37,066 research outputs found
The numerical solution of fractional differential equations: Speed versus accuracy
This paper discusses the development of efficient algorithms for a certain fractional differential equation.Manchester Centre for Computational Mathematic
Hypervelocity gun
A velocity amplifier system which uses both electric and chemical energy for projectile propulsion is provided in a compact hypervelocity gun suitable for laboratory use. A relatively heavy layer of a tamping material such as concrete encloses a loop of an electrically conductive material. An explosive charge at least partially surrounding the loop is adapted to collapse the loop upon detonation of the charge. A source of electricity charges the loop through two leads, and an electric switch which is activated by the charge explosive charge, disconnects the leads from the source of electricity and short circuits them. An opening in the tamping material extends to the loop and forms a barrel. The loop, necked down in the opening, forms the sabot on which the projectile is located. When the loop is electrically charged and the explosive detonated, the loop is short circuited and collapsed thus building up a magnetic field which acts as a sabot catcher. The sabot is detached from the loop and the sabot and projectile are accelerated to hypervelocity
Dynamic wormholes
A new framework is proposed for general dynamic wormholes, unifying them with
black holes. Both are generically defined locally by outer trapping horizons,
temporal for wormholes and spatial or null for black and white holes. Thus
wormhole horizons are two-way traversible, while black-hole and white-hole
horizons are only one-way traversible. It follows from the Einstein equation
that the null energy condition is violated everywhere on a generic wormhole
horizon. It is suggested that quantum inequalities constraining negative energy
break down at such horizons. Wormhole dynamics can be developed as for
black-hole dynamics, including a reversed second law and a first law involving
a definition of wormhole surface gravity. Since the causal nature of a horizon
can change, being spatial under positive energy and temporal under sufficient
negative energy, black holes and wormholes are interconvertible. In particular,
if a wormhole's negative-energy source fails, it may collapse into a black
hole. Conversely, irradiating a black-hole horizon with negative energy could
convert it into a wormhole horizon. This also suggests a possible final state
of black-hole evaporation: a stationary wormhole. The new framework allows a
fully dynamical description of the operation of a wormhole for practical
transport, including the back-reaction of the transported matter on the
wormhole. As an example of a matter model, a Klein-Gordon field with negative
gravitational coupling is a source for a static wormhole of Morris & Thorne.Comment: 5 revtex pages, 4 eps figures. Minor change which did not reach
publisher
Bounds on negative energy densities in flat spacetime
We generalise results of Ford and Roman which place lower bounds -- known as
quantum inequalities -- on the renormalised energy density of a quantum field
averaged against a choice of sampling function. Ford and Roman derived their
results for a specific non-compactly supported sampling function; here we use a
different argument to obtain quantum inequalities for a class of smooth, even
and non-negative sampling functions which are either compactly supported or
decay rapidly at infinity. Our results hold in -dimensional Minkowski space
() for the free real scalar field of mass . We discuss various
features of our bounds in 2 and 4 dimensions. In particular, for massless field
theory in 2-dimensional Minkowski space, we show that our quantum inequality is
weaker than Flanagan's optimal bound by a factor of 3/2.Comment: REVTeX, 13 pages and 2 figures. Minor typos corrected, one reference
adde
Cosmological and Black Hole Horizon Fluctuations
The quantum fluctuations of horizons in Robertson-Walker universes and in the
Schwarzschild spacetime are discussed. The source of the metric fluctuations is
taken to be quantum linear perturbations of the gravitational field. Lightcone
fluctuations arise when the retarded Green's function for a massless field is
averaged over these metric fluctuations. This averaging replaces the
delta-function on the classical lightcone with a Gaussian function, the width
of which is a measure of the scale of the lightcone fluctuations. Horizon
fluctuations are taken to be measured in the frame of a geodesic observer
falling through the horizon. In the case of an expanding universe, this is a
comoving observer either entering or leaving the horizon of another observer.
In the black hole case, we take this observer to be one who falls freely from
rest at infinity. We find that cosmological horizon fluctuations are typically
characterized by the Planck length. However, black hole horizon fluctuations in
this model are much smaller than Planck dimensions for black holes whose mass
exceeds the Planck mass. Furthermore, we find black hole horizon fluctuations
which are sufficiently small as not to invalidate the semiclassical derivation
of the Hawking process.Comment: 22 pages, Latex, 4 figures, uses eps
Quantum Inequalities on the Energy Density in Static Robertson-Walker Spacetimes
Quantum inequality restrictions on the stress-energy tensor for negative
energy are developed for three and four-dimensional static spacetimes. We
derive a general inequality in terms of a sum of mode functions which
constrains the magnitude and duration of negative energy seen by an observer at
rest in a static spacetime. This inequality is evaluated explicitly for a
minimally coupled scalar field in three and four-dimensional static
Robertson-Walker universes. In the limit of vanishing curvature, the flat
spacetime inequalities are recovered. More generally, these inequalities
contain the effects of spacetime curvature. In the limit of short sampling
times, they take the flat space form plus subdominant curvature-dependent
corrections.Comment: 18 pages, plain LATEX, with 3 figures, uses eps
Quantum energy inequalities in two dimensions
Quantum energy inequalities (QEIs) were established by Flanagan for the
massless scalar field on two-dimensional Lorentzian spacetimes globally
conformal to Minkowski space. We extend his result to all two-dimensional
globally hyperbolic Lorentzian spacetimes and use it to show that flat
spacetime QEIs give a good approximation to the curved spacetime results on
sampling timescales short in comparison with natural geometric scales. This is
relevant to the application of QEIs to constrain exotic spacetime metrics.Comment: 4 pages, REVTeX. This is an expanded version of a portion of
gr-qc/0409043. To appear in Phys Rev
Use of mathematical derivatives (time-domain differentiation) on chromatographic data to enhance the detection and quantification of an unknown 'rider' peak
Two samples of an anticancer prodrug, AQ4N, were submitted for HPLC assay and showed an unidentified impurity that eluted as a 'rider' on the tail of the main peak. Mathematical derivatization of the chromatograms offered several advantages over conventional skimmed integration. A combination of the second derivative amplitude and simple linear regression gave a novel method for estimating the true peak area of the impurity peak. All the calculation steps were carried out using a widely available spreadsheet program. (C) 2003 Elsevier B.V. All rights reserved
Morphology of the Nuclear Disk in M87
A deep, fuly sampled diffraction limited (FWHM ~ 70 mas) narrow-band image of
the central region in M87 was obtained with the Wide Filed and Planetary Camera
2 of the Hubble Space Telescope using the dithering technique. The
H-alpha+[NII] continuum subtracted image reveals a wealth of details in the
gaseous disk structure described earlier by Ford et al. (1994). The disk
morphology is dominated by a well defined three-arm spiral pattern. In
addition, the major spiral arms contain a large number of small "arclets"
covering a range of sizes (0.1-0.3 arcsec = 10-30 pc). The overall surface
brightness profile inside a radius ~1.5" (100 pc) is well represented by a
power-law I(mu) ~ mu^(-1.75), but when the central ~40 pc are excluded it can
be equally well fit by an exponential disk. The major axis position angle
remains constant at about PA_disk ~ 6 deg for the innermost ~1", implying the
disk is oriented nearly perpendicular to the synchrotron jet (PA_jet ~ 291
deg). At larger radial distances the isophotes twist, reflecting the gas
distribution in the filaments connecting to the disk outskirts. The ellipticity
within the same radial range is e = 0.2-0.4, which implies an inclination angle
of i~35 deg. The sense of rotation combined with the dust obscuration pattern
indicate that the spiral arms are trailing.Comment: 5 pages, 3 postscript figures, to appear in the Proceedings of the
M87 Workshop, Ringberg castle, Germany, 15-19 Sep 1997, also available from
http://jhufos.pha.jhu.edu/~zlatan/papers.htm
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