Onset Of Dynamical Instability Research Articles

Computational results of a dynamic simulation of the conforming shell gas journal bearing

A time-dependent mathematical model for the conforming shell gas journal bearing is presented. A computational simulation of the mathematical model is used to investigate the dynamic behaviour and steady state characteristics of the bearing. The onset of dynamic instabilities, violation of the minimum film thickness criteria and component separations are found to be the three factors which form upper and lower bounds on the range of acceptable loads.

Dynamical instability for shearing viscous collapse

We study the role played by the shear and the shearing viscosity in the onset of dynamical instabilities. For both the Newtonian and the relativistic regimes, the shearing viscosity decreases the instability of the fluid. The corrections due to the shear, which appear only in the post-Newtonian approximation, decrease the range of values of the'ratio of specific heats'for which the system is unstable. This result is the consequence of the fact that the collapse with shear proceeds faster than the corresponding shear-free collapse. Under otherwise identical conditions, therefore, the material of the collapsing sphere with shear should be softer than the material of the shear-free collapsing sphere

Hydrodynamics of binary coalescence. 1: Polytropes with stiff equations of state

view Abstract Citations (152) References (73) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Hydrodynamics of Binary Coalescence. I. Polytropes with Stiff Equations of State Rasio, Frederic A. ; Shapiro, Stuart L. Abstract We have performed a series of three-dimensional hydrodynamic calculations of binary coalescence using the smoothed particle hydrodynamics (SPH) method. The initial conditions are exact polytropic equilibrium configurations with $\gam > 5/3$, on the verge of dynamical instability. We calculate the emission of gravitational radiation in the quadrupole approximation. The fully nonlinear development of the instability is followed until a new equilibrium configuration is reached. We find that the properties of this final configuration depend sensitively on both the compressibility and mass ratio. An {\em axisymmetric} merged configuration is always produced when $\gam\lo2.3$. As a consequence, the emission of gravitational radiation shuts off abruptly right after the onset of dynamical instability. In contrast, {\em triaxial\/} merged configurations are obtained when $\gam\go2.3$, and the system continues to emit gravitational waves after the final coalescence. Systems with mass ratios $q\ne1$ typically become dynamically unstable before the onset of mass transfer. Stable mass transfer from one neutron star to another in a close binary is therefore probably ruled out. The maximum amplitude $h_{max}$ and peak luminosity $L_{max}$ of the gravitational waves emitted during the final coalescence are nearly independent of $\gam$, but depend very sensitively on the mass ratio $q$. Publication: The Astrophysical Journal Pub Date: September 1994 DOI: 10.1086/174566 arXiv: arXiv:astro-ph/9401027 Bibcode: 1994ApJ...432..242R Keywords: Astronomical Models; Binary Stars; Coalescing; Dynamic Stability; Equations Of State; Hydrodynamics; Mathematical Models; Neutron Stars; Nonthermal Radiation; Polytropic Processes; Stellar Interiors; Adiabatic Equations; Gravitational Waves; Mass Transfer; Quadrupoles; Astrophysics; EQUATION OF STATE; HYDRODYNAMICS; INSTABILITIES; RADIATION MECHANISMS: NONTHERMAL; STARS: BINARIES: CLOSE; STARS: INTERIORS; STARS: NEUTRON; Astrophysics E-Print: 27 pages, uuencoded compressed postscript, 16 figures upon request from BEST@sns.ias.edu, IAS-AST-94-4 full text sources arXiv | ADS | Related Materials (1) Part 2: 1995ApJ...438..887R

Dynamical instability for radiating anisotropic collapse

We study the role played by local anisotropy and radiation (in the free-streaming regime) in the onset of dynamical instabilities. In the case of anisotropy we find that, for Newtonian and post-Newtonian approximations, the relevant quantity is the anisotropy of the unperturbed fluid, and that small anisotropies may, in principle, drastically change the stability of the system. The influence of the free-streaming radiation upon stability appears to be qualitatively of the same type as that of radiative diffusion. Some speculations and prospective applications to astrophysical scenarios are presented

Equilibrium and stability of rotating masses with a toroidal magnetic field

We investigate the equilibrium, oscillations, and stability of uniformly rotating masses with a toroidal magnetic field, proportional with the distance to te axis of rotation. The equilibrium is an oblate or prolate spheroid according as the rotational energy is greater or smaller than the magnetic energy. The sequence of equilibrium figures exhibits a maximum value for the angular velocity in the oblate case and a maximum for the angular momentum in the prolate case. The dispersion relation is derived using Bryan's ‘modified’ spheroidal coordinates. One obtains 2(n−m)+4 solutions for the oscillation frequency ω ifm≠0 and 1/2n or 1/2(n+1) solutions for ω2 according asn is even or odd ifm=0. The point where the Jacobi ellipsoids bifurcate from the MacLaurin sequence is unaffected by the magnetic field. However, the points of the onset of dynamical instability corresponding to the second and third harmonics and the point where a pear-shaped sequence bifurcate, depend upon the magnetic field. They are shifted to higher values for the eccentricity and can be suppressed by a sufficiently large magnetic field.

Further studies on criteria for the onset of dynamical instability in general three-body systems

view Abstract Citations (44) References (10) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Further studies on criteria for the onset of dynamical instability ingeneral three-body systems. Pendleton, Y. J. ; Black, D. C. Abstract Numerical experiments designed for the elucidation of the conditions under which self-gravitating, three-body systems become dynamically unstable are examined of the cases of four orbital configuration types: circular, prograde, and coplanar; circular, retrograde, and coplanar; circular, direct, and inclined; and eccentric, direct, and coplanar. Results indicate that orbital inclination does not significantly affect stability in 'outer planet' configurations, while the stability of 'inner planet' configurations, where the tertiary is in close orbit about one member of the binary, is markedly less affected, once the relative orbital inclination is greater than 50 deg. It is found that the onset of dynamical instability is only weakly dependent on the eccentricity of either the binary or tertiary orbit, as long as the mass of the tertiary is comparable to the reduced mass of the binary. Publication: The Astronomical Journal Pub Date: September 1983 DOI: 10.1086/113430 Bibcode: 1983AJ.....88.1415P Keywords: Celestial Mechanics; Dynamic Stability; Orbit Perturbation; Orbital Mechanics; Three Body Problem; Circular Orbits; Eccentric Orbits; Orbital Elements; Systems Stability; Astronomy; Three-Body Problem:Stability full text sources ADS |

Adiabatic pulsations and convective instability of rotating gaseous masses

Third order virial equations have been used to investigate the oscillations and the stability of the sequence of differentially rotating, compressible Maclaurin spheroids in the presence of toroidal magnetic fields. It is shown that the neutral point occurring at eccentricitye=0.731 13, which is the analogue of the first point of bifurcation along the Dedekind sequence, remains unaffected by the presence of differential rotation or a toroidal magnetic field. The point of onset of dynamical instability corresponding to the third harmonic deformations does, however, depend upon the magnetic field. It is shifted to values higher thane=0.966 96, the value that obtains in the case of uniform rotation; and a sufficiently large magnetic field can suppress this point. Complete frequency spectra (‘Kelvin’ modes belonging to the harmonicsl=3 and compressible modes belonging tol=1) are obtained in two cases of interest: when the equilibrium state is one of equipartition, and when toroidal magnetic and velocity fields (vanishing at the surface) are present in a configuration rotating with a constant angular velocity.

Criterion for the Instability of a Uniformly Rotating Configuration in General Relativity

Uniformly rotating configurations in general relativity are considered, and a condition is obtained that they can be quasistatically deformed without violating any of the requirements for equilibrium. This condition extends, into the domain of the rotating stars, the criterion for the onset of dynamical instability (via a neutral mode of oscillation) that occurs by radial pulsations in nonrotating stars.

Adiabatic Fluid Spheres in General Relativity. II. Massive Configurations of Ideal Gas and Radiation

view Abstract Citations (14) References (15) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Adiabatic Fluid Spheres in General Relativity. II. Massive Configurations of Ideal Gas and Radiation Tooper, Robert F. Abstract General-relativistic models of massive hot non-rotating stars with adiabatic temperature gradients are dealt with in this paper. The stars are assumed to consist of a mixture of ideal gas and radiation at a finite temperature T, and the models therefore form a two-parameter family of solutions to the equa- tions of hydrostatic equilibrium in general relativity. The parameters characterizing a particular member of the sequence are the ratio a of pressure to rest energy density at the center, and the central value (denoted by Yc) of the ratio of radiation pressure to gas pressure. Results are presented as contours, in the space of these two parameters, of central temperature, rest mass, active gravitational mass, radius, binding energy, and period of linearized adiabatic radial oscillations. For each subsequence of models with constant rest mass, the onset of dynamical instability is found to occur at the point where the binding energy, considered as a function of a, has its first relative maximum. A class of general-relativistic models, with masses <1O~ Mo, stable according to our assumptions about the equation of state, but with central temperatures high enough to cause electron-positron pair formation, is shown to exist. The desirability of examining in detail the effects of pair formation on the structure and stability of these models is indicated Publication: The Astrophysical Journal Pub Date: January 1969 DOI: 10.1086/149856 Bibcode: 1969ApJ...155..145T full text sources ADS |