7,054 research outputs found
Adaptive Spectral Mapping for Real-Time Dispersive Refraction
Spectral rendering, or the synthesis of images by taking into account the wavelengths of light, allows effects otherwise impossible with other methods. One of these effects is dispersion, the phenomenon that creates a rainbow when white light shines through a prism. Spectral rendering has previously remained in the realm of off-line rendering (with a few exceptions) due to the extensive computation required to keep track of individual light wavelengths. Caustics, the focusing and de-focusing of light through a refractive medium, can be interpreted as a special case of dispersion where all the wavelengths travel together. This thesis extends Adaptive Caustic Mapping, a previously proposed caustics mapping algorithm, to handle spectral dispersion. Because ACM can display caustics in real-time, it is quite amenable to be extended to handle the more general case of dispersion. A method is presented that runs in screen-space and is fast enough to display plausible dispersion phenomena in real-time at interactive frame rates
On Holography and Cosmology
We consider a recent generalisation by Bousso of an earlier holography
proposal by Fischler and Susskind. We demonstrate that in general inhomogeneous
universes such a proposal would involve extremely complicated - possibly
fractal - light sheets. Furthermore, in general such a light sheet cannot be
known a priori on the basis of theory and moreover, the evolution of the
universe makes it clear that in general such bounds cannot remain invariant
under time reversal and will change with epoch.
We propose a modified version of this proposal in which the light sheets end
on the boundary of the past, and hence avoid contact with the caustics. In this
way the resulting light sheets and projections can be made much simpler. We
discuss the question of operational definability of these sheets within the
context of both proposals and conclude that in both cases the theoretical
existence of such sheets must be clearly distinguished from their complexity
and the difficulty of their construction in practice. This puts into
perspective the likely practical difficulties one would face in applying the
holographic principle to the real cosmos. These issues may also be of relevance
in debates regarding the applications of the holographic principle to other
settings such as string theory.Comment: Submitted to Phys Lett B on 22 July 1999; 12 pages Latex, no figure
Lensing and caustic effects on cosmological distances
We consider the changes which occur in cosmological distances due to the
combined effects of some null geodesics passing through low-density regions
while others pass through lensing-induced caustics. This combination of effects
increases observed areas corresponding to a given solid angle even when
averaged over large angular scales, through the additive effect of increases on
all scales, but particularly on micro-angular scales; however angular sizes
will not be significantly effected on large angular scales (when caustics
occur, area distances and angular-diameter distances no longer coincide). We
compare our results with other works on lensing, which claim there is no such
effect, and explain why the effect will indeed occur in the (realistic)
situation where caustics due to lensing are significant. Whether or not the
effect is significant for number counts depends on the associated angular
scales and on the distribution of inhomogeneities in the universe. It could
also possibly affect the spectrum of CBR anisotropies on small angular scales,
indeed caustics can induce a non-Gaussian signature into the CMB at small
scales and lead to stronger mixing of anisotropies than occurs in weak lensing.Comment: 28 pages, 6 ps figures, eps
Vorticity generation in large-scale structure caustics
A fundamental hypothesis for the interpretation of the measured large-scale
line-of-sight peculiar velocities of galaxies is that the large-scale cosmic
flows are irrotational. In order to assess the validity of this assumption, we
estimate, within the frame of the gravitational instability scenario, the
amount of vorticity generated after the first shell crossings in large-scale
caustics. In the Zel'dovich approximation the first emerging singularities form
sheet like structures. Here we compute the expectation profile of an initial
overdensity under the constraint that it goes through its first shell crossing
at the present time. We find that this profile corresponds to rather oblate
structures in Lagrangian space. Assuming the Zel'dovich approximation is still
adequate not only at the first stages of the evolution but also slightly after
the first shell crossing, we calculate the size and shape of those caustics and
their vorticity content as a function of time and for different cosmologies.
The average vorticity created in these caustics is small: of the order of one
(in units of the Hubble constant). To illustrate this point we compute the
contribution of such caustics to the probability distribution function of the
filtered vorticity at large scales. We find that this contribution that this
yields a negligible contribution at the 10 to 15 Mpc scales. It becomes
significant only at the scales of 3 to 4 Mpc, that is, slightly above
the galaxy cluster scales.Comment: 25 pages 16 figures; accepted for publication by A&A vol 342 (1999
Superluminal Caustics of Close, Rapidly-Rotating Binary Microlenses
The two outer triangular caustics (regions of infinite magnification) of a
close binary microlens move much faster than the components of the binary
themselves, and can even exceed the speed of light. When , where
is the caustic speed, the usual formalism for calculating the lens
magnification breaks down. We develop a new formalism that makes use of the
gravitational analog of the Li\'enard-Wiechert potential. We find that as the
binary speeds up, the caustics undergo several related changes: First, their
position in space drifts. Second, they rotate about their own axes so that they
no longer have a cusp facing the binary center of mass. Third, they grow larger
and dramatically so for . Fourth, they grow weaker roughly in
proportion to their increasing size. Superluminal caustic-crossing events are
probably not uncommon, but they are difficult to observe.Comment: 12 pages, 7 ps figures, submitted to Ap
Gravitational Lensing by Dark Matter Caustics
Dark matter caustics have specific density profiles and, therefore, precisely
calculable gravitational lensing properties. We present a formalism which
simplifies the relevant calculations, and apply it to four specific cases. In
the first three, the line of sight is tangent to a smooth caustic surface. The
curvature of the surface at the tangent point is positive, negative or zero. In
the fourth case the line of sight passes near a cusp. For each we derive the
map between the image and source planes. In some cases, a point source has
multiple images and experiences infinite magnification when the images merge.
Unfortunately, for the dark matter caustics expected in realistic galactic halo
models, the angular resolution required to resolve the multiple images is not
presently achievable. A more promising approach aims to observe the distortions
caused by dark matter caustics in the images of extended sources such as radio
jets.Comment: 36 pages, 11 figure
Mass estimation in the outer regions of galaxy clusters
We present a technique for estimating the mass in the outskirts of galaxy
clusters where the usual assumption of dynamical equilibrium is not valid. The
method assumes that clusters form through hierarchical clustering and requires
only galaxy redshifts and positions on the sky. We apply the method to
dissipationless cosmological N-body simulations where galaxies form and evolve
according to semi-analytic modelling. The method recovers the actual cluster
mass profile within a factor of two to several megaparsecs from the cluster
centre. This error originates from projection effects, sparse sampling, and
contamination by foreground and background galaxies. In the absence of velocity
biases, this method can provide an estimate of the mass-to-light ratio on
scales ~1-10 Mpc/h where this quantity is still poorly known.Comment: 14 pages, 7 figures, MN LaTeX style, MNRAS, in pres
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