Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Packing Hyperspheres in High-Dimensional Euclidean Spaces   We present the first study of disordered jammed hard-sphere packings in
four-, five- and six-dimensional Euclidean spaces. Using a collision-driven
packing generation algorithm, we obtain the first estimates for the packing
fractions of the maximally random jammed (MRJ) states for space dimensions
$d=4$, 5 and 6 to be $\phi_{MRJ} \simeq 0.46$, 0.31 and 0.20, respectively. To
a good approximation, the MRJ density obeys the scaling form $\phi_{MRJ}=
c_1/2^d+(c_2 d)/2^d$, where $c_1=-2.72$ and $c_2=2.56$, which appears to be
consistent with high-dimensional asymptotic limit, albeit with different
coefficients. Calculations of the pair correlation function $g_{2}(r)$ and
structure factor $S(k)$ for these states show that short-range ordering
appreciably decreases with increasing dimension, consistent with a recently
proposed ``decorrelation principle,'' which, among othe things, states that
unconstrained correlations diminish as the dimension increases and vanish
entirely in the limit $d \to \infty$. As in three dimensions (where $\phi_{MRJ}
\simeq 0.64$), the packings show no signs of crystallization, are isostatic,
and have a power-law divergence in $g_{2}(r)$ at contact with power-law
exponent $\simeq 0.4$. Across dimensions, the cumulative number of neighbors
equals the kissing number of the conjectured densest packing close to where
$g_{2}(r)$ has its first minimum. We obtain estimates for the freezing and
melting desnities for the equilibrium hard-sphere fluid-solid transition,
$\phi_F \simeq 0.32$ and $\phi_M \simeq 0.39$, respectively, for $d=4$, and
$\phi_F \simeq 0.19$ and $\phi_M \simeq 0.24$, respectively, for $d=5$.

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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc