470 research outputs found
Semiflexible polymers: Dependence on ensemble and boundary orientations
We show that the mechanical properties of a worm-like-chain (WLC) polymer, of
contour length and persistence length \l such that t=L/\l\sim{\cal
O}(1), depend both on the ensemble and the constraint on end-orientations. In
the Helmholtz ensemble, multiple minima in free energy near persists for
all kinds of orientational boundary conditions. The qualitative features of
projected probability distribution of end to end vector depend crucially on the
embedding dimensions. A mapping of the WLC model, to a quantum particle moving
on the surface of an unit sphere, is used to obtain the statistical and
mechanical properties of the polymer under various boundary conditions and
ensembles. The results show excellent agreement with Monte-Carlo simulations.Comment: 15 pages, 15 figures; version accepted for publication in Phys. Rev.
E; one new figure and discussions adde
Statistical mechanics of double-stranded semi-flexible polymers
We study the statistical mechanics of double-stranded semi-flexible polymers
using both analytical techniques and simulation. We find a transition at some
finite temperature, from a type of short range order to a fundamentally
different sort of short range order. In the high temperature regime, the
2-point correlation functions of the object are identical to worm-like chains,
while in the low temperature regime they are different due to a twist
structure. In the low temperature phase, the polymers develop a kink-rod
structure which could clarify some recent puzzling experiments on actin.Comment: 4 pages, 3 figures; final version for publication - slight
modifications to text and figure
Molecular elasticity and the geometric phase
We present a method for solving the Worm Like Chain (WLC) model for twisting
semiflexible polymers to any desired accuracy. We show that the WLC free energy
is a periodic function of the applied twist with period 4 pi. We develop an
analogy between WLC elasticity and the geometric phase of a spin half system.
These analogies are used to predict elastic properties of twist-storing
polymers. We graphically display the elastic response of a single molecule to
an applied torque. This study is relevant to mechanical properties of
biopolymers like DNA.Comment: five pages, one figure, revtex, revised in the light of referee's
comments, to appear in PR
A Conformal Field Theory for Eternal Inflation
We study a statistical model defined by a conformally invariant distribution
of overlapping spheres in arbitrary dimension d. The model arises as the
asymptotic distribution of cosmic bubbles in d+1 dimensional de Sitter space,
and also as the asymptotic distribution of bubble collisions with the domain
wall of a fiducial "observation bubble" in d+2 dimensional de Sitter space. In
this note we calculate the 2-,3-, and 4-point correlation functions of
exponentials of the "bubble number operator" analytically in d=2. We find that
these correlators, when carefully defined, are free of infrared divergences,
covariant under the global conformal group, charge conserving, and transform
with positive conformal dimensions that are related in a novel way to the
charge. Although by themselves these operators probably do not define a
full-fledged conformal field theory, one can use the partition function on a
sphere to compute an approximate central charge in the 2D case. The theory in
any dimension has a noninteracting limit when the nucleation rate of the
bubbles in the bulk is very large. The theory in two dimensions is related to
some models of continuum percolation, but it is conformal for all values of the
tunneling rate.Comment: 30 pages, 8 figure
Exact theory of kinkable elastic polymers
The importance of nonlinearities in material constitutive relations has long
been appreciated in the continuum mechanics of macroscopic rods. Although the
moment (torque) response to bending is almost universally linear for small
deflection angles, many rod systems exhibit a high-curvature softening. The
signature behavior of these rod systems is a kinking transition in which the
bending is localized. Recent DNA cyclization experiments by Cloutier and Widom
have offered evidence that the linear-elastic bending theory fails to describe
the high-curvature mechanics of DNA. Motivated by this recent experimental
work, we develop a simple and exact theory of the statistical mechanics of
linear-elastic polymer chains that can undergo a kinking transition. We
characterize the kinking behavior with a single parameter and show that the
resulting theory reproduces both the low-curvature linear-elastic behavior
which is already well described by the Wormlike Chain model, as well as the
high-curvature softening observed in recent cyclization experiments.Comment: Revised for PRE. 40 pages, 12 figure
Influence of the structural modulations and the Chain-ladder interaction in the compounds
We studied the effects of the incommensurate structural modulations on the
ladder subsystem of the family of compounds
using ab-initio explicitly-correlated calculations. From these calculations we
derived model as a function of the fourth crystallographic coordinate
describing the incommensurate modulations. It was found that in the
highly calcium-doped system, the on-site orbital energies are strongly
modulated along the ladder legs. On the contrary the two sites of the ladder
rungs are iso-energetic and the holes are thus expected to be delocalized on
the rungs. Chain-ladder interactions were also evaluated and found to be very
negligible. The ladder superconductivity model for these systems is discussed
in the light of the present results.Comment: 8 octobre 200
Global hydrodynamic analysis of the molecular flexibility of galactomannans
In the past, intrinsic viscosity and sedimentation velocity analyses have been used separately to assess the conformation and flexibility of guar and locust bean gum galactomannans based on worm-like chain and semi-flexible coil models. Publication of a new global method combining data sets of both intrinsic viscosity and sedimentation coefficient with molecular weight, and minimising a target (error) function now permits a more robust analysis. Using this approach, values for the persistence length of (10 ± 2) nm for guar and (7 ± 1) nm for locust bean gum are returned if the mass per unit length ML is floated as a variable. Using a fixed mass per unit length based on the known compositional data of each galactomannan yields a similar value for Lp in both cases, (8 ± 1) nm for guar and (9 ± 1) nm for locust bean gum, with combined set of data yielding (9 ± 1) nm: within experimental error the flexibilities of both galactomannans are very similar. © 2007 Elsevier Ltd. All rights reserved
Perturbation Theory for Path Integrals of Stiff Polymers
The wormlike chain model of stiff polymers is a nonlinear -model in
one spacetime dimension in which the ends are fluctuating freely. This causes
important differences with respect to the presently available theory which
exists only for periodic and Dirichlet boundary conditions. We modify this
theory appropriately and show how to perform a systematic large-stiffness
expansions for all physically interesting quantities in powers of ,
where is the length and the persistence length of the polymer. This
requires special procedures for regularizing highly divergent Feynman integrals
which we have developed in previous work. We show that by adding to the
unperturbed action a correction term , we can calculate
all Feynman diagrams with Green functions satisfying Neumann boundary
conditions. Our expansions yield, order by order, properly normalized
end-to-end distribution function in arbitrary dimensions , its even and odd
moments, and the two-point correlation function
Statistical mechanics of semiflexible ribbon polymers
The statistical mechanics of a ribbon polymer made up of two semiflexible
chains is studied using both analytical techniques and simulation. The system
is found to have a crossover transition at some finite temperature, from a type
of short range order to a fundamentally different sort of short range order. In
the high temperature regime, the 2-point correlation functions of the object
are identical to worm-like chains, while in the low temperature regime they are
different due to a twist structure. The crossover happens when the persistence
length of individual strands becomes comparable to the thickness of the ribbon.
In the low temperature regime, the ribbon is observed to have a novel
``kink-rod'' structure with a mutual exclusion of twist and bend in contrast to
smooth worm-like chain behaviour. This is due to its anisotropic rigidity and
corresponds to an {\it infinitely} strong twist-bend coupling. The
double-stranded polymer is also studied in a confined geometry. It is shown
that when the polymer is restricted in a particular direction to a size less
than the bare persistence length of the individual strands, it develops zigzag
conformations which are indicated by an oscillatory tangent-tangent correlation
function in the direction of confinement. Increasing the separation of the
confining plates leads to a crossover to the free behaviour, which takes place
at separations close to the bare persistence length. These results are expected
to be relevant for experiments which involve complexation of two or more stiff
or semiflexible polymers.Comment: 20 pages, 11 figures. PRE (in press
Binding of molecules to DNA and other semiflexible polymers
A theory is presented for the binding of small molecules such as surfactants
to semiflexible polymers. The persistence length is assumed to be large
compared to the monomer size but much smaller than the total chain length. Such
polymers (e.g. DNA) represent an intermediate case between flexible polymers
and stiff, rod-like ones, whose association with small molecules was previously
studied. The chains are not flexible enough to actively participate in the
self-assembly, yet their fluctuations induce long-range attractive interactions
between bound molecules. In cases where the binding significantly affects the
local chain stiffness, those interactions lead to a very sharp, cooperative
association. This scenario is of relevance to the association of DNA with
surfactants and compact proteins such as RecA. External tension exerted on the
chain is found to significantly modify the binding by suppressing the
fluctuation-induced interaction.Comment: 15 pages, 7 figures, RevTex, the published versio
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