Random advection of a Lagrangian tracer scalar field u(t ,x) by a one-dimensional, spatially smooth and short-correlated in time velocity field is considered. Scalar fluctuations are maintained by a source concentrated at the integral scale L . The statistical properties of both scalar differences and the dissipation field are analytically determined, exploiting the dynamical formulation of the...

We investigate spacing statistics for ensembles of various real random matrices where the matrixelements have various Probability Distribution Function (PDF: f(x)) including Gaussian. For two modifications of 2 × 2 matrices with various PDFs, we derived that spacing distribution p(s) of adjacent energy eigenvalues are distinct. Nevertheless, they show the linear level repulsion near s = 0 as αs...

In this paper, a stochastic distribution control (SDC) algorithm is presented for nonlinear and non-Gaussian stochastic systems with constraints on control inputs. A generalized entropy optimization criterion is constructed based on the probability density function (PDF) of the tracking error. An optimal control law is then obtained using the penalty function method. Stability analysis for this...

Through the wind velocity and direction monitoring system installed on Jiubao Bridge of Qiantang River, Hangzhou city, Zhejiang province, China, a full range of wind velocity and direction data was collected during typhoon HAIKUI in 2012. Based on these data, it was found that, at higher observed elevation, turbulence intensity is lower, and the variation tendency of longitudinal and lateral tu...

Based on an examination of K data from four different sites, a new stochastic fractal model, fractional Laplace motion, is proposed. This model is based on the assumption of spatially stationary ln(K) increments governed by the Laplace PDF, with the increments named fractional Laplace noise. Similar behavior has been reported for other increment processes (often called fluctuations) in the fiel...

Welch’s method for spectral estimation of averaging modified periodograms has been widely used for decades. Because such an estimate relies on random data, the estimate is also a random variable with some probability density function. Here, the pdf of a power estimate is derived for an estimate based on an arbitrary number of frequency bins, overlapping data segments, amount of overlap, and typ...

This technical report summarizes a number of results for the multivariate t distribution which can exhibit heavier tails than the Gaussian distribution. It is shown how t random variables can be generated, the probability density function (pdf) is derived, and marginal and conditional densities of partitioned t random vectors are presented. Moreover, a brief comparison with the multivariate Gau...

The probability density functions (PDF) of the firstand second-phase variation for multipath envelope in space are derived based on a wideband measured database at 5.3 GHz for indoor and outdoor mobile communications. The first-phase variation follows either a symmetrical or asymmetrical Gaussian distribution, and the second-phase variation follows a symmetrical Gaussian distribution with large...

Parameterizations of turbulence often predict several lower-order moments and make closure assumptions for higher-order moments. In principle, the lowand high-order moments share the same probability density function (PDF). One closure assumption, then, is the shape of this family of PDFs. When the higher-order moments involve both velocity and thermodynamic scalars, often the PDF shape has bee...

In this paper, we propose a threshold-system-based detector (TD) for detecting a known deterministic signal in independent non-Gaussian noise whose probability density function (pdf) is unknown but is symmetric and unimodal. The optimality of the proposed TD is proved under the assumptions of white noise, small signal, and a large number of samples. While previous TD designs need accurate infor...