Growth Rate System Research Articles

An evolution of hyperbolic magneto-hydrodynamic (HMHD) wave propagating through radiative quantum plasma including cosmic ray pressure

The gravitational (Jeans) instability of radiative quantum plasma including cosmic ray (CR) pressure and diffusion is theoretically investigated using a generalized hyperbolic magneto-hydrodynamic model. It concurrently includes the impacts of the finite electrical resistivity, the Hall parameter, and the Coriolis force. The application of normal mode technique yields a unique form of a generalized dispersion relation. This dispersion relation is further discussed in the different modes of propagation with the different axis of rotation along the direction of the magnetic field. It has been noted that all the considered parameters affect the system's growth rate in both directions, but the Hall parameter does not affect it in the transverse direction. We also explored that together with the CRs, the Hall parameter, resistivity, rotation, and quantum parameter suppressed the Jeans instability's growth rate. Thus, these parameters act as stabilizing agents to the instability. The study identified radiative instability and analyzed the impact of an arbitrary heat-loss function on the system. The current findings provide new theoretical support to the existing various astronomic observations on the cosmic plasma and in the development of unique galactic formations of distinct scale lengths.

The role of electron inertia on jeans instability of radiative quantum plasma with the impact of rotation and resistivity

With the use of the Quantum Magnetohydrodynamic (QMHD) model, we took into account the Jeans instability of rotating magnetized radiative quantum plasma under the impact of finite electron inertia and resistivity. The issue is set up and using the linearization method and normal mode technique, we can get the general dispersion relation, which is then described in terms of various modes of propagation. Within the prescribed boundaries, we also get the Jeans instability criteria. Plotting the curves between the system's growth rate and wave number for the investigation of the stability analysis of the system, which is then thoroughly explained.

Influence of FLR correction on Jeans instability in rotating radiative QMHD fluid model

ABSTRACT The descriptive exploration of Jeans instability under the QMHD fluid model for magnetized radiative plasma, preserving the consequences of rotation and finite ion Larmor radius. The problem of equations is formulated by using the quantum magnetohydrodynamic fluid model. The general dispersion relations were achieved using a standard mode analysis by formulating a linearized equation set and the dispersion relations are explained in the transverse and parallel propagations of the magnetic field. Those latter particular situations are discussed in the light of the axis of rotation in the longitudinal and transverse magnetic field. From the numerical calculation, we observe that Jean's criteria are changed due to the existence of FLR corrections, the feature of radiation, quantum correction, and magnetic field. From the graphical presentation, we find that the effect of FLR correction with rotation, quantum correction, and the magnetic field is a more stabilizing impact on comparing the system than the simple gaseous plasma medium. The result demonstrates that the system's growth rate is affected by FLR, rotation, magnetic field, and quantum correction.

Normalised quadratic controls for a class of bilinear systems

Normalised quadratic control, a modification of the conventional quadratic control method, has recently been proposed to exponentially stabilise a homogeneous bilinear system whose open-loop eigenvalues all fall on the imaginary axis. The normalised quadratic control method is now extended to a broader class of bilinear systems whose open-loop eigenvalues may fall to the left or right of the imaginary axis. It is shown that for bilinear systems that are already open-loop stable, the normalised quadratic control can add to the system an extra exponential decay rate. For open-loop unstable bilinear systems, the normalised quadratic control can stabilise the system if the extra exponential decay rate provided by the control is larger than the open-loop system's growth rate.