Nonlinear excitations in electron-positron-ion plasmas in accretion disks of active galactic nuclei

The propagation of acoustic nonlinear excitations in an electron-positron-ion (e-p-i) plasma composed of warm electrons and positrons, as well as hot ions, has been investigated by adopting a two-dimensional cylindrical geometry. The electrons and positrons are modeled by hydrodynamic fluid equations, while the ions are assumed to follow a temperature-parametrized Boltzmann distribution (the fixed ion model is recovered in the appropriate limit). This situation applies in the accretion disk near a black hole in active galactic nuclei, where the ion temperature may be as high as 3 to 300 times that of the electrons. Using a reductive perturbation technique, a cylindrical Kadomtsev-Petviashvili equation is derived and its exact soliton solutions are presented. Furthermore, real situations in which the strength of the nonlinearity may be weak are considered, so that higher-order nonlinearity plays an important role. Accordingly, an extended cylindrical Kadomtsev-Petviashvili equation is derived, which admits both soliton and double-layer solutions. The characteristics of the nonlinear excitations obtained are investigated in detail

Ion-acoustic waves in a plasma consisting of adiabatic warm ions, non-isothermal electrons and a weakly relativistic electron beam: linear and higher-order nonlinear effects

The nonlinear propagation of finite amplitude ion acoustic solitary waves in a plasma consisting of adiabatic warm ions, nonisothermal electrons, and a weakly relativistic electron beam is studied via a two-fluid model. A multiple scales technique is employed to investigate the nonlinear regime. The existence of the electron beam gives rise to four linear ion acoustic modes, which propagate at different phase speeds. The numerical analysis shows that the propagation speed of two of these modes may become complex-valued (i.e., waves cannot occur) under conditions which depend on values of the beam-to-background-electron density ratio , the ion-to-free-electron temperature ratio , and the electron beam velocity v0; the remaining two modes remain real in all cases. The basic set of fluid equations are reduced to a Schamel-type equation and a linear inhomogeneous equation for the first and second-order potential perturbations, respectively. Stationary solutions of the coupled equations are derived using a renormalization method. Higher-order nonlinearity is thus shown to modify the solitary wave amplitude and may also deform its shape, even possibly transforming a simple pulse into a W-type curve for one of the modes. The dependence of the excitation amplitude and of the higher-order nonlinearity potential correction on the parameters , , and v0 is numerically investigated.

Parametric study of nonlinear electrostatic waves in two-dimensional quantum dusty plasmas

The nonlinear properties of two-dimensional cylindrical quantum dust-ion-acoustic (QDIA) and quantum dust-acoustic (QDA) waves are studied in a collisionless, unmagnetized and dense (quantum) dusty plasma. For this purpose, the reductive perturbation technique is employed to the quantum hydrodynamical equations and the Poisson equation, obtaining the cylindrical Kadomtsev–Petviashvili (CKP) equations. The effects of quantum diffraction, as well as quantum statistical and geometric effects on the profiles of QDIA and QDA solitary waves are examined. It is found that the amplitudes and widths of the nonplanar QDIA and QDA waves are significantly affected by the quantum electron tunneling effect. The addition of a dust component to a quantum plasma is seen to affect the propagation characteristics of localized QDIA excitations. In the case of low-frequency QDA waves, this effect is even stronger, since the actual form of the potential solitary waves, in fact, depends on the dust charge polarity (positive/negative) itself (allowing for positive/negative potential forms, respectively). The relevance of the present investigation to metallic nanostructures is highlighted.

Improved Process Monitoring Using Nonlinear Principal Component Models

This paper presents two new approaches for use in complete process monitoring. The firstconcerns the identification of nonlinear principal component models. This involves the application of linear
principal component analysis (PCA), prior to the identification of a modified autoassociative neural network (AAN) as the required nonlinear PCA (NLPCA) model. The benefits are that (i) the number of the reduced set of linear principal components (PCs) is smaller than the number of recorded process variables, and (ii) the set of PCs is better conditioned as redundant information is removed. The result is a new set of input data for a modified neural representation, referred to as a T2T network. The T2T NLPCA model is then used for complete process monitoring, involving fault detection, identification and isolation. The second approach introduces a new variable reconstruction algorithm, developed from the T2T NLPCA model. Variable reconstruction can enhance the findings of the contribution charts still widely used in industry by reconstructing the outputs from faulty sensors to produce more accurate fault isolation. These ideas are illustrated using recorded industrial data relating to developing cracks in an industrial glass melter process. A comparison of linear and nonlinear models, together with the combined use of contribution charts and variable reconstruction, is presented.

A taxonomy for wavelet neural networks applied to nonlinear modelling

This article presents a novel classification of wavelet neural networks based on the orthogonality/non-orthogonality of neurons and the type of nonlinearity employed. On the basis of this classification different network types are studied and their characteristics illustrated by means of simple one-dimensional nonlinear examples. For multidimensional problems, which are affected by the curse of dimensionality, the idea of spherical wavelet functions is considered. The behaviour of these networks is also studied for modelling of a low-dimension map.

Deflation based nonlinear canonical correlation analysis

This paper introduces two new techniques for determining nonlinear canonical correlation coefficients between two variable sets. A genetic strategy is incorporated to determine these coefficients. Compared to existing methods for nonlinear canonical correlation analysis (NLCCA), the benefits here are that the nonlinear mapping requires fewer parameters to be determined, consequently a more parsimonious NLCCA model can be established which is therefore simpler to interpret. A further contribution of the paper is the investigation of a variety of nonlinear deflation procedures for determining the subsequent nonlinear canonical coefficients. The benefits of the new approaches presented are demonstrated by application to an example from the literature and to recorded data from an industrial melter process. These studies show the advantages of the new NLCCA techniques presented and suggest that a nonlinear deflation procedure should be considered. (c) 2006 Elsevier B.V. All rights reserved.