2,523 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.
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.
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
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
Collineation group as a subgroup of the symmetric group
Let be the projectivization (i.e., the set of one-dimensional vector
subspaces) of a vector space of dimension over a field. Let be a
closed (in the pointwise convergence topology) subgroup of the permutation
group of the set . Suppose that contains the
projective group and an arbitrary self-bijection of transforming a
triple of collinear points to a non-collinear triple. It is well-known from
\cite{KantorMcDonough} that if is finite then contains the
alternating subgroup of .
We show in Theorem \ref{density} below that , if
is infinite.Comment: 9 page
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