2,507 research outputs found
Topologically Driven Swelling of a Polymer Loop
Numerical studies of the average size of trivially knotted polymer loops with
no excluded volume are undertaken. Topology is identified by Alexander and
Vassiliev degree 2 invariants. Probability of a trivial knot, average gyration
radius, and probability density distributions as functions of gyration radius
are generated for loops of up to N=3000 segments. Gyration radii of trivially
knotted loops are found to follow a power law similar to that of self avoiding
walks consistent with earlier theoretical predictions.Comment: 6 pages, 4 figures, submitted to PNAS (USA) in Feb 200
Exact expressions for the mobility and electrophoretic mobility of a weakly charged sphere in a simple electrolyte
We present (asymptotically) exact expressions for the mobility and
electrophoretic mobility of a weakly charged spherical particle in an
electrolyte solution. This is done by analytically solving the electro and
hydrodynamic equations governing the electric potential and fluid flow with
respect to an electric field and a nonelectric force. The resulting formulae
are cumbersome, but fully explicit and trivial for computation. In the case of
a very small particle compared to the Debye screening length () our
results reproduce proper limits of the classical Debye and Onsager theories,
while in the case of a very large particle () we recover, both, the
non-monotonous charge dependence discovered by Levich (1958) as well as the
scaling estimate given by Long, Viovy, and Ajdari (1996), while adding the
previously unknown coefficients and corrections. The main applicability
condition of our solution is charge smallness in the sense that screening
remains linear.Comment: 6 pages, 1 figur
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