4,331 research outputs found
On the corrections to Strong-Stretching Theory for end-confined, charged polymers in a uniform electric field
We investigate the properties of a system of semi-diluted polymers in the
presence of charged groups and counter-ions, by means of self-consistent field
theory. We study a system of polyelectrolyte chains grafted to a similarly, as
well as an oppositely charged surface, solving a set of saddle-point equations
that couple the modified diffusion equation for the polymer partition function
to the Poisson-Boltzmann equation describing the charge distribution in the
system. A numerical study of this set of equations is presented and comparison
is made with previous studies. We then consider the case of semi-diluted,
grafted polymer chains in the presence of charge-end-groups. We study the
problem with self-consistent field as well as strong-stretching theory. We
derive the corrections to the Milner-Witten-Cates (MWC) theory for weakly
charged chains and show that the monomer-density deviates from the parabolic
profile expected in the uncharged case. The corresponding corrections are shown
to be dictated by an Abel-Volterra integral equation of the second kind. The
validity of our theoretical findings is confirmed comparing the predictions
with the results obtained within numerical self-consistent field theory.Comment: 15 Pages, 12 figure
Methods in Mathematica for Solving Ordinary Differential Equations
An overview of the solution methods for ordinary differential equations in
the Mathematica function DSolve is presented.Comment: 13 page
A comparison between numerical solutions to fractional differential equations: Adams-type predictor-corrector and multi-step generalized differential transform method
In this note, two numerical methods of solving fractional differential
equations (FDEs) are briefly described, namely predictor-corrector approach of
Adams-Bashforth-Moulton type and multi-step generalized differential transform
method (MSGDTM), and then a demonstrating example is given to compare the
results of the methods. It is shown that the MSGDTM, which is an enhancement of
the generalized differential transform method, neglects the effect of non-local
structure of fractional differentiation operators and fails to accurately solve
the FDEs over large domains.Comment: 12 pages, 2 figure
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