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gravity.html
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<!DOCTYPE html>
<html>
<head>
<title>Alexander Mead | Gravity</title>
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<p class="logo"><a href="index.html">AM</a></p>
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<!-- intro -->
<div class="intro">
<h3>One-dimensional gravity</h3>
</div>
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<div class="subpage-left">
<p>
The evolution of structure in the cosmos is a complicated process
in which small-amplitude initial seed fluctuations in density are
amplified by gravity. These then collapse to form bound structures
which may then virialize and merge with other collapsed
structures. The equations governing this are complicated and
non-linear, and must be solved by computers and the resulting
simulations analysed to try and glean understanding of the
gravitational amplification processes. This is complicated in
three dimensions because the phase space is six dimensional and
cannot be visualised easily. A simplified example of collapse in
only one spatial dimension is easier to analyse because the phase
space is then only two dimensional. The movie shows the
phase-space density of collapse of a series of these parallel
sheets. The horizontal axis is position while the vertical axis is
velocity. A higher density of sheets is indicated by whiter
colours. By construction, any density in the upper half of the
movie must be moving to the right and any density in the lower
half must be moving to the left. As the collapse occurs the
initial perturbed phase space forms spirals that then wind round
themselves and each other as collapse progresses. The continuity
of the phase space, and the constancy of the phase-space density
can be seen as, despite the chaotic behaviour, there are never any
discontinuities and the density merely gets stretched, smeared and
squashed. In the real collapse of cold dark matter in our
three-dimensional Universe this type of phase space mixing and
spirals are expected at all scales, but in six dimensions rather
than just two.
</p>
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<img src="images/phasespace_1D.gif" />
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© 2025 Alexander Mead. Website by
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