We investigate the average frequency of positive slope ν + α , crossing the height α = h −h in the surface growing processes. The exact level crossing analysis of the random deposition model and the Kardar-Parisi-Zhang equation in the strong coupling limit before creation of singularities are given. PACS: 52.75.Rx, 68.35.Ct.

A new model for plasma behaviour in Filippov type plasma focus (PF) systems has been described and used. This model is based on the so-called slug model and Sing Lee's model for Mather type PF devices. Using the model, the discharge current and its derivative as a function of time, and the pinch time and the maximum discharge current as a function of pressure, have been predicted. At the end, the predicted data are compared with the experimental data obtained through a Filippov type PF facility with a nominal maximum energy of 90 kJ.

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In the present study, the properties of natural clinoptilolite were successfully modified by a glow discharge plasma technique. A thorough characterization was performed to clarify the morphology, chemical composition, and porosity of untreated and plasma-treated clinoptilolites. The scanning electron microscopy images of untreated and plasma-treated clinoptilolites demonstrated that the morphology of clinoptilolite was changed from microparticle to nanorod after plasma treatment. The Brunauer−Emmett−Teller results showed that the plasma treatment has enhanced the specific surface area of clinoptilolite up to 2-fold (treated clinoptilolite 45.16 m 2 /g compared to the untreated one 23.92 m 2 /g). The catalytic performance of untreated and plasma-treated Fe-impregnated clinoptilolites was compared in the heterogeneous Fenton process for the decolorization of a textile dye solution. Results indicated that the decolorization efficiency was significantly increased from 36.93%, in the presence of untreated catalyst, to 97.66% with the use of the plasma-treated catalyst after 35 min of reaction.

We give hierarchy of one-parameter family F (a, x) of maps of the interval [0, 1] with an invariant measure. Using the measure, we calculate Kolmogorov-Sinai entropy, or equivalently Lyapunov characteristic exponent, of these maps analytically, where the results thus obtained have been approved with numerical simulation. In contrary to the usual one-parameter family of maps such as logistic and tent maps, these maps do not possess period doubling or period-n-tupling cascade bifurcation to chaos, but they have single fixed point attractor at certain parameter values, where they bifurcate directly to chaos without having period-n-tupling scenario exactly at these values of parameter whose Lyapunov characteristic exponent begins to be positive.

We generate new hierarchy of many-parameter family of maps of the interval [0,1] with an invariant measure, by composition of the chaotic maps of reference [1]. Using the measure, we calculate Kolmogorov-Sinai entropy, or equivalently Lyapunov characteristic exponent, of these maps analytically, where the results thus obtained have been approved with numerical simulation. In contrary to the usual one-dimensional maps and similar to the maps of reference [1], these maps do not possess period doubling or period-n-tupling cascade bifurcation to chaos, but they have single fixed point attractor at certain region of parameters values, where they bifurcate directly to chaos without having period-n-tupling scenario exactly at these values of parameter whose Lyapunov characteristic exponent begins to be positive.

We use the multifractal detrended fluctuation analysis (MF-DFA) to study the electrical discharge current fluctuations in plasma and show that it has multifractal properties and behaves as a weak anti-correlated process. Comparison of the MF-DFA results for the original series with those for the shuffled and surrogate series shows that correlation of the fluctuations is responsible for multifractal nature of the electrical discharge current.

Ion-acoustic solitons in a collisionless plasma consisting of warm ions, hot isothermal electrons, and a relativistic electron beam are studied by using the reductive perturbation method. The basic set of fluid equations is reduced to Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equations. The effects of ion temperature and relativistic electron beam on ion-acoustic solitons are investigated. It has been shown that the four ion-acoustic modes can be propagated in this plasma system. The compressive and rarefactive ion-acoustic solitons satisfies the KdV equation for a given soliton velocity, beam density much smaller than the background electron density and the bulk ion temperature smaller than the background electron temperature for two modes. Also it has been illustrated that there exist mKdV solitons for some critical value of electron beam density in these cases. These critical values decrease as ion temperature increases for one of two modes and increase for the other one. Finally, it has been remarked that for another two modes only rarefactive KdV ion-acoustic solitons can be obtained. One of these modes exists for the electron beam density much smaller than the bulk electron density, and the other exists for almost all values of the beam density, even if it is greater than the background electron density.