Showing papers on "Critical radius published in 1991"

Stability of a shell around a black hole.

Abstract: We study the mechanical stability of a static, infinitely thin, spherically symmetric massive shell surrounding a classical Schwarzschild black hole. The shell is taken to have a non-negative surface energy density, and a speed of sound not greater than the speed of light. We show that the shell is stable against radial perturbations only outside a critical radius which is always larger than the radius of the circular photon orbit. The surface energy density of a stable shell is always larger than twice the surface pressure, and thus satisfies the dominant energy condition by a wide margin. We briefly discuss the effects of Hawking radiation in view of a path-integral approach to black-hole thermodynamics developed by York and collaborators. Our results suggest that a macroscopic thermal equilibrium situation associated with the canonical ensemble in this approach may not be realizable with a thin matter shell in Lorentzian spacetime.

Bubble free energy at the quark - hadron phase transition

Abstract: We calculate the free energy of finite droplets of quark-gluon plasma, and of finite hadronic bubbles in the bulk plasma, near the confinement phase transition. We sum over free quark and gluon energy levels in the presence of MIT bag boundary conditions. We find that the curvature term in the free energy, proportional to the radius of the droplet or bubble, is far more important than the contribution of the surface tension, proportional to the radius squared. This affects the critical radius for nucleation of plasma droplets in the superheated hadron gas, and seems to lead to instability of the plasma (even when {ital not} supercooled) against nucleation of hadron gas bubbles.

The electrostatic nature of contaminative particles in a semiconductor processing plasma

Abstract: Two models are presented to describe the immediate environment surrounding negatively charged contaminants in an idealized argon plasma. The first model uses Poisson’s equation to determine the contaminant charge and voltage. This model predicts a critical radius of the order of the Debye length below which Poisson’s equation is no longer valid. Below the critical radius and for contaminant radii much less than the Debye length, the Coulomb potential is used to find the contaminant charge and voltage. Both models predict negative charges on the order of 10−14 C, and voltages on the same order of magnitude as the electron energy.

A New Method for Determining Hydrodynamic Effects on the Collision of Two Spheres

Abstract: A sphere falling in a fluid may collide with another sphere falling more slowly if, when the spheres are far apart vertically, the horizontal distance between their centers is less than or equal to a critical radius. Accurate prediction of aerosol particle coagulation requires a good understanding of this process. Previously reported optical techniques for measuring hydrodynamic effects on this phenomenon have inherent difficulties detecting grazing collisions and hence in determining the critical radius. In this work, a novel detection technique is demonstrated and it is shown that the critical radius may be determined from the sound generated by the collision of two spheres in a viscous liquid. The technique is shown to provide a more precise and decisive indication of when hard spheres collide.

Critical Radius and Time Course of Expansion of an Isolated Bubble in Wheat Flour Dough under Temperature Rise

Abstract: As a part of the study of bubble expansion in wheat flour dough under temperature rise, the critical radius for expansion, and the time course of expansion of an isolated bubble were investigated. As the required physical properties for the calculation of the critical bubble radius for expansion and the time course of bubble expansion, the authors measured the surface tension of the liquid phase of wheat flour batter as a function of concentration and temperature, and the apparent diffusion coefficients of air in wheat flour dough as a function of temperature. The critical radius for expansion and the time course of expansion of the isolated bubble under temperature rise were compared with the theoretical values calculated from the diffusion theory. At constant temperature, the time course of bubble shrinkage in wheat flour dough was described well by diffusion theory with the surface tension and the apparent diffusion coefficient, indicating that the bubble shrinkage would be rate-limited by the diffusio...

Theoretical Description of the Growth and Stability of Helium Platelets in Nickel

Abstract: A static computer simulation is performed in order to study the nucleation and the two-dimensional growth mode of helium-filled aggregates in nickel. The results indicate that a helium-filled aggregate expels neighbouring atoms at its outer edges. These atoms are displaced in the direction of a nearest octahedral position and they are bound to the cluster.The helium-filled aggregate grows in a planar way and an interstitial loop is formed by the emitted atoms. The two dimensional growth occurs parallel with the close-packed planes. To explain the collapse of the platelets into clusters of smaller aggregates, a theoretical model is developed to describe the total energy of a platelet. It is based partly on the results of the simulations. The variation of the total energy gives information regarding the platelet stability and is calculated in both a numerical and an analytical way. It is shown that small platelets are stable and that, once a critical radius is attained, the platelet becomes unstable and a transformation into a group of smaller aggregates takes place. The theoretical model can also explain the fact that two-dimensional helium aggregates are observed to be more stable in bcc than in fcc structures.

Nucleation in a bistable belousov-zhabotinskii system

Abstract: A new model of the Belousov-Zhabotinskii reaction is developed. It describes bistable behavior of the reaction. For this reaction -diffusion system existence results are proved. The critical radius of a nucleus is defined and studied by numerical methods.

The role of surface tension in the growth of strained quantum wire arraysa)

Abstract: The critical radius of a strained quantum wire and the potential strain stabilization of quantum wire arrays has been investigated for the InxGa1−xAs/GaAs system. The critical radius of the quantum wire was calculated using an energy balance approach. The wire was found to be more stable than the corresponding two‐dimensional quantum well structure. The use of surface tension as a stabilization force during the growth of strained quantum wire arrays is expected to have beneficial effects for arrays with greater than 7% InAs.

Stability of helium-filled platelets in nickel

Abstract: In order to explain the observed behaviour of helium platelets, which grow and then collapse into clusters of smaller aggregates, a theoretical model is developed to describe the total energy of a platelet. The model is based partly on the results of atomistic computer simulations. The variation of the total energy gives information regarding the platelet stability and is calculated in both a numerical and an analytical way. It is shown that small platelets are stable and that, once a critical radius is attained, the platelet becomes unstable and a transformation into a group of smaller aggregates takes place. The theoretical model can also explain the fact that two-dimensional helium aggregates are observed to be more stable in b.c.c. than in f.c.c. structures.