Hydrodynamic Behaviour of Floating Polygonal Platforms under Wave Action

The hydrodynamic behaviour of floating regular polygonal platforms under wave action was studied by conducting parametric studies. Considering triangular, square, hexagonal, and circular platforms of similar size and draft, the results show that their added mass, radiation damping, and RAOs are similar. However, the wave exciting forces are slightly different, particularly the horizontal forces. The polygonal platforms oriented with one of its corners in line with the prevailing wave direction can lead to a reduction in the horizontal force on the platform, a feature that helps in reducing the cost of a mooring system. Moreover, such oriented platforms are able to disperse the waves better in multiple directions and hence will not pose problems for ships or marine vessels passing by the platform on the weather side. Thus, the orientation of a polygonal platform is an important design consideration. From the comparison study among different polygonal platforms, their wave attenuation performances are slightly similar. The hydrodynamic analyses performed herein for the parametric studies were sped up considerably by using a significantly lesser number of Fourier coefficient sets for the series functions that define the velocity potentials when compared to those used by previous researchers in their analytical approaches. The adoption of the radius function defined by cosine-type radial perturbation does not only generate the geometric boundaries of polygonal platforms, but it also simplifies the formulation and quickens the computations.

Stability of a charged rotating BTZ thin shell with a different variable equation of state

Dynamics of charged rotating BTZ black holes in 2 + 1 dimensions by using the cut and paste approach is discussed. Due to the mechanical stability of rotating charged BTZ thin shell, the radial perturbation about the equilibrium throat radius and three variable equation of state (EoS) is analyzed. Several examples are displayed satisfying it, such as variable Phantom-like, variable Chaplygin gas and variable modified generalized Chaplygin gas.

Stability of charged thin-shell gravastars with quintessence

This paper develops a new solution of gravitational vacuum star in the background of charged Kiselev black holes as an exterior manifold. We explore physical features and stability of thin-shell gravastars with radial perturbation. The matter thin layer located at thin-shell greatly affects stable configuration of the developed structure. We assume three different choices of matter distribution such as barotropic, generalized Chaplygin gas and generalized phantomlike equation of state. The last two models depend on the shell radius, also known as variable equation of state. For barotropic model, the structure of thin-shell gravastar is mostly unstable while it shows stable configuration for such type of matter distribution with extraordinary quintessence parameter. The resulting gravastar structure indicates stable behavior for generalized Chaplygin gas but unstable for generalized phantomlike model. It is also found that proper length, entropy and energy within the shell show linear relation with thickness of the shell.

Mechanical stability of a class of regular thin-shell wormholes

This paper explores the stable configuration of thin-shell wormholes constructed from two regular black holes (modified Hayward and four parametric) by using Visser cut and paste approach. The components of stress-energy tensor are evaluated through the Lanczos equations. We analyze the stability of thin-shell by using radial perturbation preserving its symmetries about equilibrium static solution. It is found that modified Hayward wormholes are more stable than the Hayward wormholes. Further, the stable regions of four parametric regular wormholes are larger than the Schwarzschild, Reissner–Nordström and Ayón–Beato–García wormholes. We conclude that stable region decreases for highly charged thin-shell wormholes.

Electromagnetic effects on the stability of anisotropic cylinder

This paper is devoted to analyzing the stability of charged anisotropic cylinder using the radial perturbation scheme. For this purpose, we consider the non-static cylindrically symmetric self-gravitating system and apply both Eulerian as well as Lagrangian approaches to establish a linearized perturbed form of dynamical equations. The conservation of baryon number is used to evaluate perturbed radial pressure in terms of an adiabatic index. A variational principle is developed to find a characteristic frequency which helps to examine the combined effect of charge and anisotropy on the stability of gaseous star. It is found that dynamical instability can be prevented until the radius of cylinder exceeds the limit [Formula: see text] and anisotropy increases the instability up to the limiting value of [Formula: see text]. Finally, we conclude that the system becomes more stable by increasing the definite amount of charge gradually.

Three-dimensional axisymmetric sources for Majumdar–Papapetrou type spacetimes

From Newtonian potential-density pairs, we construct three-dimensional axisymmetric relativistic sources for a Majumdar–Papapetrou type conformastatic spacetime. As simple examples, we build two families of relativistic thick disks from the first two Miyamoto–Nagai potential-density pairs used in Newtonian gravity to model flat galaxies, and a three-component relativistic model of galaxy (bulge, disk and dark matter halo). We study the equatorial circular motion of test particles around such structures. Also the stability of the orbits is analyzed for radial perturbation using an extension of the Rayleigh criterion. In all examples, the relativistic effects are analyzed and compared with the Newtonian approximation. The models are considered satisfying all the energy conditions.

Stability of oscillating gaseous masses in massive Brans–Dicke gravity

This paper explores the instability of gaseous masses for the radial oscillations in post-Newtonian correction of massive Brans–Dicke (BD) gravity. For this purpose, we derive linearized perturbed equation of motion through Lagrangian radial perturbation which leads to the condition of marginal stability. We discuss radius of instability of different polytropic structures in terms of the Schwarzschild radius. It is concluded that our results provide a wide range of difference with those in general relativity and BD gravity.

Construction of thin shell wormholes from metric f(R) gravity

In this paper, we have constructed spherically symmetric thin-shell wormholes (WHs) by surgically grafting two geometries of charged black hole in the framework of f(R) higher curvature invariants (threaded by exotic matter). We have investigated the stable/unstable regimes for couple of f(R) models using the potential approach formulated by Eiroa with radial perturbation. We have categorized our analysis for different values of charge as well as the parameters involved in the particular mode of f(R) gravity. We have found both stable and unstable regions using modified Chaplygin gas in this scenario and the results are shown through plots. We found that there exists a parametric space for equation of state and quadratic as well as cubic gravities in which one can accommodate more stable thin-shell WHs.

The Contribution of Degenerate Electron Pressure to The Stability of The Outer Region of Thin Keplerian Accretion Disks Around a Neutron Star

The stability analysis of a geometrically thin, gas-pressure dominated accretion disk around a neutron star is presented. In purely radial perturbation case, thin disk is stable to thermal modes. The stability is analyzed at a small temperature, that is temperature approaching zero and at definite temperature. The contribution of both fully and partially degenerate electrons pressure for the stability of the disk in its outer region is investigated. We find that the disk is stable in this region, where the gas pressure is more dominant than radiation pressure.