75 research outputs found
Loops in One Dimensional Random Walks
Distribution of loops in a one-dimensional random walk (RW), or,
equivalently, neutral segments in a sequence of positive and negative charges
is important for understanding the low energy states of randomly charged
polymers. We investigate numerically and analytically loops in several types of
RWs, including RWs with continuous step-length distribution. We show that for
long walks the probability density of the longest loop becomes independent of
the details of the walks and definition of the loops. We investigate crossovers
and convergence of probability densities to the limiting behavior, and obtain
some of the analytical properties of the universal probability density.Comment: 9 two-column pages. 8 eps figures. RevTex. Submitted to Eur. Phys. J.
Attractive and repulsive polymer-mediated forces between scale-free surfaces
We consider forces acting on objects immersed in, or attached to, long
fluctuating polymers. The confinement of the polymer by the obstacles results
in polymer-mediated forces that can be repulsive (due to loss of entropy) or
attractive (if some or all surfaces are covered by adsorbing layers). The
strength and sign of the force in general depends on the detailed shape and
adsorption properties of the obstacles, but assumes simple universal forms if
characteristic length scales associated with the objects are large. This occurs
for scale-free shapes (such as a flat plate, straight wire, or cone), when the
polymer is repelled by the obstacles, or is marginally attracted to it (close
to the depinning transition where the absorption length is infinite). In such
cases, the separation between obstacles is the only relevant macroscopic
length scale, and the polymer mediated force equals ,
where is temperature. The amplitude is akin to a critical
exponent, depending only on geometry and universality of the polymer system.
The value of , which we compute for simple geometries and ideal
polymers, can be positive or negative. Remarkably, we find for
ideal polymers at the adsorption transition point, irrespective of shapes of
the obstacles, i.e. at this special point there is no polymer-mediated force
between obstacles (scale-free or not).Comment: RevTeX, 10 pages, 10 figure
Entropic Elasticity at the Sol-Gel Transition
The sol-gel transition is studied in two purely entropic models consisting of
hard spheres in continuous three-dimensional space, with a fraction of
nearest neighbor spheres tethered by inextensible bonds. When all the tethers
are present () the two systems have connectivities of simple cubic and
face-centered cubic lattices. For all above the percolation threshold
, the elasticity has a cubic symmetry characterized by two distinct shear
moduli. When approaches , both shear moduli decay as ,
where for each type of the connectivity. This result is similar to
the behavior of the conductivity in random resistor networks, and is consistent
with many experimental studies of gel elasticity. The difference between the
shear moduli that measures the deviation from isotropy decays as ,
with .Comment: 12 pages, 3 eps figures, RevTe
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