393,762 research outputs found
Polymer ejection from strong spherical confinement
We examine the ejection of an initially strongly confined flexible polymer
from a spherical capsid through a nanoscale pore. We use molecular dynamics for
unprecedentedly high initial monomer densities. We show that the time for an
individual monomer to eject grows exponentially with the number of ejected
monomers. By measurements of the force at the pore we show this dependence to
be a consequence of the excess free energy of the polymer due to confinement
growing exponentially with the number of monomers initially inside the capsid.
This growth relates closely to the divergence of mixing energy in the
Flory-Huggins theory at large concentration. We show that the pressure inside
the capsid driving the ejection dominates the process that is characterized by
the ejection time growing linearly with the lengths of different polymers.
Waiting time profiles would indicate that the superlinear dependence obtained
for polymers amenable to computer simulations results from a finite-size effect
due to the final retraction of polymers' tails from capsids.Comment: 6 pages, 9 figures, accepted for publication in Phys. Rev. E,
increased readability from previous versio
Polishness of some topologies related to word or tree automata
We prove that the B\"uchi topology and the automatic topology are Polish. We
also show that this cannot be fully extended to the case of a space of infinite
labelled binary trees; in particular the B\"uchi and the Muller topologies are
not Polish in this case.Comment: This paper is an extended version of a paper which appeared in the
proceedings of the 26th EACSL Annual Conference on Computer Science and
Logic, CSL 2017. The main addition with regard to the conference paper
consists in the study of the B\"uchi topology and of the Muller topology in
the case of a space of trees, which now forms Section
Computability and analysis: the legacy of Alan Turing
We discuss the legacy of Alan Turing and his impact on computability and
analysis.Comment: 49 page
An Upper Bound on the Complexity of Recognizable Tree Languages
The third author noticed in his 1992 PhD Thesis [Sim92] that every regular
tree language of infinite trees is in a class
for some natural number , where is the game quantifier. We
first give a detailed exposition of this result. Next, using an embedding of
the Wadge hierarchy of non self-dual Borel subsets of the Cantor space
into the class , and the notions of Wadge degree
and Veblen function, we argue that this upper bound on the topological
complexity of regular tree languages is much better than the usual
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