The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform

A.s. Gupta - One of the best experts on this subject based on the ideXlab platform.

  • effect of radial temperature gradient on the Stability of taylor dean flow between two arbitrarily spaced concentric rotating cylinders
    International Journal of Heat and Mass Transfer, 2013
    Co-Authors: Tapas Ray Mahapatra, Samir Kumar Nandy, A.s. Gupta
    Abstract:

    Abstract The effect of a radial temperature gradient on the Stability of Taylor–Dean flow of an incompressible viscous fluid between two arbitrarily spaced concentric rotating circular cylinders driven by a constant azimuthal pressure gradient is studied. Here the ratio of representative pumping and rotation velocities β is varied from −6.1613 to 1.00 and both positive and negative values of the temperature gradient parameter N are considered, where N depends on the temperature differences T2 − T1 between the outer and inner cylinders. The Linearized Stability equations form an eigenvalue problem which is solved by using a classical Runge–Kutta scheme combined with a shooting technique, termed unit disturbance method. It is found that as the gap width between the cylinders increases, the critical Taylor number progressively increases for given values of β and N. It is also found that for given values of η (the ratio of the radii of inner and outer cylinders) and β, the flow becomes more and more unstable with increase in N(>0). In the present work, emphasis is given on the point as to whether the two neutral Stability curves cross at some point for given value of N for which the flow is completely stable.

  • Stability of viscous flow driven by an azimuthal pressure gradient between two porous concentric cylinders with radial flow and a radial temperature gradient
    Acta Mechanica, 2007
    Co-Authors: Rudra Kanta Deka, A.s. Gupta
    Abstract:

    The effect of a radial temperature gradient on the Stability of viscous flow between two porous concentric circular cylinders driven by a constant azimuthal pressure gradient is studied when a radial flow through the permeable walls of the cylinders is present. The radial Reynolds number β based on the radial velocity at the inner cylinder and the inner radius R1 is varied from −130 to 30 and both positive and negative values of the parameter N are taken, where N depends on the temperature difference T2 − T1 between the outer and inner cylinders. The Linearized Stability equations form an eigenvalue problem, which are solved by using a classical Runge-Kutta scheme combined with a shooting method, termed unit disturbance method. It is found that for a given value of N the radially outward flow (β > 0) has a stabilizing effect and the stabilization is more as the gap between the cylinders increases. But the inward throughflow (β 0, the flow becomes more and more unstable with an increase in N.

Paulo Crawford - One of the best experts on this subject based on the ideXlab platform.

  • Linearized Stability analysis of thin shell wormholes with a cosmological constant
    Classical and Quantum Gravity, 2004
    Co-Authors: Francisco S N Lobo, Paulo Crawford
    Abstract:

    Spherically symmetric thin-shell wormholes in the presence of a cosmological constant are constructed applying the cut-and-paste technique implemented by Visser. Using the Darmois–Israel formalism the surface stresses, which are concentrated at the wormhole throat, are determined. This construction allows us to apply a dynamical analysis to the throat, considering Linearized radial perturbations around static solutions. For a large positive cosmological constant, i.e., for the Schwarzschild–de Sitter solution, the region of Stability is significantly increased, relatively to the null cosmological constant case, analysed by Poisson and Visser. With a negative cosmological constant, i.e., the Schwarzschild–anti de Sitter solution, the region of Stability is decreased. In particular, considering static solutions with a generic cosmological constant, the weak and dominant energy conditions are violated, while for a0 ≤ 3M the null and strong energy conditions are satisfied. The surface pressure of the static solution is strictly positive for the Schwarzschild and Schwarzschild–anti de Sitter spacetimes, but takes negative values, assuming a surface tension in the Schwarzschild–de Sitter solution, for high values of the cosmological constant and the wormhole throat radius.

  • Linearized Stability analysis of thin shell wormholes with a cosmological constant
    arXiv: General Relativity and Quantum Cosmology, 2003
    Co-Authors: Francisco S N Lobo, Paulo Crawford
    Abstract:

    Spherically symmetric thin-shell wormholes in the presence of a cosmological constant are constructed applying the cut-and-paste technique implemented by Visser. Using the Darmois-Israel formalism the surface stresses, which are concentrated at the wormhole throat, are determined. This construction allows one to apply a dynamical analysis to the throat, considering Linearized radial perturbations around static solutions. For a large positive cosmological constant, i.e., for the Schwarzschild-de Sitter solution, the region of Stability is significantly increased, relatively to the null cosmological constant case, analyzed by Poisson and Visser. With a negative cosmological constant, i.e., the Schwarzschild-anti de Sitter solution, the region of Stability is decreased. In particular, considering static solutions with a generic cosmological constant, the weak and dominant energy conditions are violated, while for $a_0 \leq 3M$ the null and strong energy conditions are satisfied. The surface pressure of the static solution is strictly positive for the Schwarzschild and Schwarzschild-anti de Sitter spacetimes, but takes negative values, assuming a surface tension in the Schwarzschild-de Sitter solution, for high values of the cosmological constant and the wormhole throat radius.

Francisco S N Lobo - One of the best experts on this subject based on the ideXlab platform.

  • Linearized Stability analysis of gravastars in noncommutative geometry
    Journal of High Energy Physics, 2013
    Co-Authors: Francisco S N Lobo, Remo Garattini
    Abstract:

    In this work, we find exact gravastar solutions in the context of noncommutative geometry, and explore their physical properties and characteristics. The energy density of these geometries is a smeared and particle-like gravitational source, where the mass is diffused throughout a region of linear dimension $ \sqrt{\alpha } $ due to the intrinsic uncertainty encoded in the coordinate commutator. These solutions are then matched to an exterior Schwarzschild spacetime. We further explore the dynamical Stability of the transition layer of these gravastars, for the specific case of β = M 2/α < 1.9, where M is the black hole mass, to Linearized spherically symmetric radial perturbations about static equilibrium solutions. It is found that large Stability regions exist and, in particular, located sufficiently close to where the event horizon is expected to form.

  • Linearized Stability analysis of gravastars in noncommutative geometry
    arXiv: General Relativity and Quantum Cosmology, 2010
    Co-Authors: Francisco S N Lobo, Remo Garattini
    Abstract:

    In this work, we find exact gravastar solutions in the context of noncommutative geometry, and explore their physical properties and characteristics. The energy density of these geometries is a smeared and particle-like gravitational source, where the mass is diffused throughout a region of linear dimension $\sqrt{(\alpha)}$ due to the intrinsic uncertainty encoded in the coordinate commutator. These solutions are then matched to an exterior Schwarzschild spacetime. We further explore the dynamical Stability of the transition layer of these gravastars, for the specific case of $\beta=M^2/\alpha<1.9$, where M is the black hole mass, to Linearized spherically symmetric radial perturbations about static equilibrium solutions. It is found that large Stability regions exist and, in particular, located sufficiently close to where the event horizon is expected to form.

  • Linearized Stability analysis of thin shell wormholes with a cosmological constant
    Classical and Quantum Gravity, 2004
    Co-Authors: Francisco S N Lobo, Paulo Crawford
    Abstract:

    Spherically symmetric thin-shell wormholes in the presence of a cosmological constant are constructed applying the cut-and-paste technique implemented by Visser. Using the Darmois–Israel formalism the surface stresses, which are concentrated at the wormhole throat, are determined. This construction allows us to apply a dynamical analysis to the throat, considering Linearized radial perturbations around static solutions. For a large positive cosmological constant, i.e., for the Schwarzschild–de Sitter solution, the region of Stability is significantly increased, relatively to the null cosmological constant case, analysed by Poisson and Visser. With a negative cosmological constant, i.e., the Schwarzschild–anti de Sitter solution, the region of Stability is decreased. In particular, considering static solutions with a generic cosmological constant, the weak and dominant energy conditions are violated, while for a0 ≤ 3M the null and strong energy conditions are satisfied. The surface pressure of the static solution is strictly positive for the Schwarzschild and Schwarzschild–anti de Sitter spacetimes, but takes negative values, assuming a surface tension in the Schwarzschild–de Sitter solution, for high values of the cosmological constant and the wormhole throat radius.

  • Linearized Stability analysis of thin shell wormholes with a cosmological constant
    arXiv: General Relativity and Quantum Cosmology, 2003
    Co-Authors: Francisco S N Lobo, Paulo Crawford
    Abstract:

    Spherically symmetric thin-shell wormholes in the presence of a cosmological constant are constructed applying the cut-and-paste technique implemented by Visser. Using the Darmois-Israel formalism the surface stresses, which are concentrated at the wormhole throat, are determined. This construction allows one to apply a dynamical analysis to the throat, considering Linearized radial perturbations around static solutions. For a large positive cosmological constant, i.e., for the Schwarzschild-de Sitter solution, the region of Stability is significantly increased, relatively to the null cosmological constant case, analyzed by Poisson and Visser. With a negative cosmological constant, i.e., the Schwarzschild-anti de Sitter solution, the region of Stability is decreased. In particular, considering static solutions with a generic cosmological constant, the weak and dominant energy conditions are violated, while for $a_0 \leq 3M$ the null and strong energy conditions are satisfied. The surface pressure of the static solution is strictly positive for the Schwarzschild and Schwarzschild-anti de Sitter spacetimes, but takes negative values, assuming a surface tension in the Schwarzschild-de Sitter solution, for high values of the cosmological constant and the wormhole throat radius.

Liqun Chen - One of the best experts on this subject based on the ideXlab platform.

  • principal parametric resonance of axially accelerating viscoelastic strings with an integral constitutive law
    Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2005
    Co-Authors: Liqun Chen
    Abstract:

    The steady-state transverse responses and the Stability of an axially accelerating viscoelastic string are investigated. The governing equation is derived from the Eulerian equation of motion of a continuum, which leads to the Mote model for transverse motion. The Kirchhoff model is derived from the Mote model by replacing the tension with the averaged tension over the string. The method of multiple scales is applied to the two models in the case of principal parametric resonance. Closed-form expressions of the amplitudes and the existence conditions of steady-state periodical responses are presented. The Lyapunov Linearized Stability theory is employed to demonstrate that the first (second) non-trivial steady-state response is always stable (unstable). Numerical calculations show that the two models are qualitatively the same, but quantitatively different. Numerical results are also presented to highlight the effects of the mean axial speed, the axial-speed fluctuation amplitude, and the viscoelastic parameters.

  • steady state response of axially moving viscoelastic beams with pulsating speed comparison of two nonlinear models
    International Journal of Solids and Structures, 2005
    Co-Authors: Liqun Chen, Xiaodong Yang
    Abstract:

    Abstract Principal parametric resonance in transverse vibration is investigated for viscoelastic beams moving with axial pulsating speed. A nonlinear partial-differential equation governing the transverse vibration is derived from the dynamical, constitutive, and geometrical relations. Under certain assumption, the partial-differential reduces to an integro-partial-differential equation for transverse vibration of axially accelerating viscoelastic nonlinear beams. The method of multiple scales is applied to two equations to calculate the steady-state response. Closed form solutions for the amplitude of the vibration are derived from the solvability condition of eliminating secular terms. The Stability of straight equilibrium and nontrivial steady-state response are analyzed by use of the Lyapunov Linearized Stability theory. Numerical examples are presented to highlight the effects of speed pulsation, viscoelascity, and nonlinearity and to compare results obtained from two equations.

  • transverse vibrations of an axially accelerating viscoelastic string with geometric nonlinearity
    Journal of Engineering Mathematics, 2004
    Co-Authors: Liqun Chen, Xiaodong Yang
    Abstract:

    Two-to-one parametric resonance in transverse vibration of an axially accelerating viscoelastic string with geometric nonlinearity is investigated. The transport speed is assumed to be a constant mean speed with small harmonic variations. The nonlinear partial differential equation that governs transverse vibration of the string is derived from Newton's second law. The method of multiple scales is applied directly to the equation, and the solvability condition of eliminating secular terms is established. Closed-form solutions for the amplitude of the vibration and the existence conditions of nontrivial steady-state response in two-to-one parametric resonance are obtained. Some numerical examples showing effects of the mean transport speed, the amplitude and the frequency of speed variation are presented. Lyapunov's Linearized Stability theory is employed to analyze the Stability of the trivial and nontrivial solutions for two-to-one parametric resonance. Some numerical examples highlighting the effects of the related parameters on the Stability conditions are presented.

Victor Varela - One of the best experts on this subject based on the ideXlab platform.

  • note on Linearized Stability of schwarzschild thin shell wormholes with variable equations of state
    Physical Review D, 2015
    Co-Authors: Victor Varela
    Abstract:

    We discuss how the assumption of variable equation of state (EoS) allows the elimination of the inStability at equilibrium throat radius $a_0=3M$ featured by previous Schwarzschild thin-shell wormhole models. Unobstructed Stability regions are found for three choices of variable EoS. Two of these EoS entail linear Stability at every equilibrium radius. Particularly, the thin-shell remains stable as $a_0$ approaches the Schwarzschild radius $2M$. A perturbative analysis of the wormhole equation of motion is carried out in the case of variable Chaplygin EoS. The squared proper angular frequency $\omega_0^2$ of small throat oscillations is linked with the second derivative of the thin-shell potential. In various situations $\omega_0^2$ remains positive and bounded in the limit $a_0\rightarrow 2M$.