19,398 research outputs found
Comparison of Dynamical Approximation Schemes for Non-Linear Gravitational Clustering
I report on controlled comparison of gravitational approximation schemes
linear/lognormal/adhesion/frozen-flow/Zel'dovich(ZA) and ZA's second--order
generalization. In the last two cases we also created new versions of the
approximation by truncation, i.e., by finding an optimum smoothing window (see
text) for the initial conditions. The Zel'dovich approximation, with optimized
initial smoothing, worked extremely well. Its second-order generalization was
slightly better. The success of our best-choice was a result of the treatment
of the phases of nonlinear Fourier components. The adhesion approximation
produced the most accurate nonlinear power spectrum and density distribution,
but its phase errors suggest mass condensations were moved somewhat
incorrectly. Due to its better reproduction of the mass density distribution
function and power spectrum, adhesion might be preferred for some uses. We
recommend either n-body simulations or our modified versions of ZA, depending
on the purpose. Modified ZA can rapidly generate large numbers of realizations
of model universes with good accuracy down to galaxy group (or smaller) mass
scales.Comment: 8 pp., plain TeX. ApJ Letters, in press. Contact
[email protected] for Figure
Hierarchical Pancaking: Why the Zel'dovich Approximation Describes Coherent Large-Scale Structure in N-Body Simulations of Gravitational Clustering
To explain the rich structure of voids, clusters, sheets, and filaments
apparent in the Universe, we present evidence for the convergence of the two
classic approaches to gravitational clustering, the ``pancake'' and
``hierarchical'' pictures. We compare these two models by looking at agreement
between individual structures -- the ``pancakes'' which are characteristic of
the Zel'dovich Approximation (ZA) and also appear in hierarchical N-body
simulations. We find that we can predict the orientation and position of N-body
simulation objects rather well, with decreasing accuracy for increasing
large- (small scale) power in the initial conditions. We examined an N-body
simulation with initial power spectrum , and found that a
modified version of ZA based on the smoothed initial potential worked well in
this extreme hierarchical case, implying that even here very low-amplitude long
waves dominate over local clumps (although we can see the beginning of the
breakdown expected for ). In this case the correlation length of the
initial potential is extremely small initially, but grows considerably as the
simulation evolves. We show that the nonlinear gravitational potential strongly
resembles the smoothed initial potential. This explains why ZA with smoothed
initial conditions reproduces large-scale structure so well, and probably why
our Universe has a coherent large-scale structure.Comment: 17 pages of uuencoded postscript. There are 8 figures which are too
large to post here. To receive the uuencoded figures by email (or hard copies
by regular mail), please send email to: [email protected]. This is
a revision of a paper posted earlier now in press at MNRA
UNDERGRADUATE EDUCATION IN DEPARTMENTS OF AGRICULTURAL ECONOMICS IN THE SOUTH: STATUS, CHALLENGES, AND OPPORTUNITIES
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