Analysis of pressure fluctuations in fluidized beds. II. Reconstruction of the data by the Fokker–Planck and Langevin equations

In this part of the sequel we develop a continuum representation of the pressure fluctuation time series p(t) for a fluidized bed (FB), analyzed in part I, by using stochastic methods based on the Markov processes. It is shown that the data may be represented by Markov series with a Markov time scale t_M that is estimated based on the data. Using the relation between the Markov processes and the Kramers–Moyal (KM) expansion that is a continuum equation that involves, in principle, an infinite number of coefficients, we represent the pressure fluctuation time series by a KM expansion. However, since the third and higher-order coefficients of the expansion are very small, the KM expansion reduces to a Fokker–Planck (FP) equation that represents p(t) in terms of a drift and a diffusion coefficients that are computed based on the data. The FP equation is, in turn, equivalent to a Langevin equation, which is used to reconstruct the data, i.e. generate the time series that mimic, in a statistical sense, the original data. Thus, the Langevin equation may also be used to make probabilistic predictions for the future values of the pressure over time scales that are of the order of the Markov time scale t_M. The accuracy of the reconstructed series and, hence, their continuum representation, is demonstrated. We also compute the frequency of level-crossing at a given level α, i.e. the relative frequency (probability) of occurrence of the event defined, for two times t_i−1 and t_i, by, , where P(x) is the probability of the event. Thus, yields the frequency that a given pressure fluctuation level may be expected. The average time that one should wait in order to observe the pressure at a given level again is also computed. The two quantities may be particularly important for modeling of the FBs. A relation is presented between the drift and diffusion coefficients of the FP equation and the Hurst exponent that has previously been used to describe the pressure fluctuation time series in terms of self-affine stochastic distributions.     

Theoretical Study of the Endogenous Production of N-13 in 115 kJ Plasma Focus Device Using Methane Gas

Mather type plasma focus device with the bank energy of 115 kJ (40 kV, 144μF) was studied for induced activity of N-13; a short-lived radioisotope β⁺ emitter with 511 keV of gamma rays and has a half-life of t_1/2 = 9.93 min through ¹²C (d, n)¹³N nuclear reaction. N-13 radioisotope is used in Positron Emission Tomography (PET) for imaging and treatment. In this paper endogenous production of ¹³N is considered. It is shown by adding 3–4 % CH₄ to the chamber, the induced activity of N-13 has increased about 4 %. Our study is representative of producing 10⁶ ? 10⁹ Bq induced activity of this SLR in IR-MPF-100 device.     

Decay Rate of an Excited Atom in Dispersive and Dissipative Plasma Media

Calculations of decay rates of an excited atom embedded in a dispersive and dissipative plasma medium are presented in this paper. The usual expression for decay rate of an initially excited atom in dipole approximation is given by Fermi’s golden rule. The electric field correlation function is related to the imaginary part of the potential Green’s function along with the fluctuation of dissipation theorem and Kubo’s formula. Using the Green’s function technique offers possibilities of closed function representations. It is applicable to evaluate the decay rate of an excited atom that allows us to understand the particular structure of the vacuum state of the electromagnetic field. In this paper, the decay rate of an excited atom in dispersive and dissipative media is estimated.     

Exploring the interactive and interactional metadiscourse in doctoral dissertation writing: a diachronic study

Scientometrics - This study explores the diachronic evolution of doctoral dissertation writing in terms of interactive and interactional metadiscourse at three time intervals of 1966, 1986, and...     

Meshless method for solving radiative transfer problems in complex two-dimensional and three-dimensional geometries

A meshless method is presented to solve the radiative transfer equation in complex 2D and 3D geometries. In order to avoid numerical oscillations, the even parity formulation of the discrete ordinates method is used. A moving least squares approximation meshless method is used to solve the second order partial differential equations. Prediction results of radiative heat transfer problems obtained by the proposed method are compared with reference in order to assess the correctness of the present method.