Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $^1$H-NMR Dipole-Dipole Relaxation in Fluids: Relaxation of Individual
  $^1$H-$^1$H Pairs versus Relaxation of Molecular Modes   The intra-molecular $^1$H-NMR dipole-dipole relaxation of molecular fluids
has traditionally been interpreted within the Bloembergen-Purcell-Pound (BPP)
theory of NMR intra-molecular relaxation. The BPP theory draws upon Debye's
theory for describing the rotational diffusion of the $^1$H-$^1$H pair and
predicts a mono-exponential decay of the $^1$H-$^1$H dipole-dipole
autocorrelation function between distinct spin pairs. Using molecular dynamics
(MD) simulations, we show that for both $n$-heptane and water this is not the
case. In particular, the autocorrelation function of individual $^1$H-$^1$H
intra-molecular pairs itself evinces a rich stretched-exponential behavior,
implying a distribution in rotational correlation times. However for the
high-symmetry molecule neopentane, the individual $^1$H-$^1$H intra-molecular
pairs do conform to the BPP description, suggesting an important role of
molecular symmetry in aiding agreement with the BPP model. The inter-molecular
autocorrelation functions for $n$-heptane, water, and neopentane also do not
admit a mono-exponential behavior of individual $^1$H-$^1$H inter-molecular
pairs at distinct initial separations. We suggest expanding the
auto-correlation function in terms of molecular modes, where the molecular
modes do have an exponential relaxation behavior. With care, the resulting
Fredholm integral equation of the first kind can be inverted to recover the
probability distribution of the molecular modes. The advantages and limitations
of this approach are noted.

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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: math
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: cs