Probability Density Function of the Output Current of Cascaded Multiplexer/Demultiplexers in Transparent Optical Networks

The influence of the concatenation of arbitrary optical multiplexers/demultiplexers (MUX/DEMUXs) on the probability density function (PDF) of the output current of a transparent optical network is assessed. All PDF results obtained analytically are compared with estimates from Monte Carlo simulation and an excellent agreement is achieved.

The non-Gaussian behavior of the PDFs, previously reported by other authors for square-law detectors, is significantly enhanced with the number of nodes increase due to the noise accumulation along the cascade of MUX/DEMUXs. The increase of the MUX/DEMUXs bandwidth and detuning also enhances the PDFs non-Gaussian behavior. The PDF shape variation with the detuning depends strongly on the number of nodes.

Explanations for the Gaussian approximation (GA) accuracy on the assessment of the performance of a concatenation of optical MUX/DEMUXs are also provided. For infinite extinction ratio and tuned MUX/DEMUXs, the GA error probabilities are, in general, pessimistic, due to the inaccurate estimation of the error probability for both bits. For low extinction ratio, the GA is very accurate due to a balance between the error probabilities estimated for the bits “1” and “0.” With the detuning increase, the GA estimates can become optimistic.     

Cascade-like and scaling behavior of wind velocity increments in the atmospheric surface layer

By using a large amount of data collected in the atmospheric surface layer, we analyze the probability density functions (PDFs), the probability of return and the moments of wind velocity increments. Results show that the PDFs change from the non-Gaussian long-tailed distributions to Gaussian with the increase of time scales. This is similar to what has been observed and interpreted as an indication of cascade in the fully developed homogeneous and isotropic turbulence. Besides, both the probability of return and the moments are found to be scaling with time scales. We then compare above results with the truncated Lévy flights and the log-normal PDF model. It is found that although both models show the cascade-like behavior in the PDFs and the scaling behavior in the probability of return and the moments under some conditions, they are not good enough for quantitatively describing the random process of wind velocity increments.     

Accuracy of Gaussian Approach for the Performance Evaluation of Direct-Detection Receiver with Partially Polarized Noise

Abstract

We investigate the accuracy of a Gaussian approach (GA) developed to estimate the performance of a direct-detection optical receiver with arbitrary optical and electrical filtering and in the presence of partially polarized noise due to polarization-dependent loss (PDL). The accuracy is assessed by comparison of the performance estimates obtained from the GA with the estimates obtained from a rigorous method (RM) based on the calculation of the moment-generating function of the current at the optical receiver output.

We show that the GA has a good accuracy when considering the variation of the optical filter bandwidth, extinction ratio, degree of polarization of the noise (DOP), and angle between signal and noise polarizations. However, it fails to predict the receiver sensitivity within 2 dB of the RM when DOP is greater than 0.7 and signal and noise polarizations are orthogonal in the Jones space.

Nevertheless, it is shown that the GA provides receiver sensitivity estimates with good accuracy in most cases of long-haul optical communication systems influenced by PDL, where the typical average DOP is below 0.15. Due to its simplicity, shorter computation time, and good accuracy, the GA is a good tool to assess the performance of such optical systems.     

New results in applied scattering theory: the physical-statistics approach,including strong multiple scatter versus classical statistical-physical methods* and the Born and Rytov approximations versus exact strong scatter probability distributions

Abstract

In order to carry out effective signal processing for signal detection and estimation in scatter-dominated environments, it is necessary to obtain the needed probability distributions and probability densities (PDFs) of the received scatter. In general, the received scatter is non-Gaussian and often strongly so. It is also dominated by multiple-scatter contributions. This is particularly the case for (radar) scatter off random interfaces at small angles, e.g.ocean wave surfaces and terrain, as well as acoustically (sonar) off the ocean surface and bottom. For ‘classical’ theory, based on statistical-physical (S-P) models and methods, the analytical construction of the required PDFs is beyond the general reach of S-P theory.

The present paper reviews, amplifies and extends with new material the author's recently developed physical-statistical (P-S) alternative equivalent to classical (S-P) formulations. Here the fundamental innovation, starting with the basic Langevin equation of propagation in operational form, is to replace the explicit physical model, including boundary and initial conditions, with a purely statistical model based on a counting functional representation of the scattering process. A decomposition principle (DP) establishes the independence of different (k≥1) orders of multiple scatter. This in turn leads to the application of Poisson statistics, from which the characteristic functions of each scatter order and their totality can then be constructed. The appropriate Fourier and Hilbert transforms next provide the desired (first-order) PDFs and exceedance probabilities (EPs).

Characteristic two-scale environments are next considered, in which the scattering ensemble is accordingly modulated slowly vis-á-vis the more rapidly decorrelating local scatter. For this it is shown that the modulation effect is physically well modelled by a Γ-PDF. The result is the well known Jakeman K-distribution. In addition, when there are a few ‘large’ scatterers (e.g.breaking waves, bubble patches, irregular terrain, etc), the author's canonical classA non-Gaussian noise model is indicated and results in the new KA-PDF. The latter is also a common phenomenon, as shown by sample data from radar and sonar experiments, and is well replicated by theory. Both ‘single-look’ and ‘multiple-look’ results are developed for the first-order PDFs and exceedance probabilities of the normalized envelope sums ?_L(=∑_l?_l) under I.i.d.conditions. A number of equivalent analytic methods for evaluating their integral forms are also developed for the more complex cases including coherent components (signals) and accompanying ambient noise.

Finally, using the classical operational form of the Langevin equation for the scattered field, one can readily show that the (nonlinear) Rytov approximation (～ exp ψ₁) contains all orders (k≥1) of scatter versus the weak-scatter Born approximation, which is linear and limited to single scatter (k=1). Furthermore, it is seen that the Rytov approximation is a quasi-weak approximation, since its magnitude is limited to |ψ₁|?2, but is still better than the Born approach, as expected. Under these conditions the Rytov approximation supports a log-normal (first-order) PDF.

The paper concludes with a concise comparison of the various capabilities of the P-S and classical S-P approaches to scattering phenomena, along with the scope of the resulting PDFs in describing clutter and reverberation.     

155~Mb/s——10~Gb/s combined FSK-IM/optical label-packet modulation signals 100~km transmission over standard single mode fiber using mid-span spectral inversion by four-wave mixing in an SOA

This paper introduces the mid-span spectral inversion by four-wave mixing in a commercially available semiconductor optical amplifier (SOA) with a length of about 1.5~mm to optical label switching network based on combined frequency shift keying (FSK)-intensiy modulation (IM)/optical label-packet modulation to overcome the dispersion limitation of fiber. The 155~Mb/s--10~Gb/s combined FSK/IM signal is experimentally transmitted over a 100~km standard single mode fiber. 10^-10 and 10⁹ BER (bit error ratio), or even better, is achieved for the FSK label and IM packet, respectively. The -19~dB power conversion efficiency is obtained for -1~nm wavelength detuning.     

Cooling rate dependence and local structure in aluminum monatomic metallic glass

Abstract

The local atomic structure in aluminium monatomic metallic glass is studied using molecular dynamics simulations combined with the embedded atom method (EAM). We have used a variety of analytical methods to characterise the atomic configurations of our system: the Pair Distribution Function (PDF), the Common Neighbour Analysis (CNA) and the Voronoi Tessellation Analysis. CNA was used to investigate the order change from liquid to amorphous phases, recognising that the amount of icosahedral clusters increases with the decrease of temperature. The Voronoi analysis revealed that the icosahedral-like polyhedral are the predominant ones. It has been observed that the PDF function shows a splitting in the second peak, which cannot be attributed to the only ideal icosahedral polyhedron 〈0, 0, 12, 0〉, but also to the formation of other Voronoi polyhedra 〈0, 1, 10, 2〉 . Further, the PDFs were then integrated giving the cumulative coordination number in order to compute the fractal dimension (d_f).     

Probability distribution functions for a single-particle vibrating in one dimension: experimental study and theoretical analysis

We consider the form of the rebound velocity, ν₀, particle velocity, ν, and height, h, probability density functions (PDFs) for the one-dimensional motion of a single particle on a sinusoidally oscillating base. The motion is considered in the limit of high excitation (vibration frequency ⪢ collision rate). Experimentally, we find that these PDFs are well-approximated by P_ν0(ν₀) ∞ ν₀ exp(− αν₀²), a Gaussian P_ν(ν) ∞ exp(− αν²) and a Boltzmann-type function P_h(h) ∞ exp(− 2αgh), where α is a constant and g is the acceleration due to gravity. We develop an analytical model which accurately predicts the general form for the rebound velocity PDF; the other two PDFs are then analytically shown to follow as a consequence. Scaling laws for the particle granular temperature with peak base velocity and particle-base restitution coefficient, determined from previous work, can also be predicted from the PDF. A fine scale “spiky” structure in the rebound velocity PDF is found, using numerical simulations, to be a consequence of resonance phenomena between the particle and vibrating base. Good agreement between scaling laws from the theory and simulation is found but insufficient data is obtainable to derive accuracy exponents experimentally.     

X‐ray pair distribution function analysis of nanostructured materials using a Mythen detector

Total scattering from nanocrystalline materials recorded on the Australian Synchrotron powder diffraction beamline has been analysed to produce atomic pair distribution functions (PDFs) for structural analysis. The capability of this beamline, which uses the massively parallel Mythen II detector, has been quantified with respect to PDF structure analysis. Data were recorded to a wavevector magnitude, Q, of 20.5 Å^?1, with successful PDFs obtained for counting times as short as 10 s for crystalline LaB₆ and 180 s for nanocrystalline (47 Å) anatase. This paper describes the aspects of a PDF experiment that are crucial to its success, with reference to the outcomes of analysis of data collected from nanocrystalline TiO₂ and microcrystalline LaB₆ and IrO₂.     

10 Gb/s Reconfigurable Optical Logic Gate Using a Single Hybrid-Integrated SOA-MZI

Abstract

A novel reconfigurable Boolean device based on a single Mach-Zehnder interferometer with semiconductor optical amplifiers is demonstrated at 10 Gb/s using intensity return-to-zero modulated signals. The experimental results show that the device can be dynamically reconfigured to operate as a logic XOR, AND, OR, and NOT gate using optical switches. By properly adjusting the input powers, an extinction ratio higher than 10 dB may be obtained. The potential of integration of this architecture makes it an interesting approach in photonic computing and optical signal processing.     

Fractality feature in incompressible three-dimensional magnetohydrodynamic turbulence

Direct Numerical Simulation (DNS) of decaying isotropic 3D magnetohydrodynamic (MHD) turbulence based on the 10243-modes in a periodic box is used to study the statistical properties of turbulence. In this paper, the presence of intermittency in MHD turbulence is investigated through the analysis of the Probability Distribution Function (PDF) for Elsässer fields and total energy fluctuations. We observe that the PDFs of the Elsässer fields fluctuations display a strong non-Gaussian behavior at small scale, which can be ascribed to multifractality feature, while the PDFs of the total energy fluctuations have the same shape over all observed scales and are monofractal. The PDFs have stretched exponential tail and satisfy the function P(|δX|) ～ exp(?A|δX| ^μ ). Numerically, we extract the exponent μ and find that it is constant for monofractal behavior as the length scale varies. To check the notion of self-similarity in the respective fluctuation, we apply the compensated structure functions.     

Anomalous diffusion in silo drainage

The silo discharge process is studied by molecular dynamics simulations. The development of the velocity profile and the probability density function for the displacements in the horizontal and vertical axis are obtained. The PDFs obtained at the beginning of the discharge reveal non-Gaussian statistics and superdiffusive behaviors. When the stationary flow is developed, the PDFs at shorter temporal scales are non-Gaussian too. For big orifices a well-defined transition between ballistic and diffusive regime is observed. In the case of a small outlet orifice, no well-defined transition is observed. We use a nonlinear diffusion equation introduced in the framework of non-extensive thermodynamics in order to describe the movements of the grains. The solution of this equation gives a well-defined relationship (γ= 2/(3-q)) between the anomalous diffusion exponent γ and the entropic parameter q introduced by the non-extensive formalism to fit the PDF of the fluctuations.     

相位编码光码分多址系统中的非高斯分析方法

随着相位编解码器关键技术的突破,精确分析相位编码光码分多址(OCDMA)系统误码率性能显得十分必要。为了精确分析相位编码光码分多址系统误码率性能,提出了一种基于判决变量的矩母函数和鞍点近似的非高斯近似方法,该方法能够精确考虑多址干扰、散粒噪声、热噪声各自的统计特性和相互间的非加性关系。比较了高斯近似、精确计算和文中所提出方法在分析相位编码系统误码率时的计算精度和复杂度,结果证明该分析方法具有分析精度高、计算复杂度低的优点。     

Prediction of local extinction and re-ignition effects in non-premixed turbulent combustion using a flamelet/progress variable approach

The flamelet/progress variable approach (FPVA) has been proposed by Pierce and Moin as a model for turbulent non-premixed combustion in large-eddy simulation. The filtered chemical source term in this model appears in unclosed form, and is modeled by a presumed probability density function (PDF) for the joint PDF of the mixture fraction Z and a flamelet parameter λ. While the marginal PDF of Z can be reasonably approximated by a beta distribution, a model for the conditional PDF of the flamelet parameter needs to be developed. Further, the ability of FPVA to predict extinction and re-ignition has also not been assessed. In this paper, we address these aspects of the model using the DNS database of Sripakagorn et al. It is first shown that the steady flamelet assumption in the context of FPVA leads to good predictions even for high levels of local extinction. Three different models for the conditional PDF of the flamelet parameter are tested in an a priori sense. Results obtained using a delta function to model the conditional PDF of λ lead to an overprediction of the mean temperature, even with only moderate extinction levels. It is shown that if the conditional PDF of λ is modeled by a beta distribution conditioned on Z, then FPVA can predict extinction and re-ignition effects, and good agreement between the model and DNS data for the mean temperature is observed.     

Dispersion Robustness of Millimeter Waves Generated by Up-Conversion Strategies

Abstract

The performance degradation caused by transmission along dispersive single-mode fibers of optically generated millimeter-wave signals using up-conversion is theoretically assessed and validated by numerical simulation. Up-conversion techniques based on optical double sideband, optical single sideband, and optical carrier suppression are considered. The generation of 60 GHz by frequency tripling using the optical single sideband is shown to be particularly tolerant to the fiber dispersion. The practical imbalance of Mach-Zehnder modulators is taken into account for optical carrier suppression modulation, where the finite extinction ratio is found to increase tolerance to fiber dispersion.     

Flexible single molecule simulation of reaction–diffusion processes

An algorithm is developed for simulation of the motion and reactions of single molecules at a microscopic level. The molecules diffuse in a solvent and react with each other or a polymer and molecules can dissociate. Such simulations are of interest e.g. in molecular biology. The algorithm is similar to the Green’s function reaction dynamics (GFRD) algorithm by van Zon and ten Wolde where longer time steps can be taken by computing the probability density functions (PDFs) and then sample from the distribution functions. Our computation of the PDFs is much less complicated than GFRD and more flexible. The solution of the partial differential equation for the PDF is split into two steps to simplify the calculations. The sampling is without splitting error in two of the coordinate directions for a pair of molecules and a molecule-polymer interaction and is approximate in the third direction. The PDF is obtained either from an analytical solution or a numerical discretization. The errors due to the operator splitting, the partitioning of the system, and the numerical approximations are analyzed. The method is applied to three different systems involving up to four reactions. Comparisons with other mesoscopic and macroscopic models show excellent agreement.     

Accuracy of Gaussian Approach for the Performance Evaluation of Direct-Detection Receiver with Partially Polarized Noise

We investigate the accuracy of a Gaussian approach (GA) developed to estimate the performance of a direct-detection optical receiver with arbitrary optical and electrical filtering and in the presence of partially polarized noise due to polarization-dependent loss (PDL). The accuracy is assessed by comparison of the performance estimates obtained from the GA with the estimates obtained from a rigorous method (RM) based on the calculation of the moment-generating function of the current at the optical receiver output.

We show that the GA has a good accuracy when considering the variation of the optical filter bandwidth, extinction ratio, degree of polarization of the noise (DOP), and angle between signal and noise polarizations. However, it fails to predict the receiver sensitivity within 2 dB of the RM when DOP is greater than 0.7 and signal and noise polarizations are orthogonal in the Jones space.

Nevertheless, it is shown that the GA provides receiver sensitivity estimates with good accuracy in most cases of long-haul optical communication systems influenced by PDL, where the typical average DOP is below 0.15. Due to its simplicity, shorter computation time, and good accuracy, the GA is a good tool to assess the performance of such optical systems.     

All-optical error-bit amplitude monitor based on NOT and AND gates in cascaded semiconductor optical amplifiers

This paper proposes and simulates a novel all-optical error-bit amplitude monitor based on cross-gain modulation and four-wave mixing in cascaded semiconductor optical amplifiers （SOAs）, which function as logic NOT and logic AND, respectively. The proposed scheme is successfully simulated for 40 Gb/s return-to-zero （RZ） signal with different duty cycles. In the first stage, the SOA is followed by a detuning filter to accelerate the gain recovery as well as improve the extinction ratio. A clock probe signal is used to avoid the edge pulse-pairs in the output waveform. Among these RZ formats, 33% RZ format is preferred to obtain the largest eye opening. The normalized error amplitude, defined as error bit amplitude over the standard mark amplitude, has a dynamic range from 0.1 to 0.65 for all RZ formats. The simulations show small input power dynamic range because of the nonlinear gain variation in the first stage. This scheme is competent for nonreturn-to-zero format at 10Gb/s as well.     

Linear and nonlinear optical response of MgxZn1−xO: A density functional study

Total and partial density of states, frequency dependent complex refractive index including extinction coefficient, optical conductivity and transmission of Mg_xZn_1−xO (0≤x≤1) in rocksalt and wurtzite phases are calculated using full potential linearized augmented plane wave (FP-LAPW) method. The real part of refractive index decreases while the extinction coefficient, optical conductivity and transmission for rocksalt phase increases with the increase in Mg concentration. In wurtzite phase, ordinary and extraordinary indices decrease while extinction coefficient, optical conductivity and transmission increase in parallel as well as perpendicular to c-axis with the increase in the Mg concentration.     

QCD analysis of CMS W+ charm measurements at LHC with s~(1/2)=7 TeV and implications for strange PDF

We calculate cross-sections and cross-section ratios of a charm quark production in association with a W gauge boson at next-to-leading order QCD using MadGraph and CTIONNLO,CT14 NNLO,and MSTW2008 NNLO PDFs.We compare the results with measurements from the CMS detector at the LHC at a center-of-mass energy of 7 TeV.Moreover,we calculate absolute and normalized differential cross-sections as well as differential cross-section ratios as a function of the lepton pseudorapidity from the W boson decay.The correlation between the CT14 NNLO PDFs and Predictions for W+charm data are studied as well.Furthermore,by employing the error PDF updating method proposed by the CTEQ-TEA group,we update CT14 NNLO PDFs,and analyze the impact of CMS 7 TeV W+charm production data to the original CT14 NNLO PDFs.By comparison of the g(x,Q),s(x,Q),u(x,Q),d(x,Q),u(x,Q),and d(x,Q) PDFs at Q=1.3 GeV and Q=100 GeV for the CT14 NNLO and CT14 NNLO+Wc,we see that the error band of the s(x,Q) PDF is reduced in the region x 0.4,and the error band of g(x,Q) PDF is also slightly reduced at region 0.01 x 0.1.     

The performance of in situ adaptive tabulation in computations of turbulent flames

This paper presents a detailed characterization of the local and global errors associated with the in situ adaptive tabulation (ISAT) algorithm, which is used in conjunction with a transported PDF method. Calculations of a non-premixed turbulent methane/air piloted jet flame (Sandia flame D) using a skeletal chemical mechanism were performed using ISAT coupled with the computational fluid dynamics (CFD) code FLUENT. The three strategies implemented in ISAT for the growing of the ellipsoids of accuracy (EOAs) are discussed, and the cumulative distribution function (CDF) of the local error is presented for each of the three growing strategies. Computations are also performed to characterize the global error in the ISAT/PDF calculation. The computations used to characterize the global error were performed in parallel to achieve substantial savings in computational time.

In general the local error is well controlled, but there is a small probability of relatively large errors. Results from the investigation suggest that large retrieve errors are due to the region of accuracy (ROA) being non-convex, where the ROA is the connected region for which the error does not exceed the error tolerance, ?_tol. The global error in ISAT is found to be small compared to statistical error for ?_tol ≤ 10^?4, and is found to vary linearly with ?_tol.