The solution of reduced Fokker–Planck–Kolmogorov (FPK) equation resulted from the problems in statistical mechanics is formulated as an exponential function of polynomials in state variables. Special measure is taken to satisfy the FPK equation in the weak sense of integration with the...

The formula for probability density functions (PDFs) has been extended to include PDF for energy dissipation rates in addition to other PDFs such as for velocity fluctuations, velocity derivatives, fluid particle accelerations, energy transfer rates, etc., and it is shown that the formula...

The purpose of this paper is to offer a unified discussion of variable-order differential operators in anomalous diffusion modeling. The characteristics of the new models, in contrast to constant-order fractional diffusion models, change with time, space, concentration or other independent...

The fluctuation of wind speed within a specific time period affects a lot the energy conversion rate of wind turbine. In this paper, the concept of fractal dimension in chaos theory is applied to investigate wind speed characterizations; numerical algorithms for the calculation of the fractal...

In this paper, the genetic algorithm (GA) is originally applied to compute the Weibull parameters for wind characterization analysis, in which an objective function required in GA for searching optimization solution has been first defined as well. Wind data analyzed are observed at a wind farm...

This paper presents a novel approach to temperature probability density distribution and function. Probability density functions and frequency are successfully used in wind speed and solar energy analyses in literature. This study applies these data to temperature data analysis. The present...

Knowing about wind speed distribution for a specific site is very essential step in wind resource utilizations. In this paper, a probability density function with the maximum entropy principle is derived using different algorithm from previous studies. Its validity considering various numbers of...

We consider the probability distribution function (pdf) and the multiscaling properties of the index and the traded volume in the Korean stock market. We observed the power law of the pdf at the fat tail region for the return, volatility, the traded volume, and changes of the traded volume. We...

We derive an integro-differential equation for the joint probability density function in phase space associated with the continuous-time random walk, with generic waiting time probability density function and external force. This equation permits us to investigate whole diffusion processes...