Analytical study of non-linear transport across a semiconductor-metal junction

In this paper we study analytically a one-dimensional model for a semiconductor-metal junction. We study the formation of Tamm states and how they evolve when the semi-infinite semiconductor and metal are coupled together. The non-linear current, as a function of the bias voltage, is studied using the non-equilibrium Green’s function method and the density matrix of the interface is given. The electronic occupation of the sites defining the interface has strong non-linearities as a function of the bias voltage due to strong resonances present in the Green’s functions of the junction sites. The surface Green’s function is computed analytically by solving a quadratic matrix equation, which does not require adding a small imaginary constant to the energy. The wave function for the surface states is given.     

Analysis of a non-linear structure by considering two non-linear formulations

In recent years, modal synthesis methods have been extended for solving non-linear dynamic problems subjected to harmonic excitation. These methods are based on the notion of non-linear or linearized modes and exploited in the case of structures affected by localized non-linearity. Actually, the experimental tests executed on non-linear structures are time consuming, particularly when repeated experimental tests are needed. It is often preferable to consider new non-linear methods with a view to decrease significantly the number of attempts during prototype tests and improving the accuracy of the dynamic behaviour.This article describes two fundamental non-linear formulations based on two different strategies. The first formulation exploits the eigensolutions of the associated linear system and the dynamics characteristics of each localized non-linearity. The second formulation is based on the exploitation of the linearized eigensolutions obtained using an iterative process. This article contains a numerical and an experimental study which examines the non-linear behaviour of the structure affected by localized non-linearities. The study is intended to validate the numerical algorithm and to evaluate the problems arising from the introduction of non-linearities. The complex responses are evaluated using the iterative Newton-Raphson method and for a series of discrete frequencies. The theory has been applied to a bi-dimensional structure and consists of evaluating the harmonic responses obtained using the proposed formulations by comparing measured and calculated transfer functions.     

Observation of fine structure in the phase locking of a non-linear oscillator

Experimental observations of one-dimensional Poincaré maps of a periodically kicked non-linearly oscillating neon lamp are reported. The complete phase-lock behavior of this oscillator, including superstable phase locking and periodic-doubling bifurcations, could easily be understood with the help of these Poincaré maps.     

The pulse response of non-linear systems

The response of a non-linear, non-conservative, single degree of freedom system subjected to a pulse excitation is analysed. A transformation of the displacement variable is effected. The transformation function chosen is the solution of the linear problem subjected to the same pulse. With this transformation the equation of motion is brought into a form where Anderson's ultraspherical polynomial approximation is applicable for the solution of the problem. The method is applied to a cubic Duffing oscillator subjected to various pulses. The pulses considered are cosine, exponentially decaying and the step function. The analytical results are compared with the digital solution obtained on an IBM 360/344 system by using a Runge-Kutta fourth order method. The analytical results compare well with the digital solution.     

A theoretical study of the non-linear response of a periodically driven bistable system

Summary In this paper, a comprehensive theory for the non-linear response of a periodically driven bistable system is presented. Analytic results for the full spectral response, including the signal-to-noise ratio (SNR), are obtained. In addition, the whole hierarchy of escape time distributions is calculated. Theoretical connection between these distributions and the SNR is made, enabling the SNR to be calculated from the knowledge of a single escape time distribution. The theoretical calculations are compared with the results of analogue simulation. Paper presented at the International Workshop ?Fluctuations in Physics and Biology: Stochastic Resonance, Signal Processing and Related Phenomena?, Elba, 5–10 June 1994.     

Surviving conduction symmetries in non-linear response

In linear response, the electric conductance of mesoscopic, two-terminal devices is symmetric with respect to the direction of an external magnetic field. The conductance symmetry, in general, breaks down in the non-linear regime of transport. Here we consider semiconductor quantum dots and show certain symmetries survive in the non-linear conductance with respect to the bias voltage and magnetic field that can be measured.     

拉盖尔-高斯光束的近场矢量结构特征

直接以麦克斯韦方程组的解表征拉盖尔-高斯光束。基于麦克斯韦方程组解的矢量角谱表述和电磁光束的矢量结构理论,利用一些数学技巧导出了拉盖尔-高斯光束的TE项和TM项在近场的解析表达式。利用所导出的公式,在近场描绘了拉盖尔-高斯光束的TE项、TM项及整个光束的光强分布。并对角度依赖分别为余弦和正弦关系的拉盖尔-高斯光束的矢量结构进行了比较,结果显示两者整个光束的光斑完全相似,唯一的区别是子瓣的空间方位不同且两者的内部矢量结构完全不相同。     

拉盖尔-高斯光束的近场矢量结构特征

直接以麦克斯韦方程组的解表征拉盖尔-高斯光束。基于麦克斯韦方程组解的矢量角谱表述和电磁光束的矢量结构理论,利用一些数学技巧导出了拉盖尔-高斯光束的TE项和TM项在近场的解析表达式。利用所导出的公式,在近场描绘了拉盖尔-高斯光束的TE项、TM项及整个光束的光强分布。并对角度依赖分别为余弦和正弦关系的拉盖尔-高斯光束的矢量结构进行了比较,结果显示两者整个光束的光斑完全相似,唯一的区别是子瓣的空间方位不同且两者的内部矢量结构完全不相同。     

Study of the non-linear dynamic response of a rotor system with faults and uncertainties

In this paper, the quantification of uncertainty effects on the variability of the nonlinear response in rotor systems with multi-faults (such as unbalance, asymmetric shaft, bow, parallel and angular misalignments) is investigated. To take account of uncertainties in this kind of nonlinear problem, it is proposed to use the Harmonic Balance Method (HBM) with a polynomial chaos expansion (PCE). The efficiency and robustness of the proposed methodology is demonstrated by comparison with Monte Carlo simulations (MCS) for different kinds and levels of uncertainties.     

Analytical prediction for the optimum operating conditions of SIS mixers

Using Tucker's quantum theory of mixing and a quasi five-frequency approximation proposed by Kerr et al., this paper explores the optimum operating conditions of SIS mixers in the frequency region of 100 to 650 GHz. Four parameters (i.e., R_nC_j product, normal state resistance R_n, RF source admittance (R_rf ^–+jB), and IF load resistance R_if) affecting the performance of an SIS mixer have been investigated. Our results indicate that, independent of the absolute value of R_n, the SIS mixer performance is dominated by R_rf/R_n and R_if/R_n; and that the mixer performance becomes quite insensitive to the R_nC_j product, as the mixer operating frequency goes up to submillimeter wavelengths. Concerning all properties of an SIS mixer, the optimum R_rf/R_n value seems proportional to f^1/n (n2), and the optimum R_if/R_n and jB/G_n values are relatively independent of frequency, about 0.5 to 1.5 and –j0.5 to –j1.0 respectively.On leave from Purple Mountain Observatory, China     

Linear and non-linear response of embedded Na clusters

We investigate Na clusters embedded in Ar matrices. The surrounding Ar atoms are modeled in terms of their dynamical polarizability and the strong electron repulsion. The calibration of the model is discussed. First results for the non-linear optical response of the Na clusters are presented for the test case of Na₈ embedded in Ar ensembles of different sizes. It is shown that blue shift through core repulsion and red shift through dipole polarizability counterweight each other to the end that very little global shift is seen in the spectra. This feature persists to all excitation strengths considered. There are, however, detailed effects, such as for example the Landau fragmentation of the Mie plasmon peak. PACS 36.40.Gk; 36.40.Vz; 31.15.Ew     

A non-linear dynamical response of an electron gas

The quadratic response of an electron gas to an external excitation is given in the self-consistent field framework.     

Graphene characterization: A fully non-linear spring-based finite element prediction

In the present study, a spring-based finite element model is formulated and utilized to predict the stress–strain behavior of single-layer graphene. Generalized force–generalized displacement behavior of the developed nonlinear springs follows the relation between the first derivative of the potential energy and the corresponding bond deformation, describing interatomic interactions. A number of different loading cases are examined in order to predict mechanical properties and characterize the graphene sheet. Predicted Young's and shear moduli, tensile and shear strength, tensile and shear failure strain, etc., under tension, compression and pure shear, are compared to results found in the literature, which are based on numerical, analytical or experimental methodologies. In all the above loading cases the graphene sheet is examined as a virtually orthotropic material, exhibiting different material properties in the armchair and zigzag directions. Different behaviors in tension and compression, as suggested by the modified Morse atomic bond stretching potential, are illustrated by the predicted stress–strain curves.