The exponential probability density function and concentration fluctuations in smoke plumes

Two-dimensional large-eddy simulations of bluff-body stabilized flames of methane and propane, exhibiting significant finite-rate chemistry effects, are presented. A partial equilibrium/two-scalar exponential probability density function (PDF) combustion submodel is applied at the subgrid level. Subgrid scale motions are modelled with a first-order closure employing an anisotropic subgrid eddy-viscosity and two equations for the subgrid turbulent kinetic and scalar energies. Statistical independence of the joint PDF scalars is avoided and the necessary moments are obtained from an extended scale-similarity assumption. Extinction is accounted for by comparing the local turbulent Damköhler number against a ‘critical’ local limit related to the Gibson scalar scale and the reaction zone thickness in mixture fraction space. The post-extinction regime is modelled via a Lagrangian transport equation for a reactedness progress variable which follows a linear deterministic relaxation to its mean value (interaction by exchange with the mean model; IEM).Comparisons between simulations and measurements suggested the ability of the adopted methodology to represent the experimental variations in the momentum and scalar fields at conditions close to the lean or the rich blow-out limit. Favourable agreement was achieved in the calculation of the recirculation lengths and the peak temperature and turbulence levels in the near-wake region. Significant experimental trends, such as the suppression of the large-scale organized motions in the developing wake at low and medium fuel injection rates, and the re-emergence of the quasi-periodic shedding activity close to the lean limit, were also reproduced. Quantitative discrepancies increased in the prediction of major species, but the measured trends due to the effects of partial extinction were adequately recovered.

The paper proposes a new variational Bayesian algorithm for l 1 -penalized multivariate regression with attribute-distributed data. The algorithm is based on the variational Bayesian version of the SAGE algorithm that realizes a training of individual agents in a distributed fashion and sparse Bayesian learning (SBL) with hierarchical sparsity prior modeling of the agent weights. The SBL introduces constraints on the weights of individual agents, thus reducing the effects of overfitting and removing/suppressing poorly performing agents in the ensemble estimator. The l 1 constraint is introduced using a product of a Gaussian and an exponential probability density function with the resulting marginalized prior being a Laplace pdf. Such a hierarchical formulation of the prior allows for a computation of the stationary points of the variational update expressions for prior parameters, as well as deriving conditions that ensure convergence to these stationary points. Using synthetic data it is demonstrated that the proposed algorithm performs very well in terms of the achieved MSE, and outperforms other algorithms in the ability to sparsify non-informative agents, while at the same time allowing distributed implementation and flexible agent update protocols.

The performance of various discrete adaptive delta modulation (ADM) systems in the presence of random signal input is analyzed. The ADM systems considered are (a) Winkler system, (b) Abate (1967) system, (c) Bosworth and Candy (1968) system, and (d) Tazaki system (1977). It is assumed that the input random signal has a slope which varies randomly having Gaussian, Rayleigh and exponential probability density function (PDF) and has rectangular and triangular power spectral density (PSD). For an input random signal with specific PSD and PDF of its slope, the SNR has been calculated and plotted against the signal power. A performance evaluation has been made and summarized for the four systems above. >

This study aims to assess the marine hydrodynamics and the potential power of sea currents by simulating the probability distribution functions of the sea current velocity values. For this aim, hourly sea current velocity and direction data measured from the Çanakkale (Turkey) measurement station in the North Aegean Sea were used. These data were measured during two separate periods: January 1 – March 24, 2017, and March 25 – December 31, 2019. First, the vertical structure of the sea currents up to 50 m depth was determined. Then, frequency distributions of hourly sea current velocities were modeled by using the Weibull, Rayleigh, and Exponential probability density functions. According to the results obtained at 5, 10, 20, 30, 40, and 50 m depths below the sea surface level, the annual sea current velocity was 28.8 ± 0.395, 26.1 ± 0.388, 19.4 ± 0.339, 16.1 ± 0.324, 17.5 ± 0.344, and 24.7 ± 0.622 cm/s, respectively, in this sea. Furthermore, the annual sea current power potential was calculated as 30.0, 25.4, 15.0, 12.2, 15.0, and 88.2 W/m2 for 5, 10, 20, 30, 40, and 50 m depths, respectively. The results demonstrated that the Weibull distribution model was the best fit for the sea current velocity in this sea.

Software maintenance phase involves modifying and making changes to software due to requirements changes and/or defects reported by users. At this phase, when defects are uncovered, users will inform the problem to software maintenance team. The team has to provide the users the estimated fixing time and then fix the errors. Fault reparation/fixing time of different kinds of errors may be varied due to fault types and program complexity. In this research, an approach to estimate fault reparation time is proposed. The exponential probability density function is mainly used to construct the estimation model. An evaluation of the approach is present by applying the approach to open source software projects. A comparison of fault reparation time estimation between considering fault types and without fault types is reported.

The paper deals with assessing blur amount in images. Blur is a common artefact that attenuates the high frequency components of an image. The main idea turns on analysing the frequency response at transitions through resolutions. To achieve that, the histogram of the multiresolution DCT coefficients is modelled by using an exponential probability density function (pdf). The steepness of the pdf is used as a cue to characterize the blur effect. Faithful scores are obtained while testing the proposed approach on five image collections. The proposed measure is validated on the JPEG2000 lossy compression algorithm and the Lucy-Richardson iterative deblurring approach.

A method for modeling the effects of finite-rate chemistry such as partial extinctions and reignitions is developed and used to compute turbulent CO/H2/N2 or CH4-air-piloted jet diffusion flames close to extinction. The method is combined with a two-dimensional Large Eddy Simulation procedure employing a partial equilibrium/two-scalar exponential Probability Density Function (PDF) combustion submodel applied at the subgrid scale (SGS) level. Subgrid motions are modeled with a first-order closure utilizing an anisotropic subgrid eddy-viscosity and two equations for the subgrid scale turbulent kinetic and scalar energies. Statistical independence of the joint PDF scalars is here avoided and the required moments are obtained from an extended scale-similarity assumption. Extinction is determined by comparing the local Damkohler number against a ‘critical’ local limit related to the Gibson scalar scale and the reaction zone thickness. The post-extinction regime is treated with a reactedness progress variable computed from a Lagrangian transport equation and a two-scalar reacledness-mixture fraction presumed PDF. Comparisons with well documented turbulent flame data suggested the ability of the presented methodology to describe many experimental trends and variations of the momentum and reactive scalar mixing fields at flame conditions close to extinction.

In this paper the mean time to acquire a stationary target by n stationary imaging sensors is computed using probability theory by making use of the well established result that the detection time for a single imaging sensor is a random variable from an exponential probability density function. Each imaging sensor is characterized by a separate P∞ value which describes the probability an observer using that sensor will eventually acquire the target and a separate t value which describes the mean time to acquire the target using that sensor. There is no restriction on the wavelength band used by the imaging sensor. There are no empirical constants in the model presented here and the results are in agreement with and generalize previously published equations. The newly developed equations have been verified by numerical simulations and also yield the expected mean detection time for all limiting values of the input parameters. The code used in the numerical simulations is exhibited. For any given scenario, the separate τ observer-sensor-target parameters P∞ and t can be estimated using the NV-IPM model or measured in perception experiments. Thus the input parameters needed by the model are generally available. Comparing results presented here with results from war game simulations such as OneSAF may improve the quality of both products.

This article involves the study of a multiple finite source queueing model with a single server and dynamic, nonpreemptive priority service discipline. The input to the queue is comprised of customers from multiple finite sources. The time which the customers spend at the corresponding sources are exponentially distributed. The service times of the customers can follow exponential, Erlang, or hyperexponential probability density function, with the same mean regardless of the class. Using an extension of mean value analysis, a recursive algorithm is developed to obtain approximate values of the mean waiting time in queues for each priority class. The mean number of waiting customers and the server utilization of each priority class can be obtained using the result of this recursive algorithm and Little's formula. Numerical examples are presented to illustrate the methodology. The algorithm developed in this article is validated using simulation.

This paper presents solutions to the entropy-constrained scalar quantizer (ECSQ) design problem for two sources commonly encountered in image and speech compression applications: sources having the exponential and Laplacian probability density functions. We use the memoryless property of the exponential distribution to develop a new noniterative algorithm for obtaining the optimal quantizer design. We show how to obtain the optimal ECSQ either with or without an additional constraint on the number of levels in the quantizer. In contrast to prior methods, which require a multidimensional iterative solution of a large number of nonlinear equations, the new method needs only a single sequence of solutions to one-dimensional nonlinear equations (in some Laplacian cases, one additional two-dimensional solution is needed). As a result, the new method is orders of magnitude faster than prior ones. We show that as the constraint on the number of levels in the quantizer is relaxed, the optimal ECSQ becomes a uniform threshold quantizer (UTQ) for exponential, but not for Laplacian sources. We then further examine the performance of the UTQ and optimal ECSQ, and also investigate some interesting alternatives to the UTQ, including a uniform-reconstruction quantizer (URQ) and a constant dead-zone ratio quantizer (CDZRQ).

The Discrete Moment Method for the numerical integration of piecewise higher order convex functions

A node in a switch architecture is examined. The node receives messages, stores and processes them locally, and transmits them to other nodes. Both message transmission and processing times depend on the message length, which is a random variable. The node is modeled as a queue with a single server where the interarrival and service times are related, and different cases are studied where this relation ranges from direct dependence to moderate correlation. Exponential and uniform probability density functions (pdf's) are examined, and the results are compared to the independent model. A relationship is developed for the system time pdf of a message, which is used to find the system time pdf and the system state probabilities. These quantities are directly related to buffer sizes and transmission delays within the architecture. >

A meandering plume model that explicitly incorporatesinternal fluctuations has been developed and used to model the evolutionof concentration fluctuations in point-source plumes in grid turbulenceobtained from a detailed water-channel simulation. This fluctuating plumemodel includes three physical parameters: the mean plume spread in fixedcoordinates, which represents the outer plume length scale; the meaninstantaneous plume spread in coordinates attached to the instantaneousplume centroid, which represents the inner plume length scale; and, theconcentration fluctuation intensity in the meandering reference frame,which represents the in-plume fluctuation scale. These parameters arespecified in terms of a set of coupled dynamical equations that modeltheir development with downstream distance from the source. Explicitexpressions for the concentration moments of arbitrary integral orderand the concentration probability density function have been obtainedfrom the fluctuating plume model. Detailed comparisons of model predictionsagainst water-channel measurements for the first four concentrationmoments and the concentration probability distributions generally showvery good overall quantitative agreement. Exact quantitative conditions,expressed in terms of the physical parameters of the fluctuating plumemodel, have been derived for the emergence of off-centreline peaks inthe concentration variance profile. These quantitative conditions havebeen illustrated in terms of a diagram of states of the dispersing plume,and the qualitatively different regimes of plume concentration variancebehaviour on this state diagram have been identified and characterized.

Representation of internal plume structure in Gifford's meandering plume model

The Performance of various estimators, such as minimum mean square error (MMSE) is strongly dependent on correctness of the proposed model for original data distribution. Therefore, the selection of a proper model for distribution of wavelet coefficients is important in wavelet based image denoising. This paper presents a new image denoising algorithm based on the modeling of wavelet coefficients in each Subband with multivariate radial exponential probability density function (pdf) with approximated MAP estimation for statistical parameter (local variance) using exponential priori. Generally these multivariate extensions do not result in a closed form expression, and the solution requires numerical solutions as in [1]. However, we drive a closed form MMSE shrinkage functions for a Radial-Exponential random vector in Gaussian noise. Experimental results show that our proposed method, MMSE_TriShrink_Radial, outperforms several exiting methods in terms of peak signal-to-noise ratio (PSNR).