S. V. Muniandy

Head-on collision of ion acoustic solitary waves in an electron-positron-ion plasma with superthermal electrons

The head-on collision of ion acoustic solitary waves in a three-component unmagnetized plasma with cold ions, Boltzmann distributed positrons, and superthermal electrons is investigated using the extended Poincare–Lighthill–Kuo method. The effects of the ratio of electron temperature to positron temperature, the spectral index, κ, of the electron kappa distribution, and fractional concentration of positron component (p) on the phase shift are studied. It is found that the presence of superthermal electrons play a significant role on the collision of ion acoustic solitary waves.

Inhomogeneous scaling behaviors in Malaysian foreign currency exchange rates

In this paper, we investigate the fractal scaling behaviors of foreign currency exchange rates with respect to Malaysian currency, Ringgit Malaysia. These time series are examined piecewise before and after the currency control imposed in 1st September 1998 using the monofractal model based on fractional Brownian motion. The global Hurst exponents are determined using the R/S analysis, the detrended fluctuation analysis and the method of second moment using the correlation coefficients. The limitation of these monofractal analyses is discussed. The usual multifractal analysis reveals that there exists a wide range of Hurst exponents in each of the time series. A new method of modelling the multifractal time series based on multifractional Brownian motion with time-varying Hurst exponents is studied.

Generalized Ornstein–Uhlenbeck processes and associated self-similar processes

We consider three types of generalized Ornstein–Uhlenbeck processes: the stationary process obtained from the Lamperti transformation of fractional Brownian motion, the process with stretched exponential covariance and the process obtained from the solution of the fractional Langevin equation. These stationary Gaussian processes have many common properties, such as the fact that their local covariances share a similar structure and they exhibit identical spectral densities at large frequency limit. In addition, the generalized Ornstein–Uhlenbeck processes can be shown to be local stationary representations of fractional Brownian motion. Two new self-similar Gaussian processes, in addition to fractional Brownian motion, are obtained by applying the (inverse) Lamperti transformation to the generalized Ornstein–Uhlenbeck processes. We study some of the properties of these self-similar processes such as the long-range dependence. We give a simulation of their sample paths based on numerical Karhunan–Loeve expansion.

On some possible generalizations of fractional Brownian motion

Abstract Fractional Brownian motion (fBm) can be generalized to multifractional Brownian motion (mBm) if the Hurst exponent H is replaced by a deterministic function H ( t ). The two possible generalizations of mBm based on the moving average representation and the harmonizable representation are first shown to be equivalent up to a multiplicative deterministic function of time by Cohen [S. Cohen, in: M. Dekking et al. (Eds.), Fractals: Theory and Applications in Engineering, Springer, Berlin, 1999, p. 3.] using the Fourier transform method. In this Letter, we give an alternative verification of such an equivalence based on the direct computation of the covariances of these two Gaussian processes. There also exists another equivalent representation of mBm, which is a variant version of the harmonizable representation. Finally, we consider a generalization based on the Riemann–Liouville fractional integral, and study the large time asymptotic properties of this version of mBm.

Dressed soliton in quantum dusty pair-ion plasma

Nonlinear propagation of a quantum ion-acoustic dressed soliton is studied in a dusty pair-ion plasma. The Korteweg–de Vries (KdV) equation is derived using reductive perturbation technique. A higher order inhomogeneous differential equation is obtained for the higher order correction. The expression for a dressed soliton is calculated using a renormalization method. The expressions for higher order correction are determined using a series solution technique developed by Chatterjee et al. [Phys. Plasmas 16, 072102 (2009)].

Generation of a dressed soliton in a four-component dusty plasma with nonthermal ions

Dust acoustic solitary waves are studied in a four-component dusty plasma. Positively and negatively charged mobile dust and Boltzmann-distributed electrons are considered. The ion distribution is taken as nonthermal. The Korteweg–de Vries equation is derived using reductive perturbation technique. We are able to reproduce the results obtained by Sayed and Mamun [Phys. Plasmas 14, 014501 (2007)] provided the Boltzmann distribution is considered for the ions. Higher order inhomogeneous differential equation is obtained for the dressed soliton. By using the renormalization method of Kodama and Taniuti [J. Phys. Soc. Jpn. 45, 298 (1978)], we derived the expression for the dressed soliton.

ION ACOUSTIC SOLITARY WAVES AND DOUBLE LAYERS IN DENSE ELECTRON–POSITRON–ION MAGNETOPLASMA

The existence of ion acoustic solitary waves is studied in a magnetized dense electron-positron-ion plasma. The ions are described by the hydrodynamic equations, and the electron and positron are assumed to follow the Thomas–Fermi density distribution. The pseudopotential is derived directly from the basic equations including Poisson’s equation without assuming the quasineutrality condition. The effect of ion temperature on the solitary waves is studied, and the ranges of parameters for which solitary waves and double layers exist are also studied in detail using Sagdeev’s technique.

Effect of ion temperature on arbitrary amplitude ion acoustic solitary waves in quantum electron-ion plasmas

Using Sagdeev’s pseudopotential technique, the effect of ion temperature on the arbitrary amplitude ion acoustic solitary waves in quantum electron-ion plasma is studied. In addition, the effect of ion temperature on the region of existence, as well as on the shape of the solitary waves, is also investigated extensively. It is shown that for large amplitude solitary wave, quantum parameter H does not play any role in determining the region of existence and on the amplitude of the solitary waves. However, H has a significant effect on the width of the solitary wave. It is worth noting that our results are in agreement with previous investigations when the effect of ion temperature is neglected.

Dressed solitons in quantum electron-positron-ion plasmas

Nonlinear propagation of quantum ion acoustic waves in a dense quantum plasma whose constituents are electrons, positrons, and positive ions is investigated using a quantum hydrodynamic model. The Korteweg–de Vries equation is derived using reductive perturbation technique. The higher order inhomogeneous differential equation is obtained for the dressed soliton. The dynamical equation for dressed soliton is solved using the renormalization method. The conditions for the validity of the higher order correction are described. The effects of quantum parameter, positron concentration, electron to positron Fermi temperature ratio, and soliton velocity on the amplitude and width of the dressed soliton are studied.

Fractional dynamics in the light scattering intensity fluctuation in dusty plasma

Light scattering intensity fluctuation in dusty plasma system is studied. The scattered electric field of the laser light is treated as a stationary stochastic process. A nonstandard form of fractional Langevin equation is solved using Green’s function approach to obtain the so-called fractional Ornstein–Uhlenbeck process. The empirical correlation function of light intensity fluctuation is fitted with four model correlation functions which are representative of different mechanisms for monodisperse particle transport, namely, the kinetic (ballistic) model, the hydrodynamical (diffusive) model, the hybrid kinetic-hydrodynamic model, and the fractional kinetic model for polydisperse particles. The shifted fractional derivative index is found to be related to power-law exponent of polydisperse dust mass distribution. It is shown that the correlation model based on fractional Ornstein–Uhlenbeck process may provide a novel insight into the complex transport behaviors in dusty plasma.