Analysis on Far-Field of Slab Waveguide and Its Gaussian Approximation

This paper researches end diffraction of slab waveguide and then matching efficiency between the far-field and its Gaussian approximate field is analyzed leads to a new definition of divergence half-angle. Finally, why the far-field can be approximated by a Gaussian function is presented according to characteristic of beam propagation factor.

Mode-field half-widths of Gaussian approximation for the fundamental mode of two kinds of optical waveguides

This paper analyzes the characteristic of matching efficiency between the fundamental mode of two kinds of optical waveguides and its Gaussian approximate field.Then, it presents a new method where the mode-field half-width of Caussian approximation for the fundamental mode should be defined according to the maximal matching efficiency method. The relationship between the mode-field half-width of the Gaussian approximate field obtained from the maximal matching efficiency and normalized frequency is studied; furthermore, two formulas of mode-field half-widths as a function of normalized frequency are proposed.

Frozen Gaussian Approximation for the Dirac Equation in Curved Space with Application to Strained Graphene

In this paper,we derive the frozen Gaussian approximation(FGA)for computing the solution to the Dirac equation in curved space in the semi-classical regime.The latter equation is used in particular for modeling electronic scattering on strained graphene surfaces.We present numerical comparisons of the Dirac solutions on curved and flat spaces,illustrating the focusing effect of graphene surfaces,as well as qualitative comparisons with a tight-binding model.A CPU-time comparison shows that FGA becomes more efficient than an IMEX pseudospectral method when the semiclassical parameter is small.

The Gaussian approximation for multi-color generalized Friedman’s urn model

The generalized Friedman’s urn model is a popular urn model which is widely used in many disciplines.In particular,it is extensively used in treatment allocation schemes in clinical trials.In this paper,we show that both the urn composition process and the allocation proportion process can be approximated by a multi-dimensional Gaussian process almost surely for a multi-color generalized Friedman’s urn model with both homogeneous and non-homogeneous generating matrices.The Gaussian process is a solution of a stochastic differential equation.This Gaussian approximation is important for the understanding of the behavior of the urn process and is also useful for statistical inferences.As an application,we obtain the asymptotic properties including the asymptotic normality and the law of the iterated logarithm for a multi-color generalized Friedman's urn model as well as the randomized-play-the-winner rule as a special case.

A phase-space formulation and Gaussian approximation of the filtering equations for nonlinear quantum stochastic systems

This paper is concerned with a filtering problem for a class of nonlinear quantum stochastic systems with multichannel nondemolition measurements. The system-observation dynamics are governed by a Markovian Hudson-Parthasarathy quantum stochastic differential equation driven by quantum Wiener processes of bosonic fields in vacuum state. The Hamiltonian and system-field coupling operators, as functions of the system variables, are assumed to be represented in a Weyl quantization form. Using the Wigner-Moyal phase-space framework, we obtain a stochastic integro-differential equation for the posterior quasi-characteristic function （QCF） of the system conditioned on the measurements. This equation is a spatial Fourier domain representation of the Belavkin-Kushner-Stratonovich stochastic master equation driven by the innovation process associated with the measurements. We discuss a specific form of the posterior QCF dynamics in the case of linear system-field coupling and outline a Gaussian approximation of the posterior quantum state.

The Gaussian approximation for generalized Friedman's urn model with heterogeneous and unbalanced updating

The Friedman's urn model is a popular urn model which is widely used in many disciplines.In particular,it is extensively used in treatment allocation schemes in clinical trials.Its asymptotic properties have been studied by many researchers.In literature,it is usually assumed that the expected number of balls added at each stage is a constant in despite of what type of balls are selected,that is,the updating of the urn is assumed to be balanced.When it is not,the asymptotic property of the Friedman's urn model is stated in the book of Hu and Rosenberger(2006) as one of open problems in the area of adaptive designs.In this paper,we show that both the urn composition process and the allocation proportion process can be approximated by a multi-dimensional Gaussian process almost surely for a general multi-color Friedman type urn model with heterogeneous and unbalanced updating.The Gaussian process is a solution of a stochastic differential equation.As an application,we obtain the asymptotic properties including the asymptotic normality and the exact law of the iterated logarithm.

Characteristic Analysis of Diffraction from Restricted Output End Surface of Multiple Quantum Wells Planar Waveguide

Based on Rayleigh-Sommerfeld scalar diffraction formula, analyzed is the diffraction field distribution of the restricted output end surface of multiple quantum wells planar waveguide by slit. Obtained is its analytical expression of field distribution, which permits accurate and effective study on the characteristic of diffraction field from the restricted output end surface of the waveguide by slit. Then, the variation curve of the beam propagation factor M2 versus the slit width is computed by the second moment method. It is useful for understanding the restricted diffraction properties of the multiple quantum wells planar waveguide. When the slit half width is bigger than the core layer's half width, the beam propagation factor M2 value tends to a constant 1.108. Therefore, the corresponding field amplitude distribution is approximated by Gaussian function, and the far field divergence half angle(θ0,G=0.091 8) is calculated by matching efficiency method.

Combined Cumulant and Gaussian Mixture Approximation for Correlated Probabilistic Load Flow Studies:A New Approach

In this paper,a probabilistic load flow analysis technique that combines the cumulant method and Gaussian mixture approximation method is proposed.This technique overcomes the incapability of the existing series expansion methods to approximate multimodal probability distributions.A mix of Gaussian,non-Gaussian,and discrete type probability distributions for input bus powers is considered.Probability distributions of multimodal bus voltages and line power flows pertaining to these inputs are precisely obtained without using any series expansion method.At the same time,multiple input correlations are considered.Performance of the proposed method is demonstrated in IEEE 14 and 57 bus test systems.Results are compared with cumulant and Gram Charlier expansion,cumulant and Cornish Fisher expansion,dependent discrete convolution,and Monte Carlo simulation.Effects of different correlation cases on distribution of bus voltages and line power flows are also studied.

Improved RB-HARQ scheme based on structured LDPC codes

Reliability-based hybrid automatic repeat request （ARQ） （RB-HARQ） is a recently introduced approach to incremental-redundancy ARQ. In RB-HARQ scheme, the bits that are to be retransmitted are adaptively selected at the receiver based on the estimated bit reliability. It could result in significant performance gain but requires huge overhead in the feedback channel. In this study, an improved RB-HARQ scheme （IRB-HARQ） for structured low-density parity-check codes is proposed, which simplifies the comparison operations needed to search the bits to be retransmitted and outperforms the RB-HARQ scheme in consideration of the bit transmission power for the requesting messages on the feedback link. Simulation results show that the IRB-HARQ scheme is more efficient and practical than the RB-HARQ scheme.

Performance analysis of the periodic sequence DSSS system against CW interference

Based on the brief account of the performance analysis result of the direct sequence spread spectrum(DSSS)system against a single tone continuous wave(CW)interference obtained from the traditional standard Gaussian approximation(SGA)hypothesis,the mathematical expression of the interference component of the symbol decision variable in the periodic sequence DSSS system under CW interference was deduced and the actual performance of the periodic sequence DSSS system against CW interference was researched through theoretical analysis and numerical simulations.The results indicate that the interference component of the symbol decision variable in the periodic sequence DSSS system under CW interference operates at a constant level or fluctuate monochromatically,which does not approach the standard Gaussian distribution,and the actual performance of the periodic sequence DSSS system against CW interference is completely different from the analytic result resorted to the standard Gaussian approximation(SGA).The bit error performance is correlative not only with the interference-signal ratio(ISR),the frequency offset and the phase of the CW interference sensitively,but also with the individual spread spectrum code sequence.