Showing papers on "Axial symmetry published in 2014"

Dissipative collapse of axially symmetric, general relativistic, sources: A general framework and some applications

Abstract: We carry out a general study on the collapse of axially (and reflection-)symmetric sources in the context of general relativity. All basic equations and concepts required to perform such a general study are deployed. These equations are written down for a general anisotropic dissipative fluid. The proposed approach allows for analytical studies as well as for numerical applications. A causal transport equation derived from the Israel-Stewart theory is applied, to discuss some thermodynamic aspects of the problem. A set of scalar functions (the structure scalars) derived from the orthogonal splitting of the Riemann tensor are calculated and their role in the dynamics of the source is clearly exhibited. The characterization of the gravitational radiation emitted by the source is discussed.

Using Fourier differential quadrature method to analyze transverse nonlinear vibrations of an axially accelerating viscoelastic beam

Abstract: In this paper, a Fourier expansion-based differential quadrature (FDQ) method is developed to analyze numerically the transverse nonlinear vibrations of an axially accelerating viscoelastic beam. The partial differential nonlinear governing equation is discretized in space region and in time domain using FDQ and Runge–Kutta–Fehlberg methods, respectively. The accuracy of the proposed method is represented by two numerical examples. The nonlinear dynamical behaviors, such as the bifurcations and chaotic motions of the axially accelerating viscoelastic beam, are investigated using the bifurcation diagrams, Lyapunov exponents, Poincare maps, and three-dimensional phase portraits. The bifurcation diagrams for the in-plane responses to the mean axial velocity, the amplitude of velocity fluctuation, and the frequency of velocity fluctuation are, respectively, presented when other parameters are fixed. The Lyapunov exponents are calculated to further identify the existence of the periodic and chaotic motions in the transverse nonlinear vibrations of the axially accelerating viscoelastic beam. The conclusion is drawn from numerical simulation results that the FDQ method is a simple and efficient method for the analysis of the nonlinear dynamics of the axially accelerating viscoelastic beam.

Circular Polarization of Periodic Leaky-Wave Antennas With Axial Asymmetry: Theoretical Proof and Experimental Demonstration

Abstract: This paper includes two contributions. First, it proves that the series and shunt radiation components, corresponding to longitudinal and transversal electric fields, respectively, are always in phase quadrature in axially asymmetric periodic leaky-wave antennas (LWAs), so that these antennas are inherently elliptically polarized. This fact is theoretically proven and experimentally illustrated by two case-study examples, a composite right/left-handed (CRLH) LWA and a series-fed patch (SFP) LWA. Second, it shows (for the case of the SFP LWA) that the axial ratio is controlled and minimized by the degree of axial asymmetry.

Axially symmetric cosmological model in f(R, T) gravity

Abstract: An axially symmetric space-time is considered in the presence of a perfect fluid source in the framework of f (R, T) gravity, where R is the Ricci scalar and T is the trace of the energy-momentum tensor proposed by Harko et al. (Phys. Rev. D 84, 024020, (2011)). We assume the variation law of mean Hubble parameter to obtain the exact solutions of the field equations. The geometrical and physical parameters for both the models are studied.

Inducing chaos by breaking axial symmetry in a black hole magnetosphere

Abstract: While the motion of particles near a rotating, electrically neutral (Kerr), and charged (Kerr-Newman) black hole is always strictly regular, a perturbation in the gravitational or the electromagnetic field generally leads to chaos. The transition from regular to chaotic dynamics is relatively gradual if the system preserves axial symmetry, whereas non-axisymmetry induces chaos more efficiently. Here we study the development of chaos in an oblique (electro-vacuum) magnetosphere of a magnetized black hole. Besides the strong gravity of the massive source represented by the Kerr metric, we consider the presence of a weak, ordered, large-scale magnetic field. An axially symmetric model consisting of a rotating black hole embedded in an aligned magnetic field is generalized by allowing an oblique direction of the field having a general inclination with respect to the rotation axis of the system. The inclination of the field acts as an additional perturbation to the motion of charged particles as it breaks the axial symmetry of the system and cancels the related integral of motion. The axial component of angular momentum is no longer conserved and the resulting system thus has three degrees of freedom. Our primary concern within this contribution is to find out how sensitive the system of bound particles is to the inclination of the field. We employ the method of the maximal Lyapunov exponent to distinguish between regular and chaotic orbits and to quantify their chaoticity. We find that even a small misalignment induces chaotic motion.

Shear-free axially symmetric dissipative fluids

Abstract: We study the general properties of axially symmetric dissipative configurations under the shear-free condition. The link between the magnetic part of the Weyl tensor and the vorticity is clearly exhibited, as well as the role of the dissipative fluxes. As a particular case, we examine the geodesic fluid. In this case, the magnetic part of the Weyl tensor always vanishes, suggesting that no gravitational radiation is produced during the evolution. In addition, for the geodesic case, in the absence of dissipation, the system evolves towards a Friedmann-Roberston-Walker spacetime if the expansion scalar is positive.

Dynamics of fluid flow over a circular flexible plate

Abstract: The dynamics of viscous fluid flow over a circular flexible plate are studied numerically by an immersed boundary–lattice Boltzmann method for the fluid flow and a finite-element method for the plate motion. When the plate is clamped at its centre and placed in a uniform flow, it deforms by the flow-induced forces exerted on its surface. A series of distinct deformation modes of the plate are found in terms of the azimuthal fold number from axial symmetry to multifold deformation patterns. The developing process of deformation modes is analysed and both steady and unsteady states of the fluid–structure system are identified. The drag reduction due to the plate deformation and the elastic potential energy of the flexible plate are investigated. Theoretical analysis is performed to elucidate the deformation characteristics. The results obtained in this study provide physical insight into the understanding of the mechanisms on the dynamics of the fluid–structure system.

Nonlinear transverse vibration of axially accelerating strings with exact internal resonances and longitudinally varying tensions

Abstract: This work explores the steady-state periodic transverse responses with their stabilities of axially accelerating viscoelastic strings. Longitudinally varying tension due to the axial acceleration is recognized in the modeling, while the tension was approximatively assumed to be longitudinally uniform in previous investigations. Exact internal resonances are highlighted in the analysis, while the resonances have been neglected in all available works. A governing equation of transverse nonlinear vibration is derived from the generalized Hamilton principle and the Kelvin viscoelastic model on the assumption that the string deformation is not infinitesimal, but still small. The axial speed is supposed to be a small simple harmonic fluctuation about the constant mean axial speed. The method of multiple scales is applied to solve the governing equation in the parametric resonances when the axial speed fluctuation frequency approaches the first three natural frequencies of the linear generating system based on 1–3 term truncations. The amplitude, the existence conditions, and the stability are determined, and the effects of the viscosity, the mean axial speed, the axial speed fluctuation amplitude, and the axial support rigidity on the amplitude and the existence are examined via the numerical examples. It is found that the 1-term, the 2-term, and the 3-term truncations yield the qualitatively same and the quantitatively close results in the case that there exist the exact internal resonances among the first three frequencies.

Rotating, Stationary, Axially Symmetric Spacetimes with Collisionless Matter

Abstract: The existence of stationary solutions to the Einstein–Vlasov system which are axially symmetric and have non-zero total angular momentum is shown. This provides mathematical models for rotating, general relativistic and asymptotically flat non-vacuum spacetimes. If angular momentum is allowed to be non-zero, the system of equations to solve contains one semilinear elliptic equation which is singular on the axis of rotation. This can be handled very efficiently by recasting the equation as one for an axisymmetric unknown on $${\mathbb{R}^5}$$ .

Chaotic Dynamics of an Axially Accelerating Viscoelastic Beam in the Supercritical Regime

Abstract: This paper focuses on the bifurcation and chaos of an axially accelerating viscoelastic beam in the supercritical regime. For the first time, the nonlinear dynamics of the system under consideration are studied via the high-order Galerkin truncation as well as the differential and integral quadrature method (DQM & IQM). The speed of the axially moving beam is assumed to be comprised of a constant mean value along with harmonic fluctuations. The transverse vibrations of the beam are governed by a nonlinear integro-partial-differential equation, which includes the finite axial support rigidity and the longitudinally varying tension due to the axial acceleration. The Galerkin truncation and the DQM & IQM are, respectively, applied to reduce the equation into a set of ordinary differential equations. Furthermore, the time history of the axially moving beam is numerically solved based on the fourth-order Runge–Kutta time discretization. Based on the numerical solutions, the phase portrait, the bifurcation diagrams and the initial value sensitivity are presented to identify the dynamical behaviors. Based on the nonlinear dynamics, the effects of the truncation terms of the Galerkin method, such as 2-term, 4-term, and 6-term, are studied by comparison with DQM & IQM.

Periodic responses and chaotic behaviors of an axially accelerating viscoelastic Timoshenko beam

Abstract: This paper investigates the steady-state periodic response and the chaos and bifurcation of an axially accelerating viscoelastic Timoshenko beam For the first time, the nonlinear dynamic behaviors in the transverse parametric vibration of an axially moving Timoshenko beam are studied The axial speed of the system is assumed as a harmonic variation over a constant mean speed The transverse motion of the beam is governed by nonlinear integro-partial-differential equations, including the finite axial support rigidity and the longitudinally varying tension due to the axial acceleration The Galerkin truncation is applied to discretize the governing equations into a set of nonlinear ordinary differential equations Based on the solutions obtained by the fourth-order Runge–Kutta algorithm, the stable steady-state periodic response is examined Besides, the bifurcation diagrams of different bifurcation parameters are presented in the subcritical and supercritical regime Furthermore, the nonlinear dynamical behaviors are identified in the forms of time histories, phase portraits, Poincare maps, amplitude spectra, and sensitivity to initial conditions Moreover, numerical examples reveal the effects of various terms Galerkin truncation on the amplitude–frequency responses, as well as bifurcation diagrams

Dynamic response of axially moving Timoshenko beams: integral transform solution

Abstract: The generalized integral transform technique (GITT) is used to find a semianalytical numerical solution for dynamic response of an axially moving Timoshenko beam with clamped-clamped and simply-supported boundary conditions, respectively. The implementation of GITT approach for analyzing the forced vibration equation eliminates the space variable and leads to systems of second-order ordinary differential equations (ODEs) in time. The MATHEMATICA built-in function, NDSolve, is used to numerically solve the resulting transformed ODE system. The good convergence behavior of the suggested eigenfunction expansions is demonstrated for calculating the transverse deflection and the angle of rotation of the beam cross-section. Moreover, parametric studies are performed to analyze the effects of the axially moving speed, the axial tension, and the amplitude of external distributed force on the vibration amplitude of axially moving Timoshenko beams.

Beyond Axial Symmetry: An Improved Class of Models for Global Data

Abstract: An important class of models for data on a spherical domain, called axially symmetric, assumes stationarity across longitudes but not across latitudes. The main aim of this work is to introduce a new and more flexible class of models by relaxing the assumption of longitudinal stationarity in the context of regularly gridded climate model output. In this investigation, two other related topics are discussed: the lack of fit of an axially symmetric parametric model compared with a non-parametric model and to longitudinally reversible processes, an important subclass of axially symmetric models. Copyright © 2014 John Wiley & Sons, Ltd

Magnetorotational Core-Collapse Supernovae in Three Dimensions

Abstract: We present results of new three-dimensional (3D) general-relativistic magnetohydrodynamic simulations of rapidly rotating strongly magnetized core collapse. These simulations are the first of their kind and include a microphysical finite-temperature equation of state and a leakage scheme that captures the overall energetics and lepton number exchange due to postbounce neutrino emission. Our results show that the 3D dynamics of magnetorotational core-collapse supernovae are fundamentally different from what was anticipated on the basis of previous simulations in axisymmetry (2D). A strong bipolar jet that develops in a simulation constrained to 2D is crippled by a spiral instability and fizzles in full 3D. While multiple (magneto-)hydrodynamic instabilities may be present, our analysis suggests that the jet is disrupted by an m=1 kink instability of the ultra-strong toroidal field near the rotation axis. Instead of an axially symmetric jet, a completely new, previously unreported flow structure develops. Highly magnetized spiral plasma funnels expelled from the core push out the shock in polar regions, creating wide secularly expanding lobes. We observe no runaway explosion by the end of the full 3D simulation at 185 ms after bounce. At this time, the lobes have reached maximum radii of 900 km.

Ideal magnetohydrodynamic equilibrium in a non-symmetric topological torus

Abstract: An alternative representation of an ideal magnetohydrodynamic equilibrium is developed. The representation is a variation of one given by A. Salat, Phys. Plasmas 2, 1652 (1995). The system of equations is used to study the possibility of non-symmetric equilibria in a topological torus, here an approximate rectangular parallelopiped, with periodicity in two of the three rectangular coordinates. An expansion is carried out in the deviation of pressure surfaces from planes. Resonances are manifest in the process. Nonetheless, provided the magnetic shear is small, it is shown that it is possible to select the magnetic fields and flux surfaces in such a manner that no singularities appear on resonant surfaces. One boundary surface of the parallelopiped is not arbitrary but is dependent on the equilibrium in question. A comparison of the solution sets of axisymmetric and non-axisymmetric equilibria suggests that the latter have a wider class of possible boundary shapes but more restrictive rotational transform profiles. No proof of convergence of the series is given.

Formation of complex two-dimensional dissipative solitons via spontaneous symmetry breaking

Abstract: We propose a complex Ginzburg-Landau equation (CGLE) with localized linear gain as a two-dimensional model for pattern formation proceeding via spontaneous breaking of the axial symmetry. Starting from steady-state solutions produced by an extended variational approximation, simulations of the CGLE generate a vast class of robust solitary structures. These are varieties of asymmetric rotating vortices carrying the topological charge (TC), and four- to ten-pointed revolving stars, whose angular momentum is decoupled from the TC. The four- and five-pointed stars feature a cyclic change of their structure in the course of the rotation.

Vibration and Stability Analysis of Axially Moving Beams with Variable Speed and Axial Force

Abstract: The well-known vibration model of axially moving beam is considered. Both axial moving speed and axial force are assumed to vary harmonically. The Method of Multiple Time Scales (a perturbation method) is used. The natural vibrations of beam are considered for different values of beam parameters. Resonances are obtained for seven different conditions. Solvability conditions for each resonance case are found analytically. Effects of transport velocity, axial force, rigidity and damping are discussed. Stability analysis are obtained for principal parametric resonances. Stable and unstable regions are obtained regarding velocity and force effects separately and together.

An axially propagating two-stream instability in the Hall thruster plasma

Abstract: Collective Thomson scattering experiments reveal the presence of high-frequency, axial electron density fluctuations at millimetric wavelengths in the Hall thruster plasma. The properties of these fluctuations are investigated experimentally and via linear kinetic theory. The relative drift of electrons and ions in the axial direction is found to be insufficient to cause excitation of the observed mode. Instead, the mode is determined to be a two-stream instability arising due to the velocity difference between singly and doubly charged ion populations in the plume.

The flow of Newtonian and power law fluids in elastic tubes

Abstract: We derive analytical expressions for the flow of Newtonian and power law fluids in elastic circularly symmetric tubes based on a lubrication approximation where the flow velocity profile at each cross section is assumed to have its axially dependent characteristic shape for the given rheology and cross sectional size. Two pressure–area constitutive elastic relations for the tube elastic response are used in these derivations. We demonstrate the validity of the derived equations by observing qualitatively correct trends in general and quantitatively valid asymptotic convergence to limiting cases. The Newtonian formulae are compared to similar formulae derived previously from a one-dimensional version of the Navier–Stokes equations.