181,488 research outputs found
A Convenient Set of Comoving Cosmological Variables and Their Application
We present a set of cosmological variables, called "supercomoving variables,"
which are particularly useful for describing the gas dynamics of cosmic
structure formation. For ideal gas with gamma=5/3, the supercomoving position,
velocity, density, temperature, and pressure are constant in time in a uniform,
isotropic, adiabatically expanding universe. Expressed in terms of these
supercomoving variables, the cosmological fluid conservation equations and the
Poisson equation closely resemble their noncosmological counterparts. This
makes it possible to generalize noncosmological results and techniques to
cosmological problems, for a wide range of cosmological models. These variables
were initially introduced by Shandarin for matter-dominated models only. We
generalize supercomoving variables to models with a uniform component
corresponding to a nonzero cosmological constant, domain walls, cosmic strings,
a nonclumping form of nonrelativistic matter (e.g. massive nettrinos), or
radiation. Each model is characterized by the value of the density parameter
Omega0 of the nonrelativistic matter component in which density fluctuation is
possible, and the density parameter OmegaX of the additional, nonclumping
component. For each type of nonclumping background, we identify FAMILIES within
which different values of Omega0 and OmegaX lead to fluid equations and
solutions in supercomoving variables which are independent of Omega0 and
OmegaX. We also include the effects of heating, radiative cooling, thermal
conduction, viscosity, and magnetic fields. As an illustration, we describe 3
familiar cosmological problems in supercomoving variables: the growth of linear
density fluctuations, the nonlinear collapse of a 1D plane-wave density
fluctuation leading to pancake formation, and the Zel'dovich approximation.Comment: 38 pages (AAS latex) + 2 figures (postscript) combined in one gzip-ed
tar file. Identical to original posted version, except for addition of 2
references. Monthly Notices of the R.A.S., in pres
Divergence from, and Convergence to, Uniformity of Probability Density Quantiles
The probability density quantile (pdQ) carries essential information
regarding shape and tail behavior of a location-scale family. Convergence of
repeated applications of the pdQ mapping to the uniform distribution is
investigated and new fixed point theorems are established. The Kullback-Leibler
divergences from uniformity of these pdQs are mapped and found to be
ingredients in power functions of optimal tests for uniformity against
alternative shapes.Comment: 13 pages, 2 figures. arXiv admin note: substantial text overlap with
arXiv:1605.0018
Strong Jumps and Lagrangians of Non-Uniform Hypergraphs
The hypergraph jump problem and the study of Lagrangians of uniform
hypergraphs are two classical areas of study in the extremal graph theory. In
this paper, we refine the concept of jumps to strong jumps and consider the
analogous problems over non-uniform hypergraphs. Strong jumps have rich
topological and algebraic structures. The non-strong-jump values are precisely
the densities of the hereditary properties, which include the Tur\'an densities
of families of hypergraphs as special cases. Our method uses a generalized
Lagrangian for non-uniform hypergraphs. We also classify all strong jump values
for -hypergraphs.Comment: 19 page
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