Document Type : Research
Authors
1 Sahand university of technology
2 Department of Chemical, Petroleum and Gas Engineering, Technical and Vocational University, Tehran,Iran
Abstract
Using quantum hydrodynamic (QHD) model, dust acoustic (DA) shock waves are studied in a quantum dusty plasma containing degenerate electrons, ions and negatively charged dust grains. Employing the reductive perturbation technique, a Kortweg-de Vries-Burgers (KdVB) equation is derived and solved theoretically and numerically. The hyperbolic tangent (tanh) method is used for theoretical solution. One of the most convenient approaches for solving the nonlinear partial differential equation in dispersive and dissipative system is the tanh method. The KdVB equation is solved numerically by fourth-order Runge – Kutta method. It is found that when dissipation dominates over dispersion, monotonic shock structure is formed, while in case of small dissipation, oscillatory shock profile is created. The influence of viscosity on DA shock waves shows that shock thickness is enhanced with the increase in viscosity. Additionally, the number and height of oscillatory shocks get increased by decreasing the viscosity. The solutions of the KdVB equation is studied in a frame moving with the phase velocity of the wave. Considering the boundary conditions, the nonlinear obtained equation is rewritten in the form of a dynamical system. In the plane, this system has two fixed points. Investigating the eigen values corresponding to these fixed points indicate that one point is always a saddle, while the other one is either a stable focus or stable node. The phase plane analysis shows that the decrease in the number of spirals show increase in dissipation.
Keywords
)