Computation of the Reflection Coefficient of a Triangular Semiconductor Prism in a Rectangular Waveguide

In this paper we present a method to solve Maxwell's equations that enables to compute waveguide structure containing a semiconductor triangular prism. The numerical study has showed that the triangular prism in the waveguide has a wider frequency band in comparison with a square rod under equal conditions. The reflection coefficient dependencies on frequency, prism size and its permittivity have been computed. The algorithm and computer programme have been tested and compared with the numerical results and experimental data of the paper [1] with good agreement.     

Rare transition event with self-consistent theory of large-amplitude collective motion

A numerical simulation method, based on Dang et al.’s self-consistent theory of large-amplitude collective motion, for rare transition events is presented. The method provides a one-dimensional pathway without knowledge of the final configuration, which includes a dynamical effect caused by not only a potential but also kinetic term. Although it is difficult to apply the molecular dynamics simulation to a narrow-gate potential, the method presented is applicable to the case. A toy model with a high-energy barrier and/or the narrow gate shows that while the Dang et al. treatment is unstable for a changing of model parameters, our method stable for it.     

Simple design technique for a triangular FBG filter based on a linearly chirped grating

A novel and simple design technique for triangular spectrum response of fibre Bragg grating (FBG) is presented based on a linear chirped grating. It is shown that this method is fast and can give a straightforward solution to meet a design target. The numerical simulation examples verified the effectiveness of the design method. A general approach to design for multichannel triangular spectral responses for FBG filters is proposed, which provides a solution that achieves a minimum change of refractive index for the fibre.     

A nodal discontinuous Galerkin finite element method for nonlinear elastic wave propagation

A nodal discontinuous Galerkin finite element method (DG-FEM) to solve the linear and nonlinear elastic wave equation in heterogeneous media with arbitrary high order accuracy in space on unstructured triangular or quadrilateral meshes is presented. This DG-FEM method combines the geometrical flexibility of the finite element method, and the high parallelization potentiality and strongly nonlinear wave phenomena simulation capability of the finite volume method, required for nonlinear elastodynamics simulations. In order to facilitate the implementation based on a numerical scheme developed for electromagnetic applications, the equations of nonlinear elastodynamics have been written in a conservative form. The adopted formalism allows the introduction of different kinds of elastic nonlinearities, such as the classical quadratic and cubic nonlinearities, or the quadratic hysteretic nonlinearities. Absorbing layers perfectly matched to the calculation domain of the nearly perfectly matched layers type have been introduced to simulate, when needed, semi-infinite or infinite media. The developed DG-FEM scheme has been verified by means of a comparison with analytical solutions and numerical results already published in the literature for simple geometrical configurations: Lamb's problem and plane wave nonlinear propagation.     

A theoretical study of resonant tunneling characteristics in triangular double-barrier diodes

Resonant tunneling characteristics of triangular double-barrier diodes have been investigated systematically in this Letter, using Airy function approach to solve time-independent Schrödinger function in triangular double-barrier structures. Originally, the exact analytic expressions of quasi-bound levels and quasi-level lifetime in symmetrical triangular double-barrier structures have been derived within the effective-mass approximation as a function of structure parameters including well width, slope width and barrier height. Based on our derived analytic expressions, numerical results show that quasi-bound levels and quasi-level lifetime vary nearly linearly with the structure parameters except that the second quasi-level lifetime changes parabolically with slope width. Furthermore, according to our improved transmission coefficient of triangular double-barrier structures under external electric field, the current densities of triangular double-barrier diodes with different slope width at 0 K have been calculated numerically. The results show that the N-shaped negative differential resistance behaviors have been observed in current–voltage characteristics and current–voltage characteristics depend on the slope width.     

On the calculation of the tunnelling probability in a heavily-doped p-n junction

Abstract

The one-dimensional Schrodinger's equation for a triangular potential barrier (appropriate to tunnel diodes) is solved directly to obtain an expression for the probability of tunnelling of an electron through it. The result has been compared with that of Kane and the W.K.B. method. It is concluded that the results based on this calculation predict the same functional dependence of the tunnelling probability on m?, E_g and F as that predicted by earlier methods.     

Numerical Simulation of the Movement of Frenkel–Kontorova Dislocations in Aluminum Single Crystals at Low Temperatures

The motion of Frenkel–Kontorova dislocations in the single crystals of aluminum at low temperatures has been studied, by means of the computer simulation. It is shown that the dislocation movement is realized by the quantum tunneling of the kinks of dislocations through the Peierls barriers. It is shown that the action of the Peierls high barrier is analogous to the action of low temperatures, and if the Peierls barrier overcome, the dislocation moves unevenly, accelerating under the action of the Peierls barrier and slowing down after overcoming the Peierls barrier. Based on the numerical experiment, the mean free path of dislocation, the distance between the Peierls potential barriers and the width of the Peierls barrier are calculated. The computed values correspond to the real values.     

Spectrum of localized states in graphene quantum dots and wires

We developed semiclassical method and show that any smooth potential in graphene describing elongated a quantum dot or wire may behave as a barrier or as a trapping well or as a double barrier potential, Fabry–Perot structure, for 1D Schrödinger equation. The energy spectrum of quantum wires has been found and compared with numerical simulations. We found that there are two types of localized states, stable and metastable, having finite life time. These life times are calculated, as is the form of the localized wave functions which are exponentially decaying away from the wire in the perpendicular direction.     

Noise-Induced Phase Transition: Zero-Dimensional Brownian Particles Varying between Ergodicity and Nonergodicity

We study in phase space a zero-dimensional system of Brownian particles which move in a periodic potential and subject to an internal time derivative Ornstein-Uhlenbeck noise. To resolve the Fokker-Planck equation in such a case, we propose an approximate analytical method. The theoretical predictions exhibit a second order noise-induced nonequilibrium phase transition, which is confirmed by numerical simulation results. The phase transition brings the system from an ergodicity to a nonergodicity phase as the potential barrier height decreases.     

High resolution finite volume scheme for the quantum hydrodynamic equations

The theory of quantum fluid dynamics (QFD) helps nanotechnology engineers to understand the physical effect of quantum forces. Although the governing equations of quantum fluid dynamics and classical fluid mechanics have the same form, there are two numerical simulation problems must be solved in QFD. The first is that the quantum potential term becomes singular and causes a divergence in the numerical simulation when the probability density is very small and close to zero. The second is that the unitarity in the time evolution of the quantum wave packet is significant. Accurate numerical evaluations are critical to the simulations of the flow fields that are generated by various quantum fluid systems.A finite volume scheme is developed herein to solve the quantum hydrodynamic equations of motion, which significantly improve the accuracy and stability of this method. The QFD equation is numerically implemented within the Eulerian method. A third-order modified Osher–Chakravarthy (MOC) upwind-centered finite volume scheme was constructed for conservation law to evaluate the convective terms, and a second-order central finite volume scheme was used to map the quantum potential field. An explicit Runge–Kutta method is used to perform the time integration to achieve fast convergence of the proposed scheme.In order to meet the numerical result can conform to the physical phenomenon and avoid numerical divergence happening due to extremely low probability density, the minimum value setting of probability density must exceed zero and smaller than certain value. The optimal value was found in the proposed numerical approach to maintain a converging numerical simulation when the minimum probability density is 10^?5 to 10^?12. The normalization of the wave packet remains close to unity through a long numerical simulation and the deviations from 1.0 is about 10^?4.To check the QFD finite difference numerical computations, one- and two-dimensional particle motions were solved for an Eckart barrier and a downhill ramp barrier, respectively. The results were compared to the solution of the Schrödinger equation, using the same potentials, which was obtained using by a finite difference method. Finally, the new approach was applied to simulate a quantum nanojet system and offer more intact theory in quantum computational fluid dynamics.     

三角晶格二维光子晶体的横磁模特性

基于平面波展开法,以介电常数分别为1F/m和12F/m的物质构成三角晶格二维光子晶体,改变空气孔半径r与晶格常数a之间的大小,数值模拟得到了三角晶格二维光子晶体横磁模带隙,当r=.4α时形成三处三角晶格二维光子晶体横磁模的带隙,其中最大三角晶格二维光子晶体横磁模带隙出现在0.6766—0.8000Hz,差值为0.1234Hz。研究结论为光子晶体器件的制作提供参考。     

Numerical study of metastability due to tunneling: The quantum string method

We generalize the string method, originally designed for the study of thermally activated rare events, to the calculation of quantum tunneling rates. This generalization is based on the formal analogy between quantum mechanics and statistical mechanics in the path-integral formalism. The quantum string method first locates the minimal action path (MAP), which is a smooth curve connecting two minima of the imaginary-time action in the space of imaginary-time trajectories. From the MAP, the saddle point of the action (called “the bounce”) associated with the exponential factor for barrier tunneling probability is obtained and the pre-exponential factor (the ratio of determinants) for the tunneling rate evaluated using stochastic simulation. The quantum string method is implemented to calculate the bounce and rate of tunneling for the Mueller potential in two dimensions. The quantum problem is much more difficult than the thermally activated barrier crossing problem for the same potential. The model calculations show the string method to be an efficient numerical tool for the study of barrier tunneling in higher dimension, from the determination of the saddle point to the computation of the pre-exponential factor.     

Numerical simulation of a flow past a triangular sail-type blade of a wind generator using the ANSYS FLUENT software package

An air flow past a single triangular sail-type blade of a wind turbine is analyzed by numerical simulation for low velocities of the incoming flow. The results of numerical simulation indicate a monotonic increase in the drag force and the lift force as functions of the incoming flow; empirical dependences of these quantities are obtained.     

Design and analysis of a wideband photonic crystal waveguide with low group-velocity and low dispersion

The slow light propagation in a line waveguide in the two-dimensional triangular photonic crystal has been numerically studied, based on which a wideband photonic crystal waveguide with low group-velocity and low dispersion is proposed. The numerical simulation analysis shows that it is possible to maximize the group index and minimize the group-velocity dispersion in wide bandwidth by increasing the radius of the basic air hole and changing the position of the first two rows of air holes in photonic crysta...     

基于新的五维多环多翼超混沌系统的图像加密算法

本文提出了一种基于新的五维多环多翼超混沌系统的数字图像加密方法.首先,将明文图像矩阵和五条混沌序列分别通过QR分解法分解成一个正交矩阵和一个上三角矩阵,将混沌系统产生的五条混沌序列分别通过LU分解法分解成一个上三角矩阵和一个下三角矩阵,分别将两个上三角矩阵和一个下三角矩阵相加,得到五个离散后的混沌序列;其次,将明文图像矩阵分解出来的正交矩阵与五个混沌序列分解出来的五个正交矩阵相乘,同时把明文图像矩阵分解出来的上三角矩阵中的元素通过混沌序列进行位置乱,再将操作后的两个矩阵相乘;最后,将相乘后的矩阵通过混沌序列进行比特位位置乱,再用混沌序列与其进行按位“异或”运算,得到最终加密图像.理论分析和仿真实验结果表明该算法的密钥空间远大于10^200,密钥敏感性强,能够有效地抵御统计分析和灰度值分析的攻击,对数字图像的加密具有很好的加密效果.     

基于微波工作室的盘荷波导耦合器设计方法

提出了一种新的盘荷波导耦合器数值设计方法; 通过分析Kyhl提出的耦合器调节原理, 将输入阻抗之间的相差关系转换为耦合器输入波导的边界条件关系, 由此 利用Microwave Studio的EigenMode Solver求解本征值问题来实现对耦合器 调谐、调匹配过程的模拟; 并给出一个实例来说明数值计算方法的可行性和可靠性.     

超短沟道MOSFET电势的二维半解析模型

本文根据超短沟道MOSFET的工作原理, 在绝缘栅和空间电荷区引入两个矩形源, 提出了亚阈值下电势二维分布的定解问题. 通过半解析法和谱方法相结合, 首次得到了该定解问题的二维半解析解, 解的结果是一个特殊函数, 为无穷级数表达式. 该模型的优点是避免了数值分析时的方程离散化, 表达式不含适配参数、运算量小、精度与数值解的精度相同, 可直接用于电路模拟程序. 文中计算了沟道长度是45—22 nm的MOSFET电势、表面势和阈值电压. 结果表明, 新模型与Medici数值分析结果相同. 关键词： 半解析法 电势 阈值电压 MOSFET     

Electrostatic field calculation in air gaps with a transverse layer of dielectric barrier

In this paper the influence of transverse layer of dielectric barrier to the electrostatic field strength of air gaps using a hyperbolic needle-to-plane configuration is investigated. A three dimensional field problem is presented for simulating the electrostatic field in the air gap. This is achieved by using the charge simulation method. Group of ring charges are used to simulate the needle surface. A genetic algorithm is used for optimum number, location, dimension and value of simulating ring charges. The used needle tip radius was 8 μm while the gap spacing varied from 0.3 cm to 50 cm. The optimum barrier position minimizes the maximum electrostatic field and the electric energy density at the needle tip and consequently maximizes the required breakdown value. The simulation result has been compared with available experimental observations. A good agreement is found between the numerical and experimental data.     

INPUT FORCES ESTIMATION OF BEAM STRUCTURES BY AN INVERSE METHOD

An on-line recursive inverse method to estimate the input forces of beam structures is presented. The inverse method is based on the Kalman filter and a recursive least-squares algorithm. The filter models the system dynamics in a linear set of state equations. The state equations of the beam structures were constructed using the finite element method. The practicability and accuracy of the estimation method were examined with numerical simulations from which the input forces of a cantilever beam with a lumped mass on the free end were estimated from the output responses. In the numerical experiments, the cantilever beam was subjected to five types of input forces, i.e., sinusoidal, triangular impulse, rectangular impulse, a series of impulses and random. The simulation results show that the inverse method has an excellent performance to estimate the input forces of beam structural systems from the noisy measurements.     

Controllable Goos-Hänchen shift in graphene triangular double barrier

We study the Goos-Hänchen (GH) shifts for Dirac fermions in graphene scattered by a triangular double barrier potential. The massless Dirac-like equation was used to describe the scattered fermions by such potential configuration. Our results show that the GH shifts is affected by the geometrical structure of the double barrier. In particular the GH shifts change sign at the transmission zero energies and exhibit enhanced peaks at each bound state associated with the double barrier when the incident angle is less than the critical angle associated with total reflection.