coulomb interaction can keep good precision and can cost much less computation time.     

Performance and analytical modelling of halo-doped surrounding gate MOSFETs

Halo structure is added to sub-100 nm surrounding-gate metal-oxide-semiconductor fieldeffect-transistors （MOS- FETs） to suppress short channel effect. This paper develops the analytical surface potential and threshold voltage models based on the solution of Poisson＇s equation in fully depleted condition for symmetric halo-doped cylindrical surrounding gate MOSFETs. The performance of the halo-doped device is studied and the validity of the analytical models is verified by comparing the analytical results with the simulated data by three dimensional numerical device simulator Davinci. It shows that the halo doping profile exhibits better performance in suppressing threshold voltage roll-off and drain-induced barrier lowering, and increasing carrier transport efficiency. The derived analytical models are in good agreement with Davinci.     

Nonparaxial propagation of a super-Lorentz-Gauss SLGmode beam

Based on the vectorial Rayleigh-Sommerfeld integral formulae,this paper derives the analytical nonparaxial propagation equation of a super-Lorentz-Gauss (SLG) SLG 01 mode beam in free space.The far field expression and the scalar paraxial result are treated with special cases of the general formulae.According to the obtained analytical representation,the nonparaxial propagation properties of the SLG 01 mode beam are illustrated and analysed with numerical examples.This research provides an approach to investigate the propagation of the SLG 01 mode beam within the framework of the nonparaxial regime.     

Analytical expressions of non-relativistic static multipole polarizabilities for hydrogen-like ions

Analytical formulas for the static multipole polarizabilities of hydrogen-like ions are derived by using the analytical wave functions and the reduced Green function and by applying a numerical fitting procedure.Our results are then applied to the studies of blackbody radiation shifts to atomic energy levels at different temperatures.Our analytical results can be served as a benchmark for other theoretical methods.     

Effective-Field Theory for Kinetic Ising Model on Honeycomb Lattice

As an analytical method, the effective-field theory （EFT） is used to study the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field. The effective-field equations of motion of the average magnetization are given for the honeycomb lattice （Z = 3）. The Liapunov exponent A is calculated for discussing the stability of the magnetization and it is used to determine the phase boundary. In the field amplitude ho / ZJ-temperature T/ZJ plane, the phase boundary separating the dynamic ordered and the disordered phase has been drawn. In contrast to previous analytical results that predicted a tricritical point separating a dynamic phase boundary line of continuous and discontinuous transitions, we find that the transition is always continuous. There is inconsistency between our results and previous analytical results, because they do not introduce sufficiently strong fluctuations.     

Approximate Solutions of Perturbed Nonlinear Schroedinger Equations

By applying Lou＇s direct perturbation method to perturbed nonlinear Schroedinger equation and the critical nonlinear SchrSdinger equation with a small dispersion, their approximate analytical solutions including the zero-order and the first-order solutions are obtained. Based on these approximate solutions, the analytical forms of parameters of solitons are expressed and the effects of perturbations on solitons are briefly analyzed at the same time. In addition, the perturbed nonlinear Schroedinger equations is directly simulated by split-step Fourier method to check the validity of the direct perturbation method. It turns out that the analytical results given by the direct perturbation method are well supported by numerical calculations.     

Unconventional Hamilton-type variational principles for analytical mechanics

According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified new way proposed by Luo, the un-conventional Hamilton-type variational principles of holonomic conservative system in analytical mechanics can be established systematically. This unconventional Hamilton-type variational principle can fully characterize the initial-value problem of analytical mechanics, so that it is an important innovation for the Hamilton-type variational principle. In this paper, an important integral relation is given, which can be considered as the expression of the generalized principle of virtual work for analytical mechanics in mechanics. Based on this relation, it is possible not only to obtain the principle of virtual work of holonomic conservative system in analytical mechanics, but also to derive systematically the complementary functionals for three-field and two-field unconventional variational principles, and the functional for the one-field one by the generalized Legendre transformation given in this paper. Further, with this new approach, the intrinsic relationship among various principles can be explained clearly. Meanwhile, the unconventional Hamilton-type variational principles of nonholonomic conservative system in analytical mechanics can also be established systematically in this paper.     

An analytical model for cross-Kerr nonlinearity in a four-level N-type atomic system with Doppler broadening

We present an analytical model for cross-Kerr nonlinear coefficient in a four-level N-type atomic medium under Doppler broadening.The model is applied to87 Rb atoms to analyze the dependence of the cross-Kerr nonlinear coefficient on the external light field and the temperature of atomic vapor.The analysis shows that in the absence of electromagnetically induced transparency(EIT)the cross-Kerr nonlinear coefficient is zero,but it is significantly enhanced when the EIT is established.It means that the cross-Kerr effect can be turned on/off when the external light field is on or off.Simultaneously,the amplitude and the sign of the cross-Kerr nonlinear coefficient are easily changed according to the intensity and frequency of the external light field.The amplitude of the cross-Kerr nonlinear coefficient remarkably decreases when the temperature of atomic medium increases.The analytical model can be convenient to fit experimental observations and applied to photonic devices.     

A Novel Analytical Approach for Multi-Layer Diaphragm-Based Optical Microelectromechanical-System Pressure Sensors

An optical microelectromechanical-system （MEMS） pressure sensor based on multi-layer circular diaphragm is described and analysed by using the proposed novel analytical approach and the traditional transfer matrix method. The analytical expressions of the deflection of multi-layer diaphragm and absolute optical reflectance are derived respectively. The influence of residual stress on the deflection of diaphragm is also analysed. Simulation results given by the finite element method are consistent with the ones which are analysed by using the analytical approach. The analytical approach will be helpful to design and fabricate the optical MEMS pressure sensors with multi-layer diaphragm based on Fabry-Perot interferometry.     

Evolution of Arbitrary States under Fock-Darwin Hamiltonian and a Time-Dependent Electric Field

The method of path integral is employed to calculate the time evolution of the eigenstates of a charged particle under the Fock-Darwin(FD) Hamiltonian subjected to a time-dependent electric field in the plane of the system.An exact analytical expression is established for the evolution of the eigenstates.This result then provides a general solution to the time-dependent Schro¨dinger equation.     

Nonparaxial propagation of a super-Lorentz－Gauss SLG01 mode beam

Based on the vectorial Rayleigh--Sommerfeld integral formulae, this paper derives the analytical nonparaxial propagation equation of a super-Lorentz--Gauss (SLG) SLG₀₁ mode beam in free space. The far field expression and the scalar paraxial result are treated with special cases of the general formulae. According to the obtained analytical representation, the nonparaxial propagation properties of the SLG₀₁ mode beam are illustrated and analysed with numerical examples. This research provides an approach to investigate the propagation of the SLG₀₁ mode beam within the framework of the nonparaxial regime.     

Weakening effect of plastic yielding inception in thin hard coating systems

Hard coatings have been widely applied to enhance tribological performance of mechanical components.However,it was predicted that thin hard coatings may have a weakening effect which could reduce the coating/substrate system’s resistance to plastic yielding compared with the uncoated substrate material.In this paper,analytical simulation is utilized to investigate the origin of weakening effect.The functions of material mechanical properties and coating thickness on the weakening effect are theoretically investigated.Partial-unloading spherical nanoindentation tests are performed on tungsten coated single crystalline silicon and copper to acquire the stress-strain curves and compared with the uncoated cases.The experimental results are in consistence with the analytical solutions,demonstrating the presence of weakening effect.     

On Direct Transformation Approach to Asymptotical Analytical Solutions of Perturbed Partial Differential Equation

In this article, we will derive an equality, where the Taylor series expansion around ε= 0 for any asymptotical analytical solution of the perturbed partial differential equation （PDE） with perturbing parameter e must be admitted. By making use of the equality, we may obtain a transformation, which directly map the analytical solutions of a given unperturbed PDE to the asymptotical analytical solutions of the corresponding perturbed one. The notion of Lie-Bgcklund symmetries is introduced in order to obtain more transformations. Hence, we can directly create more transformations in virtue of known Lie-Bgcklund symmetries and recursion operators of corresponding unperturbed equation. The perturbed Burgers equation and the perturbed Korteweg-de Vries （KdV） equation are used as examples.     

Modeling of the drain-induced barrier lowering effect and optimization for a dual-channel 4H silicon carbide metal semiconductor field effect transistor

A new analytical model to describe the drain-induced barrier lowering(DIBL) effect has been obtained by solving the two-dimensional(2D) Poisson’s equation for the dual-channel 4H-SiC MESFET(DCFET).Using this analytical model,we calculate the threshold voltage shift and the sub-threshold slope factor of the DCFET,which characterize the DIBL effect.The results show that they are significantly dependent on the drain bias,gate length as well as the thickness and doping concentration of the two channel layers.Based on this analytical model,the structure parameters of the DCFET have been optimized in order to suppress the DIBL effect and improve the performance.     

Numerical Investigation of Finite k Effect on Damping Rate of Geodesic Acoustic Mode in Collisionless Plasmas

Numerical method is applied to the investigation of the GAM damping rate with the finite k effects included. It is found that generally the damping rate given by the analytical method is smaller than that given by the numerical method, and the analytical damping rate has good approximation in the high q region （q 〉 4）. The difference between the analytical and numerical damping rates increases with the increasing kpi. However, for the short-wavelength case （kpi = 0.2）, the analytical methods are only good enough around q = 4 because of the slow convergence of Bessel function with the large variable.