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This study deals with the stochastic non-linear dynamic response of functionally graded materials (FGMs) plate with uncertain system properties subjected to time-dependent uniformly distributed transverse load in thermal environments. System properties, such as material properties of each constituent's material, volume fraction index, and transverse load, are taken as uncorrelated random input variables. Material properties are assumed as temperature dependent (TD). The formulation is based on higher-order shear deformation theory (HSDT) with von-Karman non-linear strain kinematics using modified C° continuity. A Newton-Raphson-based non-linear finite element method along with a first-order perturbation technique (FOPT) and Monte Carlo sampling (MCS) is outlined to examine the second-order statistics (mean, standard deviation (SD), and probability density function (PDF)) of the non-linear dynamic response of the FGM plate. The governing dynamic equation is solved by Newmark's time integration scheme. The effects of volume fraction index, load parameters, plate thickness ratios, and temperature changes with random system properties are examined through parametric studies. The present outlined approach is validated with the results available in the literature and by MCS. [ABSTRACT FROM AUTHOR]

Data collection process in most observational and experimental studies yield different types of variables, leading to the use of joint models that are capable of handling multiple data types. Evaluation of various statistical techniques that have been developed for mixed data in simulated environments requires concurrent generation of multiple variables. In this article, I present an important augmentation to a unified framework proposed in our previously published work for simultaneously generating binary and nonnormal continuous data given the marginal characteristics and correlation structure, via fifth-order power polynomials that are known to extend the area covered in the skewness-elongation plane and to provide a better approximation to the probability density function of the continuous variables. I evaluate how well the improved methodology performs in comparison to the original one, in a simulated setting with illustrations of algorithmic steps. Although the relative gains for the associational quantities are not substantial, the augmented version appears to better capture the marginal quantities that are pertinent to the higher-order moments, as indicated by very close resemblance between the specified and empirically computed quantities on average. [ABSTRACT FROM AUTHOR]

This paper explores the study on mixture of a class of probability density functions under type-I censoring scheme. In this paper, we mold a heterogeneous population by means of a two-component mixture of the class of probability density functions. The parameters of the class of mixture density functions are estimated and compared using the Bayes estimates under the squared-error and precautionary loss functions. A censored mixture dataset is simulated by probabilistic mixing for the computational purpose considering particular case of the Maxwell distribution. Closed-form expressions for the Bayes estimators along with their posterior risks are derived for censored as well as complete samples. Some stimulating comparisons and properties of the estimates are presented here. A factual dataset has also been for illustration. [ABSTRACT FROM AUTHOR]

Based on planar high-speed Rayleigh scattering measurements of the mixture fractionZof propane discharging from a turbulent round jet into co-flowing carbon dioxide at nozzle-based Reynolds numbersRe0= 3000–8600, we use scalar gradient trajectories to investigate the local structure of the turbulent scalar field with a focus on the scalar turbulent/non-turbulent interface. The latter is located between the fully turbulent part of the jet and the outer flow. Using scalar gradient trajectories, we partition the turbulent scalar field into these three regions according to an approach developed by Mellado et al. (J.P. Mellado, L. Wang, and N. Peters,Gradient trajectory analysis of a scalar field with external intermittency, J. Fluid Mech. 626 (2009), pp. 333–365.). Based on these different regions, we investigate in a next step zonal statistics of the scalar probability density function (pdf)P(Z) as well as the scalar difference along the trajectory ΔZand its mean scalar valueZm, where the latter two quantities are used to parameterize the scalar profile along gradient trajectories. We show that the scalar pdfP(Z) can be reconstructed from zonal gradient trajectory statistics of the joint pdfP(Zm, ΔZ). Furthermore, on the one hand we relate our results for the scalar turbulent/non-turbulent interface to the findings made in other experimental and numerical studies of the turbulent/non-turbulent interface, and on the other hand discuss them in the context of the flamelet approach and the modelling of pdfs in turbulent non-premixed combustion. Finally, we compare the zonal statistics forP(Z) with the composite model of Effelsberg and Peters (E. Effelsberg and N. Peters,A composite model for the conserved scalar pdf, Combust. Flame 50 (1983), pp. 351–360) and observe a very good qualitative and quantitative agreement. [ABSTRACT FROM PUBLISHER]