1,488 research outputs found
Liquid drop in a cone - line tension effects
The shape of a liquid drop placed in a cone is analyzed macroscopically.
Depending on the values of the cone opening angle, the Young angle and the line
tension four different interfacial configurations may be realized. The phase
diagram in these variables is constructed and discussed; it contains both the
first- and the second-order transition lines. In particular, the tricritical
point is found and the value of the critical exponent characterizing the
behaviour of the system along the line of the first-order transitions in the
neighbourhood of this point is determined.Comment: 11 pages, 4 figure
Reptation in the Rubinstein-Duke model: the influence of end-reptons dynamics
We investigate the Rubinstein-Duke model for polymer reptation by means of
density-matrix renormalization group techniques both in absence and presence of
a driving field. In the former case the renewal time \tau and the diffusion
coefficient D are calculated for chains up to N=150 reptons and their scaling
behavior in N is analyzed. Both quantities scale as powers of N: and with the asymptotic exponents z=3 and x=2, in agreement
with the reptation theory. For an intermediate range of lengths, however, the
data are well-fitted by some effective exponents whose values are quite
sensitive to the dynamics of the end reptons. We find 2.7 <z< 3.3 and 1.8 <x<
2.1 for the range of parameters considered and we suggest how to influence the
end reptons dynamics in order to bring out such a behavior. At finite and not
too small driving field, we observe the onset of the so-called band inversion
phenomenon according to which long polymers migrate faster than shorter ones as
opposed to the small field dynamics. For chains in the range of 20 reptons we
present detailed shapes of the reptating chain as function of the driving field
and the end repton dynamics.Comment: RevTeX 12 Pages and 14 figure
DNA: From rigid base-pairs to semiflexible polymers
The sequence-dependent elasticity of double-helical DNA on a nm length scale
can be captured by the rigid base-pair model, whose strains are the relative
position and orientation of adjacent base-pairs. Corresponding elastic
potentials have been obtained from all-atom MD simulation and from
high-resolution structural data. On the scale of a hundred nm, DNA is
successfully described by a continuous worm-like chain model with homogeneous
elastic properties characterized by a set of four elastic constants, which have
been directly measured in single-molecule experiments. We present here a theory
that links these experiments on different scales, by systematically
coarse-graining the rigid base-pair model for random sequence DNA to an
effective worm-like chain description. The average helical geometry of the
molecule is exactly taken into account in our approach. We find that the
available microscopic parameters sets predict qualitatively similar mesoscopic
parameters. The thermal bending and twisting persistence lengths computed from
MD data are 42 and 48 nm, respectively. The static persistence lengths are
generally much higher, in agreement with cyclization experiments. All
microscopic parameter sets predict negative twist-stretch coupling. The
variability and anisotropy of bending stiffness in short random chains lead to
non-Gaussian bend angle distributions, but become unimportant after two helical
turns.Comment: 13 pages, 6 figures, 6 table
A generalized theory of semiflexible polymers
DNA bending on length scales shorter than a persistence length plays an
integral role in the translation of genetic information from DNA to cellular
function. Quantitative experimental studies of these biological systems have
led to a renewed interest in the polymer mechanics relevant for describing the
conformational free energy of DNA bending induced by protein-DNA complexes.
Recent experimental results from DNA cyclization studies have cast doubt on the
applicability of the canonical semiflexible polymer theory, the wormlike chain
(WLC) model, to DNA bending on biological length scales. This paper develops a
theory of the chain statistics of a class of generalized semiflexible polymer
models. Our focus is on the theoretical development of these models and the
calculation of experimental observables. To illustrate our methods, we focus on
a specific toy model of DNA bending. We show that the WLC model generically
describes the long-length-scale chain statistics of semiflexible polymers, as
predicted by the Renormalization Group. In particular, we show that either the
WLC or our new model adequate describes force-extension, solution scattering,
and long-contour-length cyclization experiments, regardless of the details of
DNA bend elasticity. In contrast, experiments sensitive to short-length-scale
chain behavior can in principle reveal dramatic departures from the linear
elastic behavior assumed in the WLC model. We demonstrate this explicitly by
showing that our toy model can reproduce the anomalously large
short-contour-length cyclization J factors observed by Cloutier and Widom.
Finally, we discuss the applicability of these models to DNA chain statistics
in the context of future experiments
Fluctuations of a driven membrane in an electrolyte
We develop a model for a driven cell- or artificial membrane in an
electrolyte. The system is kept far from equilibrium by the application of a DC
electric field or by concentration gradients, which causes ions to flow through
specific ion-conducting units (representing pumps, channels or natural pores).
We consider the case of planar geometry and Debye-H\"{u}ckel regime, and obtain
the membrane equation of motion within Stokes hydrodynamics. At steady state,
the applied field causes an accumulation of charges close to the membrane,
which, similarly to the equilibrium case, can be described with renormalized
membrane tension and bending modulus. However, as opposed to the equilibrium
situation, we find new terms in the membrane equation of motion, which arise
specifically in the out-of-equilibrium case. We show that these terms lead in
certain conditions to instabilities.Comment: 7 pages, 2 figures. submitted to Europhys. Let
Long-Ranged Orientational Order in Dipolar Fluids
Recently Groh and Dietrich claimed the thermodynamic state of a dipolar fluid
depends on the shape of the fluid's container. For example, a homogeneous fluid
in a short fat container would phase separate when transferred to a tall skinny
container of identical volume and temperature. Their calculation thus lacks a
thermodynamic limit. We show that removal of demagnetizing fields restores the
true, shape independent, thermodynamic limit. As a consequence, spontaneously
magnetized liquids display inhomogeneous magnetization textures.Comment: 3 pages, LaTex, no figures. Submitted as comment to PRL, May 199
Anomalous pinning behavior in an incommensurate two-chain model of friction
Pinning phenomena in an incommensurate two-chain model of friction are
studied numerically. The pinning effect due to the breaking of analyticity
exists in the present model. The pinning behavior is, however, quite different
from that for the breaking of analyticity state of the Frenkel-Kontorova model.
When the elasticity of chains or the strength of interchain interaction is
changed, pinning force and maximum static frictional force show anomalously
complicated behavior accompanied by a successive phase transition and they
vanish completely under certain conditions.Comment: RevTex, 9 pages, 19 figures, to appear in Phys. Rev. B58 No.23(1998
Scaling for Interfacial Tensions near Critical Endpoints
Parametric scaling representations are obtained and studied for the
asymptotic behavior of interfacial tensions in the \textit{full} neighborhood
of a fluid (or Ising-type) critical endpoint, i.e., as a function \textit{both}
of temperature \textit{and} of density/order parameter \textit{or} chemical
potential/ordering field. Accurate \textit{nonclassical critical exponents} and
reliable estimates for the \textit{universal amplitude ratios} are included
naturally on the basis of the ``extended de Gennes-Fisher'' local-functional
theory. Serious defects in previous scaling treatments are rectified and
complete wetting behavior is represented; however, quantitatively small, but
unphysical residual nonanalyticities on the wetting side of the critical
isotherm are smoothed out ``manually.'' Comparisons with the limited available
observations are presented elsewhere but the theory invites new, searching
experiments and simulations, e.g., for the vapor-liquid interfacial tension on
the two sides of the critical endpoint isotherm for which an amplitude ratio
is predicted.Comment: 42 pages, 6 figures, to appear in Physical Review
Critical equation of state from the average action
The scaling form of the critical equation of state is computed for
-symmetric models. We employ a method based on an exact flow equation for
a coarse grained free energy. A suitable truncation is solved numerically.Comment: Latex, 8 pages, 2 uuencoded figure
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