Bending of pinned dust-ion acoustic solitary waves in presence of charged space debris.

We consider a low temperature plasma environment in the low Earth orbital region in the presence of charged space debris particles. The dynamics of (2+1)-dimensional nonlinear dust-ion acoustic waves with weak transverse perturbation, generated in the system, is found to be governed by a forced Kadomtsev-Petviashvili equation, where the forcing term depends on charged space debris function. The bending phenomena of some exact dust-ion acoustic solitary wave solutions in the x-t and x-y planes are shown; they result from the consideration of different types of possible localized debris functions. A family of exact pinned accelerated solitary wave solutions has been obtained where the velocity changes over time but the amplitude remains constant. The shape of the debris function also changes during its propagation. Also, a special exact solitary wave solution has been derived for the dust-ion acoustic wave that gets curved in spatial dimensions with the curvature depending upon the nature of the forcing debris function. Such intricate solitary wave solutions may be useful in modeling real experimental data.

Using wavelet analysis to investigate synchronization.

Wavelet analysis is shown to be a more robust technique than previously used methods in the investigation of synchronization. The highlight of the technique is that it encompasses most of the information obtained by conventional methods into a single picture, while giving a deeper insight into the dynamics of the system. Order parameters derived from continuous wavelet transform coefficients are proposed, which can be used in the quantification of measure synchronization in Hamiltonian systems and identical synchronization in dissipative systems, irrespective of the nature of coupling, the nature of synchronization (complete or partial, quasiperiodic or chaotic), and the number of coupled subsystems.

Detection of self-organized criticality behavior in an electronic circuit designed to solve a third order non-linear ODE (NL-ODE) for a damped KdV equation.

In this work, we present an electronic implementation of a damped Korteweg-de Vries equation modeled as a third order nonlinear autonomous ordinary differential equation (jerk equation). The circuit has been realized using operational amplifiers, multipliers, and passive electronic components which provides the time series solution of the equation in agreement with the numerical simulation results. Using nonlinear time series analysis on the acquired waveform data, we have obtained different types of phase space portraits and further analysis reflected long range correlation in the chaotic time series. Important findings include hysteresis induced bifurcation and self-organized criticality behavior in the system which is mentioned in this work.

Frequency and wavelet based analyses of partial and complete measure synchronization in a system of three nonlinearly coupled oscillators.

Measure Synchronization (MS) is the generalization of synchrony to Hamiltonian Systems. Partial measure synchronization (PMS) and complete measure synchronization in a system of three nonlinearly coupled one-dimensional oscillators have been investigated for different initial conditions on the basis of numerical computation. The system is governed by the classical SU(2) Yang-Mills-Higgs (YMH) Hamiltonian with three degrees of freedom. Various transitions in the quasiperiodic (QP) region, namely, QP unsynchronized to PMS, PMS to PMS, and PMS to chaos are identified through the average bare energies and interaction energies route maps as the coupling strength is varied. The transition from quasiperiodicity to chaos is seen to be associated with a gradual transition to complete chaotic measure synchronization (CMS) which is followed by chaotic unsynchronized states, the most stable state in this case. The analyses illustrate the dependence on initial conditions. The explanation of the behavior in the QP regime is sought from the power spectral analysis. The existence of PMS is confirmed using the order parameter M (here M α ß for different combination pairs of oscillators), best suited to identify MS in coupled two-oscillator systems, and this definition is extended to obtain a new order parameter, M 3 , aiding to distinguish complete MS of three oscillators from other forms of motion. The study of wavelet coefficient spectra sheds new light on the relative phase information of the oscillators in the QP PMS regions, also highlighting the intertwined role played by the various frequency components and their amplitudes as they vary temporally. Furthermore, this technique helps to draw a sharp distinction between CMS and chaotic unsynchronized states. Based on the Continuous Wavelet Transform coefficients of the three oscillators, an order parameter M w a v is defined to indicate the extent of synchronization of the various scales (frequencies) for different coupling strengths in the chaotic regime.

Stickiness in double-curl Beltrami magnetic fields.

The double-curl Beltrami magnetic field in the presence of a uniform mean field is considered for investigating the nonlinear dynamical behavior of magnetic field lines. The solutions of the double-curl Beltrami equation being non-force-free in nature belong to a large class of physically interesting magnetic fields. A particular choice of solution for the double-curl equation in three dimensions leads to a wholly chaotic phase space. In the presence of a strong mean field, the phase space is a combination of closed magnetic surfaces and weakly chaotic regions that slowly tends to global randomness with a decreasing mean field. Stickiness is an important feature of the mixed phase space that describes the dynamical trapping of a chaotic trajectory at the border of regular regions. The global behavior of such trajectories is understood by computing the recurrence length statistics showing a long-tail distribution in contrast to a wholly chaotic phase space that supports a distribution which decays rapidly. Also, the transport characteristics of the field lines are analyzed in connection with their nonlinear dynamical properties.

Exploring the route to measure synchronization in non-linearly coupled Hamiltonian systems.

Measure Synchronization is a general term used for weak synchronization in Hamiltonian systems. Route to measure synchronization in a system of two non-linearly coupled one-dimensional oscillators, the potential of which is represented by the Pullen-Edmonds Potential is investigated on the basis of numerical computation. Transitions to measure synchronization and unsynchronization, both quasiperiodic and chaotic, are investigated and distinguished on the basis of the variation of average bare energies, average interaction energy, root-mean-square value of oscillations, phase difference, and frequencies with the coupling strength. A suitable order parameter to identify and characterize both quasiperiodic and chaotic measure synchronous states is sought, and drawbacks of the various order parameters, suggested previously, are discussed.

Evolution of self-organized two-dimensional patterns of nanoclusters through demixing.

A mixture of dodecanethiol-capped Au nanoparticles (AuNPs) and the amphiphilic fatty acid, stearic acid, spread as a monomolecular layer on water surface, is observed with Brewster angle microscopy (BAM) to form a two-dimensional network of AuNP clusters through demixing, at concentration of AuNPs by weight (ρ[over ¯])>10% and the surface pressure (π)≥10mNm^{-1}. For π=15mNm^{-1}, the number of nodes (n) remains unchanged till ∼2 hours and then changes over to a lower n state, where the pattern consists of almost perfect circles with greater in-plane thickness of the AuNP lamellae. For the higher n state the mean-square fluctuation of BAM intensity remains flat and then decays as f(ξ)=ξ^{2α} with α∼0.6 (correlated fluctuations) over the length scales of 400µm-6µm and below 6µm, respectively. For the lower n state the fluctuation decays almost over the entire length scale with α=0.3, indicating emergence of aperiodicity from quasiperiodicity and a changeover to anticorrelated fluctuations. These patterns can be looked at as two distinct chaotic trajectories in the I-I^{'} phase space of the system (I being the scattered light intensity at any position of the pattern and I^{'} its gradient) with characteristic Lyapunov exponents.

Intrinsic noise induced coherence resonance in a glow discharge plasma.

Experimental evidence of intrinsic noise induced coherence resonance in a glow discharge plasma is being reported. Initially the system is started at a discharge voltage (DV) where it exhibited fixed point dynamics, and then with the subsequent increase in the DV spikes were excited which were few in number and with further increase of DV the number of spikes as well as their regularity increased. The regularity in the interspike interval of the spikes is estimated using normalized variance. Coherence resonance was determined using normalized variance curve and also corroborated by Hurst exponent and power spectrum plots. We show that the regularity of the excitable spikes in the floating potential fluctuation increases with the increase in the DV, up to a particular value of DV. Using a Wiener filter, we separated the noise component which was observed to increase with DV and hence conjectured that noise can play an important role in the generation of the coherence resonance. From an anharmonic oscillator equation describing ion acoustic oscillations, we have been able to obtain a FitzHugh-Nagumo like model which has been used to understand the excitable dynamics of glow discharge plasma in the presence of noise. The numerical results agree quite well with the experimental results.

Phase-modulated solitary waves controlled by a boundary condition at the bottom.

A forced Korteweg-de Vries (KdV) equation is derived to describe weakly nonlinear, shallow-water surface wave propagation over nontrivial bottom boundary condition. We show that different functional forms of bottom boundary conditions self-consistently produce different forced KdV equations as the evolution equations for the free surface. Solitary wave solutions have been analytically obtained where phase gets modulated controlled by bottom boundary condition, whereas amplitude remains constant.

Chaotic magnetic fields in Vlasov-Maxwell equilibria.

Stationary solutions of Vlasov-Maxwell equations are obtained by exploiting the invariants of single particle motion leading to linear or nonlinear functional relations between current and vector potential. For a specific combination of invariants, it is shown that Vlasov-Maxwell equilibria have an associated Hamiltonian that exhibits chaos.

Shear flow instability in a strongly coupled dusty plasma.

Linear stability analysis of strongly coupled incompressible dusty plasma in presence of shear flow has been carried out using the generalized hydrodynamical (GH) model. With the proper Galilean invariant GH model, a nonlocal eigenvalue analysis has been done using different velocity profiles. It is shown that the effect of elasticity enhances the growth rate of shear flow driven Kelvin- Helmholtz (KH) instability. The interplay between viscosity and elasticity not only enhances the growth rate but the spatial domain of the instability is also widened. The growth rate in various parameter space and the corresponding eigenfunctions are presented.

Spheromak as a relaxed state with minimum dissipation.

The principle of minimum dissipation of energy is utilized to obtain the spheromak configuration as a relaxed state. The Euler-Lagrange equation for the minimum dissipative relaxed state is solved in terms of Chandrasekhar-Kendall eigenfunctions analytically generalized in the complex domain. This state is non-force-free and further shows the nonconstancy of the ratio of parallel current to the magnetic field.