2,321 research outputs found
Randomly Charged Polymers, Random Walks, and Their Extremal Properties
Motivated by an investigation of ground state properties of randomly charged
polymers, we discuss the size distribution of the largest Q-segments (segments
with total charge Q) in such N-mers. Upon mapping the charge sequence to
one--dimensional random walks (RWs), this corresponds to finding the
probability for the largest segment with total displacement Q in an N-step RW
to have length L. Using analytical, exact enumeration, and Monte Carlo methods,
we reveal the complex structure of the probability distribution in the large N
limit. In particular, the size of the longest neutral segment has a
distribution with a square-root singularity at l=L/N=1, an essential
singularity at l=0, and a discontinuous derivative at l=1/2. The behavior near
l=1 is related to a another interesting RW problem which we call the "staircase
problem". We also discuss the generalized problem for d-dimensional RWs.Comment: 33 pages, 19 Postscript figures, RevTe
Collapse of Randomly Self-Interacting Polymers
We use complete enumeration and Monte Carlo techniques to study
self--avoiding walks with random nearest--neighbor interactions described by
, where is a quenched sequence of ``charges'' on the
chain. For equal numbers of positive and negative charges (), the
polymer with undergoes a transition from self--avoiding behavior to a
compact state at a temperature . The collapse temperature
decreases with the asymmetry Comment: 8 pages, TeX, 4 uuencoded postscript figures, MIT-CMT-
Ground States of Two-Dimensional Polyampholytes
We perform an exact enumeration study of polymers formed from a (quenched)
random sequence of charged monomers , restricted to a 2-dimensional
square lattice. Monomers interact via a logarithmic (Coulomb) interaction. We
study the ground state properties of the polymers as a function of their excess
charge for all possible charge sequences up to a polymer length N=18. We
find that the ground state of the neutral ensemble is compact and its energy
extensive and self-averaging. The addition of small excess charge causes an
expansion of the ground state with the monomer density depending only on .
In an annealed ensemble the ground state is fully stretched for any excess
charge .Comment: 6 pages, 6 eps figures, RevTex, Submitted to Phys. Rev.
Elasticity of Gaussian and nearly-Gaussian phantom networks
We study the elastic properties of phantom networks of Gaussian and
nearly-Gaussian springs. We show that the stress tensor of a Gaussian network
coincides with the conductivity tensor of an equivalent resistor network, while
its elastic constants vanish. We use a perturbation theory to analyze the
elastic behavior of networks of slightly non-Gaussian springs. We show that the
elastic constants of phantom percolation networks of nearly-Gaussian springs
have a power low dependence on the distance of the system from the percolation
threshold, and derive bounds on the exponents.Comment: submitted to Phys. Rev. E, 10 pages, 1 figur
A Method for Measuring Desquamation and its Use for Assessing the Effects of Some Common Exfoliants
Desquamation has been measured in the past by a counting chamber technique after corneocytes are removed from the skin surface and disaggregated in a dilute surfactant solution. However, we have found that complete corneocyte disaggregation is not always possible when these aggregates are recovered from sites where patent peeling is induced. Corneocyte counting in such instances is difficult or impossible. We have devised a method of measuring desquamation wherein the desquamating cells are determined as the total alkali-soluble protein after they are removed from the skin surface with an inert, self-hardening gel. Highly reproducible desquamation rates are obtained, characteristic of the individual subject. Using some common exfoliants, we show that pharmacologic response, observed as an increase in desquamation rate, is also an individual characteristic
Phase transitions of a tethered surface model with a deficit angle term
Nambu-Goto model is investigated by using the canonical Monte Carlo
simulations on fixed connectivity surfaces of spherical topology. Three
distinct phases are found: crumpled, tubular, and smooth. The crumpled and the
tubular phases are smoothly connected, and the tubular and the smooth phases
are connected by a discontinuous transition. The surface in the tubular phase
forms an oblong and one-dimensional object similar to a one-dimensional linear
subspace in the Euclidean three-dimensional space R^3. This indicates that the
rotational symmetry inherent in the model is spontaneously broken in the
tubular phase, and it is restored in the smooth and the crumpled phases.Comment: 6 pages with 6 figure
Polymer-mediated entropic forces between scale-free objects
The number of configurations of a polymer is reduced in the presence of a
barrier or an obstacle. The resulting loss of entropy adds a repulsive
component to other forces generated by interaction potentials. When the
obstructions are scale invariant shapes (such as cones, wedges, lines or
planes) the only relevant length scales are the polymer size R_0 and
characteristic separations, severely constraining the functional form of
entropic forces. Specifically, we consider a polymer (single strand or star)
attached to the tip of a cone, at a separation h from a surface (or another
cone). At close proximity, such that h<<R_0, separation is the only remaining
relevant scale and the entropic force must take the form F=AkT/h. The amplitude
A is universal, and can be related to exponents \eta governing the anomalous
scaling of polymer correlations in the presence of obstacles. We use
analytical, numerical and epsilon-expansion techniques to compute the exponent
\eta for a polymer attached to the tip of the cone (with or without an
additional plate or cone) for ideal and self-avoiding polymers. The entropic
force is of the order of 0.1 pN at 0.1 micron for a single polymer, and can be
increased for a star polymer.Comment: LaTeX, 15 pages, 4 eps figure
Two-Dimensional Polymers with Random Short-Range Interactions
We use complete enumeration and Monte Carlo techniques to study
two-dimensional self-avoiding polymer chains with quenched ``charges'' .
The interaction of charges at neighboring lattice sites is described by . We find that a polymer undergoes a collapse transition at a temperature
, which decreases with increasing imbalance between charges. At the
transition point, the dependence of the radius of gyration of the polymer on
the number of monomers is characterized by an exponent , which is slightly larger than the similar exponent for homopolymers. We
find no evidence of freezing at low temperatures.Comment: 4 two-column pages, 6 eps figures, RevTex, Submitted to Phys. Rev.
Polyelectrolyte Bundles
Using extensive Molecular Dynamics simulations we study the behavior of
polyelectrolytes with hydrophobic side chains, which are known to form
cylindrical micelles in aqueous solution. We investigate the stability of such
bundles with respect to hydrophobicity, the strength of the electrostatic
interaction, and the bundle size. We show that for the parameter range relevant
for sulfonated poly-para-phenylenes (PPP) one finds a stable finite bundle
size. In a more generic model we also show the influence of the length of the
precursor oligomer on the stability of the bundles. We also point out that our
model has close similarities to DNA solutions with added condensing agents,
hinting to the possibility that the size of DNA aggregates is under certain
circumstances thermodynamically limited.Comment: 10 pages, 8 figure
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