61,450 research outputs found
Bending rigidity of stiff polyelectrolyte chains: Single chain and a bundle of multichains
We study the bending rigidity of highly charged stiff polyelectrolytes, for
both a single chain and many chains forming a bundle. A theory is developed to
account for the interplay between competitive binding of counterions and charge
correlations in softening the polyelectrolyte (PE) chains. The presence of even
a small concentration of multivalent counterions leads to a dramatic reduction
in the bending rigidity of the chains that are nominally stiffened by the
repulsion between their backbone charges. The variation of the bending rigidity
as a function of , the fraction of charged monomers on the chain, does
not exhibits simple scaling behavior; it grows with increasing below a
critical value of . Beyond the critical value, however, the chain
becomes softer as increases. The bending rigidity also exhibits
intriguing dependence on the concentration of multivalent counterion ;
for highly charged PEs, the bending rigidity decreases as increases from
zero, while it increases with increasing beyond a certain value of
. When polyelectrolyte chains form a -loop condensate (e.g., a
toroidal bundle formed by turns (winds) of the chain), the inter-loop
coupling further softens the condensate, resulting in the bending free energy
of the condensate that scales as for large .Comment: 11 pages, 2 figure
Semiflexible Chains under Tension
A functional integral formalism is used to derive the extension of a stiff
chain subject to an external force. The force versus extension curves are
calculated using a meanfield approach in which the hard constraint
is replaced by a global constraint where is the
tangent vector describing the chain and is the arc length. The theory
``quantitatively'' reproduces the experimental results for DNA that is subject
to a constant force.
We also treat the problems of a semiflexible chain in a nematic field. In the
limit of weak nematic field strength our treatment reproduces the exact results
for chain expansion parallel to the director. When the strength of nematic
field is large, a situation in which there are two equivalent minima in the
free energy, the intrinsically meanfield approach yields incorrect results for
the dependence of the persistence length on the nematic field.Comment: 14 pages, 1 figure available upon request, submitted to J. Chem. Phy
Entanglement witnesses arising from Choi type positive linear maps
We construct optimal PPTES witnesses to detect PPT entangled
edge states of type constructed recently \cite{kye_osaka}. To do this,
we consider positive linear maps which are variants of the Choi type map
involving complex numbers, and examine several notions related to optimality
for those entanglement witnesses. Through the discussion, we suggest a method
to check the optimality of entanglement witnesses without the spanning
property.Comment: 18 pages, 4 figures, 1 tabl
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