Effects of two-temperature electrons, external oblique magnetic field, and higher-order nonlinearity on dust acoustic solitary waves in a dusty plasma with vortex-like ion distribution

Nonlinear properties of the dust acoustic (DA) solitary waves in a dusty plasma consisting of negatively variable-charged dust particles, vortex-like distributed ions and two-temperature isothermal electrons are reported. A reductive perturbation theory has been used to derive a modified Korteweg-de Vries (mKdV) equation for the first-order perturbed potential and a linear inhomogeneous mKdV-type equation for the second-order perturbed potential. The renormalization method is used to obtain stationary solutions of these coupled equations. The modifications in the amplitude and width of the solitary wave structure due to the inclusion of two different types of isothermal electrons, external oblique magnetic field, higher-order nonlinearity, and vortex-like distributed ions are investigated. Also a method based on energy consideration was used to obtain the stability condition. Moreover, the numerical results are applied to investigate some nonlinear characteristics of the DA solitary waves.     

Effects of two-temperature electrons, external oblique magnetic field, concentration of charged dust grains and higher-order nonlinearity on dust ion-acoustic solitary waves in Saturn's E-ring

The purpose of the present work is to investigate some nonlinear properties of the dust ion-acoustic (DIA) solitary waves in a four-component hot-magnetized dusty plasma consisting of charged dust grains, positively charged ions and two-temperature isothermal electrons. Applying a reductive perturbation theory, a nonlinear Korteweg-de Vries (KdV) equation for the first-order perturbed potential and a linear inhomogeneous KdV-type equation for the second-order perturbed potentials are derived. Stationary solutions of these coupled equations are obtained using a renormalization method. A method based on energy consideration is used to obtain a condition for stable solitons. The effects of two different types of isothermal electrons, external oblique magnetic field, concentration of negatively (positively) charged dust grains and higher-order nonlinearity on the nature of the DIA solitary waves are discussed. The numerical results are applied to Saturn's E-ring.     

Dust-acoustic solitary waves and double layers with two temperature ions in a nonextensive dusty plasma

Small amplitude dust-acoustic solitary waves in an unmagnetized dusty plasma consisting of electrons and two temperature ions obeying the q-nonextensive distribution are investigated. Employing reductive perturbation method, the Korteweg-de Vries (KdV) equation is derived. From the solitonic solutions of KdV equation, the influence of nonextensivity of electrons as well as ions and dust concentration on the amplitude and width of dust-acoustic solitary waves has been studied. It is observed that both positive and negative potential dust acoustic solitary waves occur in this case. The modified KdV (mKdV) equation is derived in order to examine the solitonic solutions for the critical plasma parameters for which KdV theory fails. The parametric regimes for the existence of mKdV solitons and double layers (DLs) have also been determined. Positive potential double layers are found to occur in the present study.     

A special perturbation method in orbital dynamics

The special perturbation method considered in this paper combines simplicity of computer implementation, speed and precision, and can propagate the orbit of any material particle. The paper describes the evolution of some orbital elements based in Euler parameters, which are constants in the unperturbed problem, but which evolve in the time scale imposed by the perturbation. The variation of parameters technique is used to develop expressions for the derivatives of seven elements for the general case, which includes any type of perturbation. These basic differential equations are slightly modified by introducing one additional equation for the time, reaching a total order of eight. The method was developed in the Grupo de Dinámica de Tethers (GDT) of the UPM, as a tool for dynamic simulations of tethers. However, it can be used in any other field and with any kind of orbit and perturbation. It is free of singularities related to small inclination and/or eccentricity. The use of Euler parameters makes it robust. The perturbation forces are handled in a very simple way: the method requires their components in the orbital frame or in an inertial frame. A comparison with other schemes is performed in the paper to show the good performance of the method.     

Quasi-viscous accretion flow – I. Equilibrium conditions and asymptotic behaviour

In a novel approach to studying viscous accretion flows, viscosity has been introduced as a perturbative effect, involving a first-order correction in the α-viscosity parameter. This method reduces the problem of solving a second-order non-linear differential equation (Navier–Stokes equation) to that of an effective first-order equation. Viscosity breaks down the invariance of the equilibrium conditions for stationary inflow and outflow solutions, and distinguishes accretion from wind. Under a dynamical systems classification, the only feasible critical points of this 'quasi-viscous' flow are saddle points and spirals. On large spatial scales of the disc, where a linearized and radially propagating time-dependent perturbation is known to cause a secular instability, the velocity evolution equation of the quasi-viscous flow has been transformed to bear a formal closeness with Schrödinger's equation with a repulsive potential. Compatible with the transport of angular momentum to the outer regions of the disc, a viscosity-limited length-scale has been defined for the full spatial extent over which the accretion process would be viable.     

Expansion formulae in canonical transformations depending on a small parameter

The theory of perturbation based on Lie transforms is considered. Deprit's equation is reduced to a form which enables us to generate simplified general recursion formulae. These expansions are then modified to speed up the implementation of such perturbation theory in the computerized symbolic manipulation.     

The formation of primordial stars triggered by the evolution of large-scale density perturbations

This paper summarizes the basic idea of coupling of density perturbation modes in Newtonian cosmology and the formation of primordial stars. The way of deriving the second-order differential equation governing the growth of two coupled adiabatic density perturbation modes in the matter era is briefly discussed. A Jeans criterion for the growth of short wavelength perturbations is given. A mechanism is proposed for the cosmological origin of Population III stars.     

Cylindrical Zakharov–Kuznestov equation for ion-acoustic waves with electrons featuring non-extensive distribution

Cylindrical Zakharov–Kuznestov equation for ion-acoustic waves comprising of ions and electrons featuring non-extensive distribution are derived from the fluid equations through reductive perturbation technique. System of first order ordinary differential equations is obtained from Zakharov–Kuznestov equation through dynamical system approach and ultimately it is solved using numerical method. It is found that the electron to positron ratio parameter and the non-extensive distributed parameter due to electron play crucial role on the solution.     

Nonlinear ion-acoustic solitons in a warm plasma with adiabatic positive and negative ions and hot non-isothermal electrons

The propagation of an ion-acoustic soliton in a collisionless plasma with adiabatic positive and negative ions (with equal ion temperature) and hot non-isothermal electrons is studied by use of the renormalization method introduced by Kodama and Taniuti in the reductive perturbation method. The basic set of fluid equations describing the system is reduced to a Korteweg-de Vries (K-dV)-type equation for the first-order perturbed potential and to a linear inhomogeneous differential equation to the second-order of the perturbed potential. A stationary solution of the coupled equations is obtained.     

Effect of the presence of excess superthermal hot electrons on electron-acoustic solitary waves in auroral zone plasma

A theoretical investigation is carried out for the nonlinear properties of small amplitude electron acoustic solitary waves (EAWs) in an unmagnetized collisionless plasma consisting of a cold electron fluid and hot electrons obeying κ velocity distribution, and stationary ions. The Korteweg de Vries (KdV) equation that contains the lowest-order nonlinearity and dispersion is derived from the lowest order of perturbation and a linear inhomogeneous (KdV-type) equation that accounts for the higher-order nonlinearity and dispersion is obtained. A stationary solution for equations resulting from higher-order perturbation theory has been found using the renormalization method. The effects of the spectral index κ and the higher-order corrections are found to significantly change the properties (viz. the amplitude, width, electric field ) of the EASWs. A comparison with the Viking Satellite observations in the dayside auroral zone are also discussed.     

Non-stationary motion of a rotating infinitely flattened self-gravitating system near an equilibrium state

An example of a rotating infinitely flattened self-gravitating particle system in steady state is considered. Non-stationary motion of the system in the neighborhood of this equilibrium solution is determined through the sencond-order perturbation. The first order perturbation terms give rise to a configuration of straight bars emanating from the center which become skewed under the influence of the second-order terms. In the case of a single bar, as in a barred spiral, the skewing is in the arms leading or arms trailing sense, according to whether the system is developing away from or approaching the equilibrium state.     

Large-scale bias in the Universe — II. Redshift-space bispectrum

The determination of the density parameter Ω₀ from the large-scale distribution of galaxies is one of the major goals of modern cosmology. However, if galaxies are biased tracers of the underlying mass distribution, linear perturbation theory leads to a degeneracy between Ω₀ and the linear bias parameter b , and the density parameter cannot be estimated. In Matarrese, Verde &38; Heavens we developed a method based on second-order perturbation theory to use the bispectrum to lift this degeneracy by measuring the bias parameter in an Ω₀-independent way. The formalism was developed assuming that one has perfect information on the positions of galaxies in three dimensions. In galaxy redshift surveys, the three-dimensional information is imperfect, because of the contaminating effects of peculiar velocities, and the resulting clustering pattern in redshift space is distorted. In this paper we combine second-order perturbation theory with a model for collapsed, virialized structures, to extend the method to redshift space, and demonstrate that the method should be successful in determining with reasonable accuracy the bias parameter from state-of-the-art surveys such as the Anglo-Australian 2 degree Field Survey and the Sloan Digital Sky Survey.     

Critical density solitary waves structures in a hot dusty plasma with vortex-like ion distribution in phase space

The nonlinear properties of solitary waves structure in a hot dusty plasma consisting of isothermal hot electrons, non isothermal ions and high negatively charged massive dust grains, are reported. A modified Korteweg-de Vries equation (modified KdV), which admits a solitary waves solution for small but finite amplitude, is derived using a reductive perturbation theory. A nonisothermal ions distribution provides the possibility of coexistence of amplitude rarefactive as well as compressive solitary waves. On the other hand, consideration of a critical ions density gives a stationary solution of solitary waves and the dynamics of small but finite amplitude of solitary waves is governed by Korteweg-de Vries equation (KdV). The properties of solitary waves in the two cases are discussed.     

Notes on Hori Method for Canonical Systems

In this paper a slightly different approach is proposed for the process of determining the functions S _m and H _m ^* of the algorithm of the canonical version of Hori method. This process will be referred to as integration theory of the mth order equation of the method. It will be shown that the ordinary differential equation with an auxiliary parameter t ^* as independent variable, introduced through Hori auxiliary system, can be replaced by a partial differential equation in the time t. In this way, the mth order equation of the algorithm assumes a form very similar to the one of other perturbation methods. In virtue of this new approach of the integration theory for Hori method, Lagrange's variational equations introduced by Sessin are revised. As an example, the Duffing equation is solved through this new approach.     

An extended canonical perturbation method

In this investigation, a procedure is described for extending the application of canonical perturbation theories, which have been applied previously to the study of conservative systems only, to the study of non-conservative dynamical systems. The extension is obtained by imbedding then-dimensional non-conservative motion in a 2n-dimensional space can always be specified in canonical form, and, consequently, the motion can be studied by direct application of any canonical perturbation method. The disadvantage of determining a solution to the 2n-dimensional problem instead of the originaln-dimensional problem is minimized if the canonical transformation theory is used to develop the perturbation solution. As examples to illustrate the application of the method, Duffing's equation, the equation for a linear oscillator with cubic damping and the van der Pol equation are solved using the Lie-Hori perturbation algorithm.This research was supported by the Office of Naval Research under Contract N00014-67-a-0126-0013.     

Higher order corrections to dust-acoustic ZK-solitons in a magnetized quantum dusty plasma

Nonlinear propagation of two dimensional dust-acoustic solitary waves in a magnetized quantum dusty plasma whose constituents are electrons, ions, and negatively charged heavy dust particles are investigated using quantum hydrodynamic model. The Zakharov-Kuznetsov (ZK) equation is derived by using reductive perturbation technique (RPT). The higher order inhomogeneous ZK-type differential equation is obtained for the correction to ZK- soliton. The dynamical equation for dressed soliton is solved by using renormalization method. The effects of obliqueness (l _x ) of the wave vector, magnetic field strength (B ₀), quantum parameter for ions (H _i ), soliton velocity (θ) and Fermi temperature ratio (σ) on amplitudes and widths of the ZK-soliton and as well as of the dressed soliton are investigated. The conditions for the validity of the higher order correction are described. Suitable parameter ranges for the existence of compressive and rarefactive dressed solitons are also discussed.     

Two-stream instability in the presence of longitudinal magnetic field

A multiple sclaes perturbation theory has been applied to investigate the nonlinear behaviour of beam-plasma system near a marginally stable state in the presence of longitudinal magnetic field. The perturbation method leads to a nonlinear Schrödinger equation for the finite amplitude. The coefficients of this equation show that only if the beam is compressed isothermally can there exist a range of wavenumbers for which stabilization might occur. The stable region increases with the applied magnetic field.     

Effect of high relativistic ions on ion acoustic solitons in electron-ion-positron plasmas with nonthermal electrons and thermal positrons

Propagation of ion acoustic solitary waves are studied in e-p-i plasmas containing high relativistic ions, Maxwell–Boltzmann distributed positrons and nonthermal electrons. Reductive perturbation method is used and the Korteweg-de Vries (KdV) equation is derived. The effects of high relativistic ions and nonthermal electrons on soliton characters are studied.     

The highly excited hydrogen b n -factors calculated

Radio recombination line intensities are functions of highly excited atom nonequilibrium populations. These populations are determined by the spontaneous, collision and induced radiation transition rates that arise from the balance equations. The population balance equations are solved in a diffusion approximation which is proved for the departure factors from LTE. Diffusion equation departure coefficients are far from LTE due to the spontaneous transition flow, found as a second-order differential equation general solution. This solution is chosen in an explicit form from a physical situation with the temperature and density determined. The background radiation induced transition rates strongly influence the population flow to the equilibrium distribution. Radio recombination line amplification coefficients are calculated for the different medium temperatures and electron densities; these coefficients permit interpretation of the line intensities in the actual experiments.