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Caustics
in dark matter halos, R. Mohayaee and S.F. Shandarin
(2005) derive semianalytically the limits on density in the region of caustics
due to thermal velocity dispersion of dark matter particles.
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Probing
dark matter caustics with weak lensing. R. Gavazzi, R. Mohayaee,
B. Fort (2005)
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Cusps
in CDM halos: The density profile of a billion particle halo. J.
Diemand, M. Zemp, B. Moore, J. Stadel and M. Carollo (2005)
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Adhesive
gravitational clustering. T. Buchert and A. Dominguez (2005)
review the issue of multi-streaming in cosmological models and coarse-graining
in phase space.
-
A
Cosmological Kinetic Theory for the Evolution of Cold Dark Matter Halos
with Substructure: Quasi-Linear Theory. C.-P. Ma and E. Berschinger
(2004) give applications to galaxy halos.
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Universality
in the distribution of caustics in the expanding Universe. T. Yano,
H. Koyama, T. Buchert and N. Gouda (2004)
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Diurnal
and Annual Modulation of Cold Dark Matter Signals. Fu-Sin
Ling, P. Sikivie and S. Wick (2004) derive the diurnal and annual modulation
signatures of a cold dark matter flow in axion and WIMP direct detection
experiments, taking account not only of the orbital motion of the Earth,
but also the gravity of the Sun, the rotation of the Earth and the gravitational
field of the Earth.
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Evidence
for Ring Caustics in the Milky Way. P.Sikivie (2003) finds evidence
for caustic rings of dark matter in the Milky Way, again with radii obeying
the a_n \propto 1/n law. The evidence is based upon the existence
of sharprises in the rotation curve of our galaxy and on the appearance
of a triangular feature in an IRAS map of the Galactic plane.
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Gravitational
Lensing by Dark Matter Caustics. C. Charmousis, V. Onemli,
Z. Qiu and P. Sikivie (2003) derive the gravitational lensing signatures
of cold dark matter caustics for a variety of cases.
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Solar
Wakes of Dark Matter Flows. P. Sikivie and S. Wick (2002)
analyze the effect of the gravitational field of the Sun on a cold dark
matter flow in our neighborhood. Describes the caustics (called 'spike'
and 'skirt') that occur in this case.
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Caustic
Rings and Cold Dark Matter. Ben Moore (2000)
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Evidence
for universal structure in galactic halos. W.H. Kinney and P.Sikivie
(2000) analyze the rotation curves of 32 external galaxies and finds evidence
for caustic rings of dark matter with radii obeying the a_n \propto 1/n
law.
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The
caustic ring singularity. P. Sikivie (1999) gives a detailed
description of the structure of caustic rings of dark matter in terms of
the elliptic umbilic catastrophe, emphasizes that caustics will be present
in cold dark matter halos for general model-independent reasons.
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The
geometry of phase mixing. S.Tremaine (1999) discusses the expected
dimensionality of phase-space structures and suggests that the most prominent
features in surveys with K>=D (where D is the dimensionally of the phase
structure and K is the number of observables) will be stable singularities
(catastrophes).
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Caustic
rings of dark matter. P. Sikivie (1998) shows the existence
of inner caustics in dark matter halos, describes them as caustic rings,
gives a law (a_n \propto 1/n) for the caustic ring radii in the case of
self-similar infall, points to observational evidence for caustic rings
of dark matter.
-
Morphology
in Cosmological Gravitational Clustering and Catastrophe Theory. N.
Gouda (1998)
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Evolution
of the Power Spectrum and Self-Similarity in the Expanding One-dimensional
Universe. T. Yano and N. Gouda (1998)
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The
performance of Lagrangian perturbation schemes at high resolution.
T.
Buchert, G. Karakatsanis, R. Klaffl and P. Schiller (1997)
-
Nonlinear
Growth of Two-dimensional Cosmological Density Fluctuations and Type of
Singularity in Accord with the Catastrophe Theory. N. Gouda
(1996)
-
Lagrangian
perturbation approach to the formation of large-scale structure. T.
Buchert (1996). A tutorial on Lagrangian perturbation theory.
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Phase-space
structure of cold dark matter halos. P. Sikivie and J.R. Ipser(1992)
give the general arguments why cold dark matter particles are distributed
on a 3-dim hypersurface in 6-dim phase-space.The appearance of discrete
flows of dark matter and caustics are a direct consequence of this phase-space
structure.
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High
spatial resolution in three dimensions - A challenge for large-scale structure
formation models. T. Buchert and M. Bartelmann (1991)
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Non-Linear
Growth of One-Dimensional Cosmological Density Fluctuation and Catastrophe
Theory N. Gouda and T. Nakamura (1989)
-
Non-Linear
Growth of Density Fluctuations in the Spherically Symmetric Expanding Universe
and Catastrophe Theory. N. Gouda (1989)
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The
large-scale structures of the universe : Turbulence, intermittency, structures
in a self-garvitating medium. S.F. Shandarin, Ya. B. Zeldovich
(1989) give the review of the structure formation and discuss all generic
caustics (including metamorphoses) for the potential mapping in one, two
and three dimensions.
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A
class of solutions in Newtonian cosmology and the pancake theory. T.
Buchert (1989) gives high-resolution calculations and illustrations
of caustics and their metamorphoses in Lagrangian perturbation solutions.
-
J.W. Bruce. J. Lond. Math. Soc., 33,
375. (1986). What changes for the stability of Lagrangian singularities,
if vorticity is present in the flow.
-
Singularities of Differentiable Maps. V.I.
Arnol'd, S.M. Gusein--Sade and A.N. Varchenko. Vol. I (1982) &
II (1985) summarize the mathematical theory of Lagrangian and Legendrian
singularities. Edited by Birkhäuser, Boston.
-
Laboratory
observation of caustics, optical simulation of the motion of particles,
and cosmology. Ya. B. Zeldovich, A.V. Mamaev, S.F. Shandarin
(1983) discuss the relation of gravitational instability in two dimensions
and caustics of geometric optics.
-
Universal
power-law tails for singularity-dominated strong fluctuations. M.V.
Berry (1982)
-
Evolution
of singularities of potential flows in collisionless media and transformations
of caustics in three-dimensional space. V.I. Arnol'd (1982)
gives detailed pictures of caustics and their metamorphoses (in Russian).
-
The
large scale structure of the universe. I - General properties One- and
two-dimensional models. V.I. Arnold, S.F. Shandarin, Ya. B.
Zeldovich (1982) give a detailed application of the Lagrange-singularity
theory to two--dimensional cosmological continua.
-
The elements of the large-scale structure of
the universe. V.I. Arnold, Ya. B. Zeldovich, S.F. Shandarin.
Usp. Math. Nauk 36, 214-216 (1981) discuss some subtle mathematical issues
related to caustics of Lagrangian mappings.
-
Focusing
and twinkling : critical exponents from catastrophes in non-Gaussian random
short waves. M.V. Berry (1977)
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Structural Stability and Morphogenesis. R.
Thom (1975) is a book on catastrophe theory edited at W.A.Benjamin
Inc. Massachusetts.
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