235 research outputs found
Statistical properties of eigenvectors in non-Hermitian Gaussian random matrix ensembles
Statistical properties of eigenvectors in non-Hermitian random matrix
ensembles are discussed, with an emphasis on correlations between left and
right eigenvectors. Two approaches are described. One is an exact calculation
for Ginibre's ensemble, in which each matrix element is an independent,
identically distributed Gaussian complex random variable. The other is a
simpler calculation using as an expansion parameter, where is the
rank of the random matrix: this is applied to Girko's ensemble. Consequences of
eigenvector correlations which may be of physical importance in applications
are also discussed. It is shown that eigenvalues are much more sensitive to
perturbations than in the corresponding Hermitian random matrix ensembles. It
is also shown that, in problems with time-evolution governed by a non-
Hermitian random matrix, transients are controlled by eigenvector correlations
Intrinsic viscosity of a suspension of weakly Brownian ellipsoids in shear
We analyze the angular dynamics of triaxial ellipsoids in a shear flow
subject to weak thermal noise. By numerically integrating an overdamped angular
Langevin equation, we find the steady angular probability distribution for a
range of triaxial particle shapes. From this distribution we compute the
intrinsic viscosity of a dilute suspension of triaxial particles. We determine
how the viscosity depends on particle shape in the limit of weak thermal noise.
While the deterministic angular dynamics depends very sensitively on particle
shape, we find that the shape dependence of the intrinsic viscosity is weaker,
in general, and that suspensions of rod-like particles are the most sensitive
to breaking of axisymmetry. The intrinsic viscosity of a dilute suspension of
triaxial particles is smaller than that of a suspension of axisymmetric
particles with the same volume, and the same ratio of major to minor axis
lengths.Comment: 14 pages, 6 figures, 1 table, revised versio
Effect of weak fluid inertia upon Jeffery orbits
We consider the rotation of small neutrally buoyant axisymmetric particles in
a viscous steady shear flow. When inertial effects are negligible the problem
exhibits infinitely many periodic solutions, the "Jeffery orbits". We compute
how inertial effects lift their degeneracy by perturbatively solving the
coupled particle-flow equations. We obtain an equation of motion valid at small
shear Reynolds numbers, for spheroidal particles with arbitrary aspect ratios.
We analyse how the linear stability of the \lq log-rolling\rq{} orbit depends
on particle shape and find it to be unstable for prolate spheroids. This
resolves a puzzle in the interpretation of direct numerical simulations of the
problem. In general both unsteady and non-linear terms in the Navier-Stokes
equations are important.Comment: 5 pages, 2 figure
Extension of nano-confined DNA: quantitative comparison between experiment and theory
The extension of DNA confined to nanochannels has been studied intensively
and in detail. Yet quantitative comparisons between experiments and model
calculations are difficult because most theoretical predictions involve
undetermined prefactors, and because the model parameters (contour length, Kuhn
length, effective width) are difficult to compute reliably, leading to
substantial uncertainties. Here we use a recent asymptotically exact theory for
the DNA extension in the "extended de Gennes regime" that allows us to compare
experimental results with theory. For this purpose we performed new
experiments, measuring the mean DNA extension and its standard deviation while
varying the channel geometry, dye intercalation ratio, and ionic buffer
strength. The experimental results agree very well with theory at high ionic
strengths, indicating that the model parameters are reliable. At low ionic
strengths the agreement is less good. We discuss possible reasons. Our approach
allows, in principle, to measure the Kuhn length and effective width of a
single DNA molecule and more generally of semiflexible polymers in solution.Comment: Revised version, 6 pages, 2 figures, 1 table, supplementary materia
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