Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gaussian fluctuations of spatially inhomogeneous polymers   Inhomogeneous polymers play an important role in various cellular processes,
both in nature and in biotechnological applications. At finite temperatures,
inhomogeneous polymers exhibit non-trivial thermal fluctuations. In a broader
context, these are relatively simple examples for fluctuations in spatially
inhomogeneous systems, which are less understood compared to their homogeneous
counterparts. We develop a statistical theory of torsional, extensional and
bending Gaussian fluctuations of inhomogeneous polymers, where the
inhomogeneity is an inclusion of variable size and mechanical properties, using
both continuum and discrete approaches. First, we analytically calculate the
complete eigenvalue and eigenmode spectrum of the inhomogeneous polymer within
a continuum field theory. In particular, we show that the wavenumber inside and
outside of the inclusion is nearly linear in the eigenvalue index, with a
nontrivial coefficient. Second, we solve the corresponding discrete problem,
and highlight fundamental differences between the continuum and discrete
spectra. In particular, we demonstrate that above a certain wavenumber the
discrete spectrum changes qualitatively and discrete evanescent eigenmodes,
that do not have continuum counterparts, emerge. The statistical thermodynamic
implications of these differences are then explored by calculating
fluctuation-induced forces associated with free-energy variations with either
the inclusion properties (e.g.~inhomogeneity formed by adsorbing molecules) or
with an external geometric constraint. The former, which is the
fluctuation-induced contribution to the adsorbing molecules binding force, is
shown to be affected by short wavelengths and thus cannot be calculated using
the continuum approach. The latter, on the other hand, is shown to be dominated
by long wavelength shape fluctuations and hence is properly described by the
continuum theory.

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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex