Md. Nurujjaman

Realization of SOC behavior in a dc glow discharge plasma

Experimental observations consistent with Self Organized Criticality (SOC) have been obtained in the electrostatic floating potential fluctuations of a dc glow discharge plasma. Power spectrum exhibits a power law which is compatible with the requirement for SOC systems. Also the estimated value of the Hurst exponent (self similarity parameter), H being greater than 0.5, along with an algebraic decay of the autocorrelation function, indicate the presence of temporal long-range correlations, as may be expected from SOC dynamics. This type of observations in our opinion has been reported for the first time in a glow discharge system.

Parametric investigation of nonlinear fluctuations in a dc glow discharge plasma

Glow discharge plasmas exhibit various types of self-excited oscillations for different initial conditions like discharge voltages and filling pressures. The behavior of such oscillations associated with the anode glow has been investigated using nonlinear techniques like correlation dimension, largest Lyapunov exponent, etc. It is seen that these oscillations go to an ordered state from a chaotic state with an increase in input energy, i.e., with discharge voltages implying occurrence of inverse bifurcations. These results are different from the other observations wherein the fluctuations have been observed to go from ordered to chaotic state.

Continuous wavelet transform based time-scale and multifractal analysis of the nonlinear oscillations in a hollow cathode glow discharge plasma

Continuous wavelet transform (CWT) based time-scale and multifractal analyses have been carried out on the anode glow related nonlinear floating potential fluctuations in a hollow cathode glow discharge plasma. CWT has been used to obtain the contour and ridge plots. Scale shift (or inversely frequency shift), which is a typical nonlinear behavior, has been detected from the undulating contours. From the ridge plots, we have identified the presence of nonlinearity and degree of chaoticity. Using the wavelet transform modulus maxima technique we have obtained the multifractal spectrum for the fluctuations at different discharge voltages and the spectrum was observed to become a monofractal for periodic signals. These multifractal spectra were also used to estimate different quantities such as the correlation and fractal dimension, degree of multifractality, and complexity parameters. These estimations have been found to be consistent with the nonlinear time series analysis.

Noise-invoked resonances near a homoclinic bifurcation in the glow discharge plasma

Stochastic resonance (SR) and coherence resonance (CR) have been studied experimentally in discharge plasmas close to a homoclinic bifurcation. For the SR phenomenon, it is observed that a superimposed subthreshold periodic signal can be recovered via stochastic modulations of the discharge voltage. Furthermore, it is realized that even in the absence of a subthreshold deterministic signal, the system dynamics can be recovered and optimized using noise. This effect is defined as CR in the literature. In the present experiments, induction of SR and CR is quantified using the absolute mean difference and normalized variance techniques, respectively.

Chaotic-to-ordered state transition of cathode-sheath instabilities in DC glow discharge plasmas

Transition from chaotic to ordered state has been observed during the initial stage of a discharge in a cylindrical DC glow discharge plasma. Initially it shows a chaotic behavior but increasing the discharge voltage changes the characteristics of the discharge glow and shows a period subtraction of order 7 period → 5 period → 3 period → 1 period, i.e. the system goes to single mode through odd cycle subtraction. On further increasing the discharge voltage, the system goes through period doubling, like 1 period → 2 period → 4 period. On further increasing the voltage, the system goes to stable state through two period subtraction, like 4 period → 2 period → stable.

Canard and mixed mode oscillations in an excitable glow discharge plasma in the presence of inhomogeneous magnetic field

We report on the experimental observation of canard orbit and mixed mode oscillations (MMOs) in an excitable glow discharge plasma induced by an external magnetic field perturbation using a bar magnet. At a small value of magnetic field, small amplitude quasiperiodic oscillations were excited, and with the increase in the magnetic field, large amplitude oscillations were excited. Analyzing the experimental results, it seems that the magnetic field could be playing the role of noise for such nonlinear phenomena. It is observed that the noise level increases with the increase in magnetic field strength. The experimental results have also been corroborated by a numerical simulation using a FitzHugh-Nagumo like macroscopic model derived from the basic plasma equations and phenomenology, where the noise has been included to represent the internal plasma noise. This macroscopic model shows MMO in the vicinity of the canard point when an external noise is added.

Effect of discrete time observations on synchronization in Chua model and applications to data assimilation.

Data assimilation is a tool, which incorporates observations in the model to improve the forecast, and it can be thought of as a synchronization of the model with observations. This paper discusses results of numerical identical twin experiments, with observations acting as master system coupled unidirectionally to the slave system at discrete time instances. We study the effects of varying the coupling constant, the observational frequency, and the observational noise intensity on synchronization and prediction in a low dimensional chaotic system, namely, the Chua circuit model. We observe synchrony in a finite range of coupling constant when coupling the x and y variables of the Chua model, but not when coupling the z variable. This range of coupling constant decreases with increasing levels of noise in the observations. The Chua system does not show synchrony when the time gap between observations is greater than about one-seventh of the Lyapunov time. Finally, we also note that the prediction errors are much larger when noisy observations are used than when using observations without noise.

Fractal Dimension of the 2001 El Salvador Earthquake Time Series

Earthquakes occur on the earth’s surface as a result of rearrangement of terrestrial cortex or higher part of the mantle. The energy released in this process propagates over long distances in the form of elastic seismic waves [1]. In order to predict earthquakes many models have been proposed [2, 3]. Dynamics of an earthquake is so complicated that it is quite difficult to predict using available models. Seismicity is a classic example of a complex phenomenon that can be quantified using fractal concepts [4]. In this paper we have estimated the fractal dimension, maximum, as well as minimum of the singularities, and the half-width of the multifractal spectrum of the El Salvador Earthquake signal at different stations. The data has been taken from the California catalogue (http://nsmp.wr.usgs.gov/nsmn eqdata.html). The paper has been arranged as follows: In Sect. 2 the basic theory of multifractality has been discussed, and the results have been presented in Sect. 3.