2,161 research outputs found
A Model Ground State of Polyampholytes
The ground state of randomly charged polyampholytes is conjectured to have a
structure similar to a necklace, made of weakly charged parts of the chain,
compacting into globules, connected by highly charged stretched `strings'. We
suggest a specific structure, within the necklace model, where all the neutral
parts of the chain compact into globules: The longest neutral segment compacts
into a globule; in the remaining part of the chain, the longest neutral segment
(the 2nd longest neutral segment) compacts into a globule, then the 3rd, and so
on. We investigate the size distributions of the longest neutral segments in
random charge sequences, using analytical and Monte Carlo methods. We show that
the length of the n-th longest neutral segment in a sequence of N monomers is
proportional to N/(n^2), while the mean number of neutral segments increases as
sqrt(N). The polyampholyte in the ground state within our model is found to
have an average linear size proportional to sqrt(N), and an average surface
area proportional to N^(2/3).Comment: 8 two-column pages. 5 eps figures. RevTex. Submitted to Phys. Rev.
Self-consistent variational theory for globules
A self-consistent variational theory for globules based on the uniform
expansion method is presented. This method, first introduced by Edwards and
Singh to estimate the size of a self-avoiding chain, is restricted to a good
solvent regime, where two-body repulsion leads to chain swelling. We extend the
variational method to a poor solvent regime where the balance between the
two-body attractive and the three-body repulsive interactions leads to
contraction of the chain to form a globule. By employing the Ginzburg
criterion, we recover the correct scaling for the -temperature. The
introduction of the three-body interaction term in the variational scheme
recovers the correct scaling for the two important length scales in the globule
- its overall size , and the thermal blob size . Since these two
length scales follow very different statistics - Gaussian on length scales
, and space filling on length scale - our approach extends the
validity of the uniform expansion method to non-uniform contraction rendering
it applicable to polymeric systems with attractive interactions. We present one
such application by studying the Rayleigh instability of polyelectrolyte
globules in poor solvents. At a critical fraction of charged monomers, ,
along the chain backbone, we observe a clear indication of a first-order
transition from a globular state at small , to a stretched state at large
; in the intermediate regime the bistable equilibrium between these two
states shows the existence of a pearl-necklace structure.Comment: 7 pages, 1 figur
Effects of Self-Avoidance on the Tubular Phase of Anisotropic Membranes
We study the tubular phase of self-avoiding anisotropic membranes. We discuss
the renormalizability of the model Hamiltonian describing this phase and derive
from a renormalization group equation some general scaling relations for the
exponents of the model. We show how particular choices of renormalization
factors reproduce the Gaussian result, the Flory theory and the Gaussian
Variational treatment of the problem. We then study the perturbative
renormalization to one loop in the self-avoiding parameter using dimensional
regularization and an epsilon-expansion about the upper critical dimension, and
determine the critical exponents to first order in epsilon.Comment: 19 pages, TeX, uses Harvmac. Revised Title and updated references: to
appear in Phys. Rev.
Theta-point universality of polyampholytes with screened interactions
By an efficient algorithm we evaluate exactly the disorder-averaged
statistics of globally neutral self-avoiding chains with quenched random charge
in monomer i and nearest neighbor interactions on
square (22 monomers) and cubic (16 monomers) lattices. At the theta transition
in 2D, radius of gyration, entropic and crossover exponents are well compatible
with the universality class of the corresponding transition of homopolymers.
Further strong indication of such class comes from direct comparison with the
corresponding annealed problem. In 3D classical exponents are recovered. The
percentage of charge sequences leading to folding in a unique ground state
approaches zero exponentially with the chain length.Comment: 15 REVTEX pages. 4 eps-figures . 1 tabl
Strongly regular graphs satisfying the 4-vertex condition
We survey the area of strongly regular graphs satisfying the 4-vertex
condition and find several new families. We describe a switching operation on
collinearity graphs of polar spaces that produces cospectral graphs. The
obtained graphs satisfy the 4-vertex condition if the original graph belongs to
a symplectic polar space.Comment: 19 page
A Census Of Highly Symmetric Combinatorial Designs
As a consequence of the classification of the finite simple groups, it has
been possible in recent years to characterize Steiner t-designs, that is
t-(v,k,1) designs, mainly for t = 2, admitting groups of automorphisms with
sufficiently strong symmetry properties. However, despite the finite simple
group classification, for Steiner t-designs with t > 2 most of these
characterizations have remained longstanding challenging problems. Especially,
the determination of all flag-transitive Steiner t-designs with 2 < t < 7 is of
particular interest and has been open for about 40 years (cf. [11, p. 147] and
[12, p. 273], but presumably dating back to 1965). The present paper continues
the author's work [20, 21, 22] of classifying all flag-transitive Steiner
3-designs and 4-designs. We give a complete classification of all
flag-transitive Steiner 5-designs and prove furthermore that there are no
non-trivial flag-transitive Steiner 6-designs. Both results rely on the
classification of the finite 3-homogeneous permutation groups. Moreover, we
survey some of the most general results on highly symmetric Steiner t-designs.Comment: 26 pages; to appear in: "Journal of Algebraic Combinatorics
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.
Crumpling a Thin Sheet
Crumpled sheets have a surprisingly large resistance to further compression.
We have studied the crumpling of thin sheets of Mylar under different loading
conditions. When placed under a fixed compressive force, the size of a crumpled
material decreases logarithmically in time for periods up to three weeks. We
also find hysteretic behavior when measuring the compression as a function of
applied force. By using a pre-treating protocol, we control this hysteresis and
find reproducible scaling behavior for the size of the crumpled material as a
function of the applied force.Comment: revtex 4 pages, 6 eps figures submitted to Phys Rev. let
Damping of sound waves in superfluid nucleon-hyperon matter of neutron stars
We consider sound waves in superfluid nucleon-hyperon matter of massive
neutron-star cores. We calculate and analyze the speeds of sound modes and
their damping times due to the shear viscosity and non-equilibrium weak
processes of particle transformations. For that, we employ the dissipative
relativistic hydrodynamics of a superfluid nucleon-hyperon mixture, formulated
recently [M.E. Gusakov and E.M. Kantor, Phys. Rev. D78, 083006 (2008)]. We
demonstrate that the damping times of sound modes calculated using this
hydrodynamics and the ordinary (nonsuperfluid) one, can differ from each other
by several orders of magnitude.Comment: 15 pages, 5 figures, Phys. Rev. D accepte
Folding transition of the triangular lattice in a discrete three--dimensional space
A vertex model introduced by M. Bowick, P. Di Francesco, O. Golinelli, and E.
Guitter (cond-mat/9502063) describing the folding of the triangular lattice
onto the face centered cubic lattice has been studied in the hexagon
approximation of the cluster variation method. The model describes the
behaviour of a polymerized membrane in a discrete three--dimensional space. We
have introduced a curvature energy and a symmetry breaking field and studied
the phase diagram of the resulting model. By varying the curvature energy
parameter, a first-order transition has been found between a flat and a folded
phase for any value of the symmetry breaking field.Comment: 11 pages, latex file, 2 postscript figure
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