22 research outputs found
Experimental study of workpiece-level variability in blind-via electroplating
The acid copper electroplating process for the manufacture of printed wire boards was studied by statistical techniques. The objectives of this study were to investigate the effects of process and product parameters on the workpiece-level uniformity during the acid copper plating of blind vias and to explore the minimization of the deposit thickness variation. The parameters studied were the concentrations of copper sulphate, sulphuric acid and additive, average current density (ACD), electrode separation (ES), the aspect ratio and the depth ratio of the via holes. Multifactor two-level factorial and the central composite rotatable five-level experiments were designed and conducted sequentially to generate statistical process models. Only the average current density and the electrode separation were found to be significant. A second-order model was then developed for the process in the proximity of the optimum region and verified experimentally to locate the optimum combinations of ACD and ES with respect to minimum thickness variability across the whole workpiece. Post-optimal analysis showed that the optimum solution was more sensitive to the electrode separation than the average current density
Quasinormal modes for the SdS black hole : an analytical approximation scheme
Quasinormal modes for scalar field perturbations of a Schwarzschild-de Sitter
(SdS) black hole are investigated. An analytical approximation is proposed for
the problem. The quasinormal modes are evaluated for this approximate model in
the limit when black hole mass is much smaller than the radius of curvature of
the spacetime. The model mirrors some striking features observed in numerical
studies of time behaviour of scalar perturbations of the SdS black hole. In
particular, it shows the presence of two sets of modes relevant at two
different time scales, proportional to the surface gravities of the black hole
and cosmological horizons respectively. These quasinormal modes are not
complete - another feature observed in numerical studies. Refinements of this
model to yield more accurate quantitative agreement with numerical studies are
discussed. Further investigations of this model are outlined, which would
provide a valuable insight into time behaviour of perturbations in the SdS
spacetime.Comment: 12 pages, revtex, refs added and discussion expanded, version to
appear in Phys. Rev.
Interior Structure of a Charged Spinning Black Hole in -Dimensions
The phenomenon of mass inflation is shown to occur for a rotating black hole.
We demonstrate this feature in dimensions by extending the charged
spinning BTZ black hole to Vaidya form. We find that the mass function diverges
in a manner quantitatively similar to its static counterparts in ,
and dimensions.Comment: 5 pages, 2 figures (appended as postscript files), WATPHYS-TH94/0
Scalar wave propagation in topological black hole backgrounds
We consider the evolution of a scalar field coupled to curvature in
topological black hole spacetimes. We solve numerically the scalar wave
equation with different curvature-coupling constant and show that a rich
spectrum of wave propagation is revealed when is introduced. Relations
between quasinormal modes and the size of different topological black holes
have also been investigated.Comment: 26 pages, 18 figure
Radiative falloff in Einstein-Straus spacetime
The Einstein-Straus spacetime describes a nonrotating black hole immersed in
a matter-dominated cosmology. It is constructed by scooping out a spherical
ball of the dust and replacing it with a vacuum region containing a black hole
of the same mass. The metric is smooth at the boundary, which is comoving with
the rest of the universe. We study the evolution of a massless scalar field in
the Einstein-Straus spacetime, with a special emphasis on its late-time
behavior. This is done by numerically integrating the scalar wave equation in a
double-null coordinate system that covers both portions (vacuum and dust) of
the spacetime. We show that the field's evolution is governed mostly by the
strong concentration of curvature near the black hole, and the discontinuity in
the dust's mass density at the boundary; these give rise to a rather complex
behavior at late times. Contrary to what it would do in an asymptotically-flat
spacetime, the field does not decay in time according to an inverse power-law.Comment: ReVTeX, 12 pages, 14 figure
Scalar Synchrotron Radiation in the Schwarzschild-anti-de Sitter Geometry
We present a complete relativistic analysis for the scalar radiation emitted
by a particle in circular orbit around a Schwarzschild-anti-de Sitter black
hole. If the black hole is large, then the radiation is concentrated in narrow
angles- high multipolar distribution- i.e., the radiation is synchrotronic.
However, small black holes exhibit a totally different behavior: in the small
black hole regime, the radiation is concentrated in low multipoles. There is a
transition mass at , where is the AdS radius. This behavior is
new, it is not present in asymptotically flat spacetimes.Comment: 13 pages, 6 figures, published version. References adde
Radiative falloff of a scalar field in a weakly curved spacetime without symmetries
We consider a massless scalar field propagating in a weakly curved spacetime
whose metric is a solution to the linearized Einstein field equations. The
spacetime is assumed to be stationary and asymptotically flat, but no other
symmetries are imposed -- the spacetime can rotate and deviate strongly from
spherical symmetry. We prove that the late-time behavior of the scalar field is
identical to what it would be in a spherically-symmetric spacetime: it decays
in time according to an inverse power-law, with a power determined by the
angular profile of the initial wave packet (Price falloff theorem). The field's
late-time dynamics is insensitive to the nonspherical aspects of the metric,
and it is governed entirely by the spacetime's total gravitational mass; other
multipole moments, and in particular the spacetime's total angular momentum, do
not enter in the description of the field's late-time behavior. This extended
formulation of Price's falloff theorem appears to be at odds with previous
studies of radiative decay in the spacetime of a Kerr black hole. We show,
however, that the contradiction is only apparent, and that it is largely an
artifact of the Boyer-Lindquist coordinates adopted in these studies.Comment: 17 pages, RevTeX
Black hole collision with a scalar particle in four, five and seven dimensional anti-de Sitter spacetimes: ringing and radiation
In this work we compute the spectra, waveforms and total scalar energy
radiated during the radial infall of a small test particle coupled to a scalar
field into a -dimensional Schwarzschild-anti-de Sitter black hole. We focus
on and 7, extending the analysis we have done for . For small
black holes, the spectra peaks strongly at a frequency , which
is the lowest pure anti-de Sitter (AdS) mode. The waveform vanishes
exponentially as , and this exponential decay is governed
entirely by the lowest quasinormal frequency. This collision process is
interesting from the point of view of the dynamics itself in relation to the
possibility of manufacturing black holes at LHC within the brane world
scenario, and from the point of view of the AdS/CFT conjecture, since the
scalar field can represent the string theory dilaton, and 4, 5, 7 are
dimensions of interest for the AdS/CFT correspondence.Comment: 16 pages, 13 figures. Published versio
Gravitational quasinormal radiation of higher-dimensional black holes
We find the gravitational resonance (quasinormal) modes of the higher
dimensional Schwarzschild and Reissner-Nordstrem black holes. The effect on the
quasinormal behavior due to the presence of the term is investigated.
The QN spectrum is totally different for different signs of . In more
than four dimensions there excited three types of gravitational modes: scalar,
vector, and tensor. They produce three different quasinormal spectra, thus the
isospectrality between scalar and vector perturbations, which takes place for
D=4 Schwarzschild and Schwarzschild-de-Sitter black holes, is broken in higher
dimensions. That is the scalar-type gravitational perturbations, connected with
deformations of the black hole horizon, which damp most slowly and therefore
dominate during late time of the black hole ringing.Comment: 13 pages, 2 figures, several references are adde
Area Spectrum of Extremal Reissner-Nordstr\"om Black Holes from Quasi-normal Modes
Using the quasi-normal modes frequency of extremal Reissner-Nordstr\"om black
holes, we obtain area spectrum for these type of black holes. We show that the
area and entropy black hole horizon are equally spaced. Our results for the
spacing of the area spectrum differ from that of schwarzschild black holes.Comment: 6 pages, no figure, accepted for publication in Phys. Rev.