Nonplanar electron acoustic shock waves

The properties of cylindrical and spherical electron acoustic shock waves (EASWs) in an unmagnetized plasma consisting of cold electrons, immobile ions and Boltzmann distributed hot electrons are investigated by employing the reductive perturbation method. A Korteweg–de Vries Burgers (KdVB) equation is derived and its numerical solution is obtained. The effects of several parameters and ion kinematic viscosity on the basic features of EA shock waves are discussed in nonplanar geometry. It is found that nonplanar EA shock waves behave quite differently from their one-dimensional planar counterpart.     

Parametric instability of twisted cross-ply laminated panels

The present paper deals with the study of the vibration, buckling and parametric instability characteristics of general laminated cross-ply pre-twisted cantilever flat and curved panels. The effects of angles of pre-twist, aspect ratio, static load factor, and the lamination parameters of the cross-ply twisted curved panels on the principal instability regions are studied using Bolotin?s approach. An eight-noded isoparametric quadratic shell element with five degrees of freedom per node is used to develop the finite element procedure. The first order shear deformation theory is used to model the twisted cross-ply curved panels considering the effects of transverse shear deformation and rotary inertia. The linear part of the strain is used to derive the elastic stiffness matrix and the non-linear part of the strain is used to derive the geometric stiffness matrix. The global matrices are obtained by assembling the corresponding element matrices using skyline technique. Subspace iteration method is used throughout to solve the eigenvalue problem. Reduced integration technique is adopted in order to avoid possible shear locking. Based on the parametric studies, it is found that the instability behavior of twisted cross-ply cantilever panels is greatly influenced by the geometry, material, angle of twist and lamination parameters. So, this can be used to advantage in tailoring during design of crossply twisted cantilever panels.     

Nonlinear quantum ion acoustic shock wave dynamics with exchange-correlation effects

The dynamics of linear and nonlinear electrostatic shock excitations is studied in homogeneous, unmagnetized, unbounded and dissipative quantum plasma consisting of electrons and ions. The dissipation in the system is taken into account by incorporating the ion kinematic viscosity. The system is modelled using the quantum hydrodynamic equations in which the electrons are significantly affected by the quantum forces, viz., the quantum statistical pressure, the quantum Bohm potential and electron exchange-correlations due to electron spin. In the weakly nonlinear limit, using reductive perturbation method deformed Korteweg-de Vries Burgers’s (KdVB) equation, which elegantly combines the effects of nonlinearity, dispersion and dissipation is derived. It is found that the present model predicts the existence of both nonlinear oscillatory and monotonic shock structures. The temporal evolution, stability and phase-space dynamics of nonlinear ion acoustic shocks are investigated numerically to elucidate the effects of quantum diffraction, electron exchange correlation and ion kinematic viscosity.     

Excitation of electrostatic plasma waves by a moving charged source in a quantum plasma

Within a quantum hydrodynamic model and using the reductive perturbation technique, the nonlinear ion-acoustic wave (IAW) excitations due to a moving charged object in an electron-pair-ion quantum plasma are studied both analytically and numerically. In such quantum plasmas we have derived forced Korteweg-de Vries (fKdV) type equation for finite amplitude nonlinear IAWs. The effect of relevant plasma parameters on solitonic excitations is investigated. Numerical simulation shows the generation of advancing solitons ahead of the forcing term traveling at a faster rate with trailing wakes behind the forcing disturbance. It is found that propagation characteristics of nonlinear excitations are significantly affected by quantum parameter. Additionally, we have pursued our analysis by extending it to account for arbitrary amplitude IA solitons, and derived a system of nonlinear differential equations which are analyzed numerically to study the dynamics. Nonlinear analysis predicts the existence of periodic and quasiperiodic nature of the nonlinear system and reveals that the transition from quasiperiodic to periodic behavior occurs due to the variation of quantum diffraction.